Talk:Mathematics/Archive 14

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weasely, contradictory and unsuported "It has no generally accepted definition"

1) It makes no sense to define the topic in sentence 1 and then say it has no definition in sentence 2.

2) The references don't seem to say that it has no accepted definition. One reference is about what teachers think mathematics is (interesting but not relevant), and the other says no consensus has been reached about whether mathematics is a natural science, a branch of the humanities, or an art form. (Something can obviously have a definition while being hard to categorize)

I understand the first paragraph has been extensively discussed but this second sentence is terrible. I have no opinion on the first sentence. Bhny (talk) 02:13, 26 June 2013 (UTC)

Could I ask as a favor that you glance over my remarks at talk:mathematics/Archive 13#Definition as description vs definition as demarcation? It's not extremely short, but not extremely long either, and it would explain the terminology I'd like to discuss the question with.

(Assuming you've read it.) What is really meant here is that there is no generally accepted demarcation between that which is mathematics, and that which is not. That is, some people would like to say that mathematics is whatever comes out of rigorous proof, but others find that unnecessarily limiting (and possibly including stuff that they don't want to include, such as proofs in philosophy). That's why the article should start with a non-exclusive list of things that are generally accepted as mathematics, but make it clear that these may not exhaust the topic, and confess failure in giving a complete definition.

I think those are the principles we should strive for. That said, I'm not in love with the current first sentence, which does seem to be in the form of a demarcation. --Trovatore (talk) 02:47, 26 June 2013 (UTC)

I'd like to stay out of arguing about the 1st sentence- a descriptive definition is fine by me. But this 2nd sentence is a disaster and should just be deleted. Are you are suggesting it should be changed to- There is no accepted demarcation of what is and what is not mathematics. ? Bhny (talk) 02:57, 26 June 2013 (UTC)

No, I'm just as happy staying away from any active denial that such a thing exists, just as long as we ourselves don't write something that appears to be one. --Trovatore (talk) 03:08, 26 June 2013 (UTC)

OK we seem to agree that it should be deleted Bhny (talk) 03:42, 26 June 2013 (UTC)

Well, if the first sentence is explicitly open-ended, which it isn't right now. Also we don't want it to be a one-sentence paragraph, and it wouldn't be too unnatural to note positively that there's a range of opinion on the exact definition (as opposed to negatively saying there's no exact definition). --Trovatore (talk) 05:35, 26 June 2013 (UTC)

• There is an enormous amount of disagreement as to what mathematics is, in at least two respects:

1. What is the extension of the concept "mathematics"? I.e., exactly what subject matter is included under that term?
2. What is the nature of mathematics? I.e., granted "1+1=2" is included under the heading "mathematics", what does it mean to say that it is "mathematics"? What is it about some things which makes that "mathematics", as distinct from other things which are not "mathematics"?

Of course, the two issues are intertwined, and not independent, but they are not by any means the same. Even among mathematicians and philosophers who substantially agree on the answer to the first point, there has been much debate and disagreement about the second.

I believe it is right that the lead should contain, very early on, a statement indicating that there is no agreement on what mathematics is. I don't at all agree that the "second sentence is terrible", though it is not perfect, and could no doubt be improved. Simply removing it, and putting nothing in its place, would not be at all helpful. Indeed, doing so while leaving the first sentence in place would give the extremely misleading impression that the first sentence is an adequate definition. Leaving the sentence even in its present imperfect form is a much better option than removing it.

• I have considerable reservations about the first sentence, particularly in its present form, which is due to a recent undiscussed change, which replaced "abstract" with "scientific". To me, it is clear that mathematics is abstract, and by no means clear that it is scientific: that depends critically both on what one sees as the nature of mathematics and on what one sees as the nature of science. For now, on the bold, revert, discuss principle, I shall revert that change, though that will still leave me somewhat unhappy with the rest of the sentence.

• One last point. In answer to the "It makes no sense to define the topic in sentence 1 and then say it has no definition in sentence 2", Who said that the first sentence was a definition? It makes perfect sense to make an attempt to describe in general terms what the subject of discourse is, and then mention the difficulty, or even impossibility, of giving a precise definition which is universally accepted. JamesBWatson (talk) 09:23, 26 June 2013 (UTC)

An editor has tried a couple of times to insert, without reference, the statement that mathematics is always true. This is a question much debated, and cannot be settled here. Is mathematics true, or is mathematics merely valid. For a discussion of this subject, see the book Plato's ghost by Jeremy Gray. Rick Norwood (talk) 14:04, 27 June 2013 (UTC)

Indeed. "Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true ... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true" - Bertrand Russell. Gandalf61 (talk) 15:03, 27 June 2013 (UTC)

For better or worse the first sentence is a definition- "Mathematics is <definition>". I stand by my comment that the second sentence contradicts the first. Can we come up with a sentence or two that actually says something about the scope and demarcation? Bhny (talk) 15:30, 27 June 2013 (UTC)

Well, that looks rather like a categorical statement that only one interpretation of the word "definition" is acceptable. Trovatore has done a pretty good job of outlining some of the variation in what that word may mean, in the archive page linked to, and I see no benefit in insisting that the word can be taken in only one way. However, accepting for the present that we interpret the word in a way which encompasses the first sentence of the article, how and why does the second sentence contradict it? It seems to me perfectly possible to give a definition and then go on to state that it is not the definition, and that no one definition is universally accepted. By all means, the article stands to be improved by replacing the blank statement "It has no generally accepted definition" by a more comprehensive statement, that goes some way towards indicating how and why it has no generally accepted definition, but it is a clear and unambiguous fact that mathematics does have no generally accepted definition, and it would not be at all helpful to pretend that it does. However, I see no contradiction at all in recording the fact that there is no generally accepted definition, while at the same time trying to give at least a general indication of what sort of thing is meant by "mathematics", whether or not we choose to call that "general indication" a "definition". JamesBWatson (talk) 16:07, 27 June 2013 (UTC)

We are defining a topic for an article. It doesn't have to satisfy every one on earth and we can we can specifically state the limits of our article topic. (It has no generally accepted definition implies we don't have a topic) Bhny (talk) 20:46, 27 June 2013 (UTC)

The point of my mini-essay that I linked above (here, for convenience) is that there is a confusion between the sort of definition you're correctly talking about, and the sort of definition mathematicians are used to when defining mathematical objects. We need a definition in the former sense, because that's how WP articles start. We should make it clear, by stating it in an explicitly open-ended form, that it is not a definition in the latter sense.

That's why I propend for the "shopping-cart" style definition, something along the lines as Mathematics is the field of study that concerns itself with such topics as ..., without ever attempting to definitively characterize what these topics have in common. --Trovatore (talk) 21:19, 27 June 2013 (UTC)

"It has no generally accepted definition implies we don't have a topic" is close to (though not identical to) what Geach called "the Socratic fallacy". The fact that we can't give a definition of a topic which everyone will accept does not by any means imply that the topic doesn't exist, and, frankly, I am bewildered as to why anyone might think it does. We can give a "definition" in the sense of a general description of what sort of thing we are referring to, but no matter how we word such a description there will be someone who doesn't think it's right. I have known quite heated arguments among mathematics teachers in secondary schools about whether a particular topic is included in mathematics or not. British university mathematics faculties teach topics which they regard as "applied mathematics", but which continental European universities do not regard as mathematics at all. That means that any definition we give will either include content which some people do not accept as mathematics, exclude content which some do accept as mathematics, or both. However, it does not mean that we can't provide a description giving a general idea of what sort of things mathematics deals with. That means, as far as I can see, that we can give a "definition" in the sense in which Bhny is using the word, but that the definition will not be universally accepted. Where is the contradiction there? JamesBWatson (talk) 07:19, 28 June 2013 (UTC)

• There is no generally accepted definition of "tree". Most people accept the concept of a banana tree, but some insist that it is not truly a tree, because it lacks sufficient lignified tissue. Many people regard elder (Sambucus nigra) as a tree, to others it is unambiguously a shrub. Does this mean that the word "tree" has no meaning? Of course not. JamesBWatson (talk) 07:23, 28 June 2013 (UTC)

  Yes, but it is true that (without having looked), I doubt that the second sentence of the tree article explicitly asserts that there is no accepted definition. I think the situation can be adequately dealt with without the second sentence, by giving a definition that is sufficiently (and sufficiently obviously) open-ended. We had one, for a while, until someone added the bit about "anything quantitative", which again appears to be an attempt at a demarcation. Maybe that bit should just be removed.

  Even if it is removed, of course, we don't want to leave a one-sentence opening paragraph, and something about the wide variety of attempts to give a more comprehensive and unified definition might be in order. But it's probably better if it's stated positively rather than negatively. --Trovatore (talk) 07:32, 28 June 2013 (UTC)

I would be careful about specualting what an article does and does not say "without having looked". The first sentence of the Wikipedia article Tree gives a definition of "tree", and the second sentence goes on to indicate that usage varies. It does not use the words "no generally accepted definition", but that is the fact that it conveys. (It does better than the article Mathematics, because it briefly indicates the sort of variations that there are, rather than just stating that there are variations, but there is no more a "contradiction" in the one article than in the other, and it is no more true to say that the topic doesn't exist because there is no universal agreement as to its extension in the one case than in the other.) JamesBWatson (talk) 07:35, 28 June 2013 (UTC)

Completely agree with you on the last point, but I don't think that's Bhny's main complaint. --Trovatore (talk) 07:43, 28 June 2013 (UTC)

Somebody added the assertation that everything that involved quantities was mathematics. I removed it as too broad.Rick Norwood (talk) 15:34, 28 June 2013 (UTC)

Our reader reads the first sentence- "ah this is how our topic is defined", then reads the second sentence. I don't how to be clearer- this is a contradiction. Maybe there are two senses of "definition" being used but it doesn't say that. I believe the second sentence should just be deleted, but if it stays it has to be re-worded to actually say something. It could say- "In academia the scope of mathematics varies and disagreement is common especially concerning...." Then it has to say what the main disagreements are otherwise it is uninformative weaselness. Bhny (talk) 17:27, 28 June 2013 (UTC)

I don't think anybody is that far apart here. Isn't it acceptable to everyone to make the first sentence open-ended, and rephrase the second one in positive terms to talk about disagreements as to the scope of mathematics? --Trovatore (talk) 20:18, 28 June 2013 (UTC)

ok, I'll let someone else draft this new 2nd sentence. It would be good to source it of course. Bhny (talk) 21:21, 28 June 2013 (UTC)

I suggest: "Many attempts have been made to define mathematics, but none has been universally accepted." Rick Norwood (talk) 00:32, 29 June 2013 (UTC)

I would prefer something stated in such a way that we don't have to find a source denying that any is universally accepted. How about something along the lines of

There is a range of views among mathematicians and philosophers of mathematics as to the exact scope of the discipline. Some of these are summarized at definitions of mathematics.

It's not ideal; I usually prefer to avoid referring to other articles by mention rather than use. But I can't think of a way to do that that doesn't either seem contrived, or else undesirably resurrect the conflict between the definitions of the word "definition" that we're trying to escape here. --Trovatore (talk) 00:42, 29 June 2013 (UTC)

You know, the more I think about it, the more disturbed I am by the article-reference issue. My proposed third sentence would make no sense at all in a printed version, where you don't see that there's a wikilink. So I don't think this exact language will work. But you see the general direction I'd like to go; maybe someone can come up with a fix. --Trovatore (talk) 00:49, 29 June 2013 (UTC)

Is the 2nd sentence more true of math, than of physics, psychology, or literature? It seems unnecessary to me. Biology is the study of life, but defining life is problematic. But, biologists are the primary virologists, not geologists. The 2nd sentence is about this Talk page, not about math. itself. JJL (talk) 01:16, 29 June 2013 (UTC)

Well, we need to have a second sentence. We definitely don't want the article to start with a one-sentence paragraph. To me a remark about there being a range of views on the subject's scope seems like a fairly natural continuation, but I might be persuaded that there's some better direction to go. --Trovatore (talk) 02:09, 29 June 2013 (UTC)

Yes, I think mathematicians have argued more about the definition of mathematics than people in other disciplines have about the definition of their discipline, maybe because within mathematics precise definitions are so important. The big question is: is mathematics a method (deduction from axioms using formal rules of logic) or a set of subjects: numbers and shapes (plus some other stuff). The article art has a similar problem, and solves it by mentioning several views without explicitly saying that there is no single definition of art. We might follow that example, giving two or three major definitions without preferencing any one definition.Rick Norwood (talk) 12:09, 29 June 2013 (UTC)

Most mathematicians don't bother to try to precisely characterize what mathematics is. I think the best choice is to open with a description-definition rather than a demarcation-definition, and make it obviously open-ended so that no one thinks it's a demarcation-definition. It should be possible to give a head-check to the "method" view within such a format, though I don't have an exact proposed wording at this time. --Trovatore (talk) 20:47, 29 June 2013 (UTC)

I once asked Philip J. Davis to define numerical analysis for me and instead he gave me an explanation of why he was refusing to do so on principle. To my mind defining math. is best left to the philosophers, though what I'm hearing is a distinction between (neo)-Platonism (number, shape) and formalism (method) that I view more as a discussion of how math. is done than what math. actually is. Regardless, the current 2nd sentence is fine by me. I too am a little bit queasy about directing change to calculus but frankly that is what we are principally talking about by change here, I assume--not stuff like topological deformations and such. JJL (talk) 17:06, 21 July 2013 (UTC)

I did a first pass at a new second sentence based on the suggestion above. It is at the very least better than what was there Bhny (talk) 21:34, 29 June 2013 (UTC)

Not bad from my POV, with some minor concerns:

1. First sentence didn't end in a period and didn't have an "and" before "change". I've fixed that.
2. First sentence needs to be explicitly open-ended. Fixed that too.
3. I don't like the WP:EGG of piping "change" to "calculus". This needs further thought.
4. Though it's not my personal view, Rick Norwood does have a point — something needs to be said about the "method" view. Something is said, in the following paragraph. Rick, can you accept this as it is, given that it's obviously not trying to characterize mathematics, but just point the reader to the subject of the article?

--Trovatore (talk) 21:47, 29 June 2013 (UTC)

I like it a lot. I hope it will be stable. Rick Norwood (talk) 23:11, 29 June 2013 (UTC)

Edit request on 31 August 2013 from Franco Boggi, concerning the first origin of the term mathematics

For the origin of the term mathematics is necessary to go Egyptian word maat, in which composition appears the symbol of the cubit, linear measuring instrument: a first approach to the mathematical concept. Geometric symbol of this order is a rectangle, from which appears the plumed head of the Egyptian goddess Maat, the personification of the concepts of order, truth and justice, daughter of Ra, the only One, Creator of all things, not even the father can live without daughter: his demiurgic power being limited and ordered by mathematical laws. At the beginning of the Rhind papyrus is this statement: "The accurate calculation is the gateway to the knowledge of all things and the dark mysteries." The term maat reappears in Coptic, in Babylonian and in greek. In greek the root ma, math, met enter in the composition of words that contain the ideas of reason, discipline, science, education, right measurement, and in Latin the term materia indicates what can be measured.

Source: Boris de Rachewiltz - Magic Religius Egipt. Chapter: Mathematical Universe, cult of Maat, abstract goodness of truth and giustice.

Franco.boggi (talk) 09:07, 31 August 2013 (UTC)

In the above message, "Magic Religius Egipt" was replaced by "Egitto Magico Religioso" by 2.33.197.47 after I had replied to the comment below, thus making nonsense of my quoting it. I am restoring the original text, to make the context of my reply clear. JamesBWatson (talk) 20:01, 31 August 2013 (UTC)

 Not done Is there any reliable source that establishes a connection between this Egyptian word and "mathematics"? Does de Rachewiltz present the firm evidence for the connection, or just give it as a speculation? I am unable to find any mention of "Magic Religius Egipt" anywhere at all. JamesBWatson (talk) 11:58, 31 August 2013 (UTC)

I'm not an espert of egiptology, this is fruit of an holiday lecture (I'm just a engineer, in Europe there is time in summer for divagations) but seemed to me very interesting. This book is only edited in italian. Just now, I have discovered that the author is a mistic involved in a process for neo fascism, but I think, neverthless, that the connection between the goodness Maat and the origin of mathematics is to take in account. I'm non an expert titolate to affirm it, but I invite the comunity to go deeper. Thank You — Preceding unsigned comment added by 2.33.197.47 (talk • contribs) 12:47, 31 August 2013 (UTC)

Please sign your talk page messages with four tildes (~~~~). Thanks.

That doesn't look like a wp:reliable source to me. - DVdm (talk) 13:29, 31 August 2013 (UTC)

Semi-protected edit request on 20 January 2014

197.77.0.57 (talk) 19:43, 20 January 2014 (UTC)

Not done: as you have not requested a change.
If you want to suggest a change, please request this in the form "Please replace XXX with YYY" or "Please add ZZZ between PPP and QQQ".
Please also cite reliable sources to back up your request, without which no information should be added to any article. - Arjayay (talk) 19:47, 20 January 2014 (UTC)

Mathmatical origin

Well, I think that it was the Babalonians that probably invented math when their nation just started. --Jutty10 (talk) 22:47, 18 March 2014 (UTC)

It's a little more complicated than that. Civilizations all over the earth, from England to India, observed that a triangle with sides of lengths 3, 4, and 5 was a right triangle. It is true that the Babylonians took this further, discovering many more Pythagorean triples, and the Greeks further still, proving the Pythagorean Theorem in complete generality. Rick Norwood (talk) 12:02, 19 March 2014 (UTC)

Issue with the "Mathematics as profession"

The "Mathematics as profession" section does not talk about the profession of mathematics. It only talks about accolades awarded in the field of mathematics. However, it would be hard to argue that the purpose of professional mathematics (or any profession) is to pursue such rewards.

Suggest renaming the section to "Mathematical Accolades" or "Mathematical Rewards". — Preceding unsigned comment added by Tac-Tics (talk • contribs) 04:01, 14 March 2014 (UTC)

Well I think it's fine as it is.--BarsofGold (talk) 17:00, 29 May 2014 (UTC)

Semi-protected edit request on 21 July 2014

14.98.92.232 (talk) 05:59, 21 July 2014 (UTC)

Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format. Anupmehra -Let's talk! 09:17, 21 July 2014 (UTC)

Semi-protected edit request on 27 July 2014

Sorry, I wanna translate the "Mathematics" from English to My language.Unfortunately, There is no edit button.How could I find any way or choices to translate the semi-lock.Thanks! :-D Sereysopea Ung (talk) 13:57, 27 July 2014 (UTC)

I have created Talk:Mathematics/Sandbox with a complete copy of the current article. You should be able to access that for your translation purposes. Let us know when you are done so I can delete it.--agr (talk) 14:25, 27 July 2014 (UTC)

I plan to delete it after Wednesday, August 13, per Wikipedia:Miscellany for deletion/Talk:Mathematics/Sandbox. So if you are using it, please make a local copy for yourself.--agr (talk) 03:26, 10 August 2014 (UTC)

Isn't there a "View source" tab instead of the usual "Edit" tab ? DexDor (talk) 04:43, 10 August 2014 (UTC)

I just tried on a browser that was not logged in and indeed there is. I should have checked for that first, sorry for the added bother.--agr (talk) 15:47, 10 August 2014 (UTC)

"Math" vs "Maths"

An editor has boldly declared that "most speakers of English use math", and changed the article to reflect that claim. He has (eventually) provided sources, but I find them unconvincing. One demanded that I log on to the site. I won't do that.

The article has been stable in this area for quite some time before this editor's somewhat aggressive changes. I have asked that editor to discuss. He didn't. He simply reverted. We need a calm discussion of this with clear, quality, reliable sources. HiLo48 (talk) 06:40, 14 September 2014 (UTC)

I don't see it really matters which is used by more speakers (or readers, or writers) as this article is about mathematics, not contrastive linguistics. One of the two abbreviations has to be mentioned first though, I suggest "math" on alphabetical and historical grounds (even the OED says it's 'earlier'). How about something like: It is often shortened to "math" (North American English) or "maths" (British English). Qwfp (talk) 09:54, 14 September 2014 (UTC)

It seems beyond bizarre to me for a less popular, newer form to be listed in front of a more common, better attested form, even if we don't consider the fact that this article is in American English and therefore the American usage should be given first. It just seemed weird to me to do it the way the article had done it. Red Slash 18:45, 14 September 2014 (UTC)

I've said it before, and it continues to be my view, that we should not mention either abbreviation at all. --Trovatore (talk) 19:03, 14 September 2014 (UTC)

There is a lot of history around this topic (see archives). A description of the OED would be useful in determining which is more prevalent. If its just "British" as in the Isles, that would be on thing, but if its British as in British Empire, that would lean the other. --John (User:Jwy/talk) 20:28, 14 September 2014 (UTC)

But first it should be decided whether we should mention them at all. As I say, we should not. That makes it all very easy. --Trovatore (talk) 20:29, 14 September 2014 (UTC)

I would assume its continued inclusion since the old discussions makes that decision already made: insufficient support. And if we have an etymology section, I would argue it belongs there. --John (User:Jwy/talk) 20:50, 14 September 2014 (UTC)

If we're going to revisit the order, we should also revisit whether it's worth mentioning at all. What use is it to mention at all? --Trovatore (talk) 21:15, 14 September 2014 (UTC)

Trovatore - I'd like your proposal to be our answer. I'm not sure some people here will give up. HiLo48 (talk) 00:36, 15 September 2014 (UTC)

Egyptian origin of the term Mathematics

For the origin of the term it is impossible to ignore the Egyptian word Maat, the composition of which is the symbol of the cubit, linear measuring instrument: a first approach to the mathematical concept. The Egyptian goddess Maat is the personification of the concepts of order, truth and justice. Daughter of Ra, the Only One Creator of all things, but not even the father can live without daughter, his demiurgic power being limited and ordered by mathematical laws. Thoth, patron of the exact sciences, figure as her husband, even more precisely, fertilizing of Maat. Geometric symbol of this order is a rectangle from which rises the plumed head of the goddess, which also defines the so-called Lake of Truth. At the beginning of the Rhind Papyrus is this statement: "The accurate calculation is the gateway to the knowledge of all things and the dark mysteries." The term maat reappears in Coptic, in Babylonian and in Greek. In Greek the root "ma", "math", "met" enter in the composition of words that contain the ideas of reason, discipline, science, education, right measure, and in Latin the word "materia" means what that can be measured. Echoed by Franco Boggi (engineer and author), read in Boris de Rachewiltz's Egitto Magico Religioso. 151.25.222.244 (talk) 15:09, 28 September 2014 (UTC)

That reads like some excellent original research, but if you read that link you will see that's not sufficient for us to make use of it in Wikipedia. Such an idea needs to have been written about in a high quality, secondary, reliable source. HiLo48 (talk) 21:41, 28 September 2014 (UTC)

OK, dont state it on main page, keep it just as discussion matter, the argument is so big and evident that I hope some enforcement will come from some specialist, to add reliability to the source: (Boris de Rachewiltz's Egitto Magico Religioso, at the moment edited in Italy by Terre di Mezzo.2.33.196.203 (talk) 11:01, 29 September 2014 (UTC)

Incorrect citation

The citation in footnote #7 contains an error in the author's name:

Mura, Robert (Dec 1993). "Images of Mathematics Held by University Teachers of Mathematical Sciences". Educational Studies in Mathematics 25 (4): 375–385.

"Robert" should be changed to "Roberta". Please see the link in the citation for evidence. I would change it myself if the article wasn't locked.

Thanks! — Preceding unsigned comment added by 108.80.94.100 (talk) 14:19, 27 October 2014 (UTC)

why no mention of Aryabhatta?

Aryabhatta was Indian mathematician and astronomer who is credited for early use of decimal system & zero without which modern maths isn't possible and we would have been sick with Roman numerals.

Albert Einstein: "We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made." — Preceding unsigned comment added by Du 409 (talk • contribs) 05:26, 28 October 2014 (UTC)

For what it's worth, the Āryabhaṭīya is discussed in the history of mathematics article. --Ancheta Wis   (talk | contribs) 05:35, 28 October 2014 (UTC)

Venn diagram image colors

Does anyone else think that the Venn diagram used to represent set theory under Foundations and philosophy in the section Fields of mathematics, would fit better if it were not color-coded, considering the images used to represent other fields? It's a stark contrast against a sea of black and white that stands out quite a bit. — Fuebar ^{[talk | cont]} 21:41, 21 December 2014 (UTC)

Looks fine to me, right now. There are other color images in the respective fields below the one you refer to, such as the Rubik's cube; an all-B&W gallery instead would stick out just as much, when compared to the other galleries. --Ancheta Wis   (talk | contribs) 23:17, 21 December 2014 (UTC)

"maths"

that's disgusting, and yes I'm aware it's in the archive. In common informal speech it's one thing, appropriate in that register. Here not. Lycurgus (talk) 02:45, 7 May 2015 (UTC)

I think we can treat the matter more dispassionately; I don't see any need to get "disgusted". But I would support removing the "often shortened to..." clause from the first sentence, and I don't feel any strong need to mention "math" or "maths" anywhere else in the article either. --Trovatore (talk) 03:33, 7 May 2015 (UTC)

Why not go whole hog with some "mafs"? Lycurgus (talk) 10:44, 7 May 2015 (UTC)

For what it's worth, the short forms "math" and "maths" are both noted prominently in the mathematics articles of OED and MathWorld. Mgnbar (talk) 12:05, 7 May 2015 (UTC)

The OED is a dictionary, not an encyclopedia. MathWorld is a terrible example for almost anything. --Trovatore (talk) 18:10, 7 May 2015 (UTC)

Since the common speech versions redirect to this article, I believe it important they be mentioned near the top. And I truly don't understand your (even if toned down) aversion to having them mentioned. --John (User:Jwy/talk) 14:28, 7 May 2015 (UTC)

Redirected terms should be mentioned if it is otherwise reasonably likely that readers would be surprised to end up at a given article. "Wait a minute, I searched for infundibulum; why did I wind up at Kurt Vonnegut?" (Not an actual example but just to give the idea.)

For "math" and "maths", I don't think that's very likely. Anyone entering those terms into the search box already knows what they are short for, and will arrive at the intended article.

I just don't see the point of mentioning them at all. This is not a dictionary, so we don't need to talk much about the word. I'm fine with a blurb about the etymology; that gives actual information, even if it's not information about mathematics. But why do we need to talk about the informal versions? It's just a distraction that conveys very little information that a reader cannot already be assumed to know, unless it's "look at those funny Yanks (Brits); they spell maths (math) wrong", which is something that IMO is better omitted from an article on mathematics. --Trovatore (talk) 18:10, 7 May 2015 (UTC)

Also there's a tiny but non-zero chance I placed it. I do use that in speech, and I've not checked the log for the origin. CYA. Lycurgus (talk) 19:10, 7 May 2015 (UTC)

Maths

The beginning of Maths is much earlier than Greeks such as Pythagores and Eulucid. This is nothing offending to Greek users, if some are offended this must be because of their mindset, there are some civilisations just predating them by time and thus by certain fields such as maths and biology, some can't accept this, but the article needs to be neutralised. Because the style now emphasizing the Greek contributors as primary who are in fact late contributors based on the works of those predating them and earlier civilisations than Greece; actually the "birthplace" or so called "creadle" is the quarto - China, Babylon, Egypt and India, later Greek mathemathics were based on Babylonian and Egyptian and later Arabic on Greek, all this is cited in the sources:

"Four nations Babylon, Egypt, India and China all developed their own special features and brilliant achievements in mathematics. Subsequently, Greek civilization built on the heritage of Babylon and Egypt... Babylonia has fared much better than Egypt in the history of mathematics. Babylonian scribes wrote their mathematics on clay tablets, Egyptians used papyrus. Both produced massive ammounts of written text, including works describing, performing, and explaining mathematical operations. For much of the twentieth century Babylonia and Egypt were perceived as the cradle of (modern) mathematics.... The Greek mathematicians Eudoxus, Thateles (d. 546 BC), Pythagoras (500 BC) were reported to have widely traveled in Egypt and Babylonia and learned much of their mathematics from these areas, some sources even credit Pythagoras with having travelled as far as India in search of knowledge, which could explain the parallels between Indian and Pythagorian philosophy and religion [1] (Oxford University Press) [2] --Evropariver (talk) 17:21, 14 July 2015 (UTC)

Your edits are extremely problematic because you are trying to cram as many mentions that "Mathematics began in Egypt" and "the Greeks got all their math in Egypt", by cherry picking sources and repeating over and over. True, ancient Egyptian mathematics did influence ancient Greek mathematics, but the influence was limited. Egyptian mathematics was very simple, with only a 2-3 mathematical papyri surviving to the present day. Ancient Greek mathematics, while in its earliest stages influenced by Egypt, far surpassed Egyptian mathematics. The mathematical proof, the backbone of modern mathematics, was developed in Greece. The Pythagoreans were the to study mathematics as a subject on its own right, because of its intrinsic interest. All theose that came before them used mathematics to build stuff and for farming, etc..., but did not pursue mathematics as topic in its own right. For a more complete description of the subject, I recommend Carl Boyer's "A History of Mathematics". I also strongly object how you keep trying to cram the same thing over and over in the lede of the article, in order to ensure maximum visibility for your POV. Athenean (talk) 17:48, 14 July 2015 (UTC)

You dislike the inclusion of Egypt, but this is understandable when you have a certain nationality, however Egypt is very prominent(probably most) civilization and must not be excluded in a field where it is considered by most sources the CRADLE of mathematics both by contemporaries like Aristotle and present-day writers of Oxford university for example. Now the article is totally biased and problematic in my eyes.

All prominent Greek mathematician got their knowledge from Egypt, evidently studied in Egypt. Pythagoras theorem, etc all is derived from Egypt, it was much more than you are saying, including massive amount of written text as Oxford is saying. if you find a source claiming that Greece achieved more in mathematics than Egypt I will stop editing the article, I found a source claiming the opposite. I cite my statements from this [3].--Evropariver (talk) 19:08, 14 July 2015 (UTC)

Did you even read what I wrote above? Personal attacks are very poor arguments, and repeating yourself over and over is not very convincing. You are misunderstanding everything, both what I write and what your own sources write. Athenean (talk) 19:10, 14 July 2015 (UTC)

You actually do not use any sources, damage or use mine as your own falsification, as you did in Biology article and continue with manipulative claims even in the discussion for personal attacks, I would better rarely discuss with you. --Evropariver (talk) 19:28, 14 July 2015 (UTC)

It would help if you actually knew a little about mathematics and biology and the other subjects you are pushing your POV on. Greek mathematics is famous for many contributions, including the mathematical proof (arguably the most significant development in the history of mathematics), the method of exhaustion (direct precursor to calculus), conic sections, etc... I encourage you to learn a little about these topics before coming back here. You may learn that much of modern mathematics was actually developed by ancient Greek mathematicians. This is in contrast to Egyptian mathematics, which was not very advanced, and is mostly just famous for being old). True, it is old, but that's about it. The entirety of what's left of Egyptian mathematics consists of only three papyri containing little more than simple geometric formulas (e.g. calculating the area of a pyramidal frustum. So you can find a lot of sources filled with superlative generalizations of the type "Egyptian mathematics is incredibly old bla bla bla", "Egypt is the cradle of mathematics bla bla bla", but not much more than that. And you can try to fill the article with such superlatives, but not much more than that, because surprise, there isn'y much more than that to be said. And unlike you, I try to assume good faith (as hard as it is in your case), because I could easily infer that your anti-Greek obsession could be driven by the fact that you are from a neighboring country with a much less interesting and much shorter history, with far fewer contributions to human civilization (to put it mildly), but I don't. Athenean (talk) 20:23, 14 July 2015 (UTC)

I don't say anything against Greek mathematics, but against the way some users modified the article, like it has been the only and most important of all. Neither Ancient Egyptian, nor Greek is the same as modern mathematics, both are part of the past and have to be mentioned as such in the intro. I can't say which of both is more significant, but I am sure that those predating the Greek had practiced earlier most of what was practiced in Greek mathematics. What clearly is a fact as you mentioned is that one of the two is older which taught the newer. The Babylonian mathematics(1830-1531 BC, one sample even dating to 7289 BC featuring an approximation of the square root of 2 in four sexagesimal figures so far in the past) had quadratic equation and cubic equations, geometry, algebra and the Pythagorean theorem long before Pythagoras was alive and Greek mathematics(from just 600 BC, whose knowledge was achieved mostly through prominent scholars studying in Egypt or Babylonia as I cited), so major things come from there, you can not disregard that or regard it to Greece. So you are saying that all this should be excluded and the whole article should be concentrated on Greek mathematics, which is nothing but a bias, see the policy on neutrality/ I shall not have limited views neither the article should be limited only to Greece as you want, that would be ridiculous, not this not the Biology article, just because of your limited regards to the global contribution of many civilisations to certain sciences, emphasizing only Greece which is a very late civilisation.--Evropariver (talk) 21:00, 14 July 2015 (UTC)

Anything else besides the usual rants and false accusations and deliberate misconstructions of my position? Your above post is nothing but a straw man filled with insinuations and personal attacks. It is quite apparent you simply pretend not to listen to what I am saying, which means interacting with you is a total waste of time. Athenean (talk) 21:17, 14 July 2015 (UTC)

Standard deviation clarification

what is difference between elobrate between STDEV, STDEVA, STDEVP and STDEVPA in microsoft excel — Preceding unsigned comment added by Trmathan (talk • contribs) 12:13, 1 October 2015 (UTC)

This talk page exists for discussing edits to Wikipedia's Mathematics article. It is not a help desk for general mathematical or statistical questions. For those, try Wikipedia:Reference desk/Mathematics.

But your question is actually better answered by searching the wider Internet for Excel-specific help. For example, a Google search for "stdev excel function" led me to this page, which explains that stdev is the sample standard deviation (descriptive statistics) and stdevp is a kind of population standard deviation (inferential). Mgnbar (talk) 13:29, 1 October 2015 (UTC)

 Done -- Google-search is truly amazing, often coming to Wikipedia. -- Charles Edwin Shipp (talk) 02:43, 6 November 2015 (UTC)

New NEWS today, for future editing

Amazing kid who talked at two months; hitting the news a lot today.

Headline-1: Teenagers’ maths theorem could pave way for interstellar travel

• http://metro.co.uk/2015/11/05/teenagers-maths-theorums-could-pave-way-for-interstellar-travel-5481549/

QUOTE: "Xuming Liang and Ivan Zelich, both 17, corresponded through an online maths forum when they realised they were both working on the same problem. It is now said the result of their collaboration may change the face of mathematics forever." -- Charles Edwin Shipp (talk) 06:24, 6 November 2015 (UTC) -- PS: FYI for future editing. This kid deserves his own Wikipedia page, sooner or later.

Headline-2: Meet the schoolboy genius who began speaking at TWO MONTHS of age and developed a maths theorem that calculates problems faster than a computer

• http://www.dailymail.co.uk/news/article-3304659/Schoolboy-genius-17-develops-maths-theory-calculates-problems-faster-COMPUTER-idea-did-it.html

QUOTE: "A Brisbane teen has developed a theorem experts say has changed maths; Ivan Zelich's findings will be crucial to our knowledge of the universe; When applied, the maths theorem calculates answers faster than a computer; Ivan, 17, has an IQ of 180 and said his first words at just two months of age; He was offered a place at university at 14, but chose to stay at school; He says school was in the way of his research, will soon sit his final exams." -- Charles Edwin Shipp (talk) 06:28, 6 November 2015 (UTC) -- PS: FYI for additional future editing.

Headline-3: Schoolboy genius stuns academics with maths theory that calculates answers faster than computer

• http://www.mirror.co.uk/news/world-news/schoolboy-genius-stuns-academics-maths-6772522

QUOTE: "A teenager has stunned academics by developing a maths theory which solves problems FASTER than a computer .

Figures boffins say that the theory has changed maths, and could help our understanding of the universe.

Ivan Zelich, who is just 17, is believed to have an IQ of 180, and has always been ahead of his age.

The Brisbane, Australia native stunned his parents when he started speaking at the age of two months.

And now working with a San Diego teen, he has developed the groundbreaking Liang Zelich Theorem." -- Charles Edwin Shipp (talk) 06:34, 6 November 2015 (UTC) -- PS: FYI for additional future editing. Also, if this goes anywhere, these two teens each deserve a Wikipedia page!

There are certainly many news articles covering this. The paper itself seems not to be published. Most of its bibliographic entries are pre-prints and blog posts, rather than articles published in reputable journals. (The content seems to be very classical Euclidean or projective geometry of cubics.) Coverage in Wikipedia seems premature to me.

This talk page is for discussing edits to the Wikipedia article Mathematics, not for planning other articles about mathematics. To talk to the wider community about that kind of thing, see Wikipedia:Wikiproject Mathematics. Mgnbar (talk) 12:25, 6 November 2015 (UTC)

BOTTOM LINE: We can wait and see. -- Charles Edwin Shipp (talk) 14:55, 6 November 2015 (UTC)

Empirical nature of mathematics

The quote "The role of empirical experimentation and observation is negligible in mathematics, compared to natural sciences such as psychology, biology, or physics", is not universally accepted. There should probable be some discussion or reference to the various philosophies of mathematics, including ones that include empirical, quasi-empirical, and new empirical view.--user:167.146.1.100, 21:24, 10 November 2015‎

When asked how he came upon his theorems, Gauss replied "... durch planmässiges Tattonieren. (... through systematic, palpable experimentation.)" as quoted in A L Mackay, Dictionary of Scientific Quotations (London 1994) --Ancheta Wis   (talk | contribs) 03:29, 11 November 2015 (UTC)

That quote ("The role of empirical experimentation and observation is negligible in mathematics, compared to natural sciences such as psychology, biology, or physics") is hopelessly wrong, at least with respect to modern mathematics. First of all, mathematicians must necessarily do many experiments within their own field in order to get a sense of what it true. Then if they find something that appears to be true in generality, they will try to prove it. In many cases, if a proof cannot be found in generality, the results of the experiments will still be worth publishing as new information. These discovered facts will still be true and of interest to other mathematicians who study the same subjects.

If, on the other hand, a proof in generality is in fact found, then it is true that the results of the mathematical experiments that led up to this proof will not be as important as the statement and proof of the theorem.Daqu (talk) 15:20, 4 February 2016 (UTC)

Semi-protected edit request on 16 February 2016

9 is the only divine number. The reason I say this is because 9 is the only number that you can multiply by any number and it remains 9 as a digit. 9x1=9 9x2=18 (1+8=9) 9x3=27 (2+7=9) 9x4=36 (3+6=9) And it goes on like this forever! — Preceding unsigned comment added by 72.94.95.69 (talk) 15:41, 16 February 2016 (UTC)

Classification errors

I strongly believe that several fields that are listed under "applied mathematics" should be instead listed under (pure) mathematics. In particular, probability theory and game theory. These can be applied, but that is true of almost all fields of mathematics.

Probability theory might be called a subfield or offshoot of measure theory, but it is overwhelmingly composed of theorems and proofs. The corresponding applied field is known as statistics.

Game theory, too, has a substantial core of theorems and proofs. Its applications could be called "applied game theory", but pure game theory is a branch of mathematics — regardless of the applications that may have inspired its development.

Many — in fact, almost all — areas of pure mathematics were originally inspired by real-world phenomena. They are nevertheless part of pure mathematics.Daqu (talk) 07:05, 9 January 2016 (UTC)

Richard Feynman once said "Probability is best defined by betting." Sounds like the field is still informed by its roots — gambling, in which there are winners and losers (the fundamental insight of game theory). --Ancheta Wis   (talk | contribs) 14:49, 9 January 2016 (UTC)

First, I agree that probability is mis-classified. The classification in this article has lots of problems. My previous complaints about it have never been remedied. Ideally the classification would be backed up by some reliable sources.

Second, it's not clear to me that "having theorems and proofs" qualifies a topic as pure math. For example, theoretical computer science has lots of theorems and proofs. Mgnbar (talk) 14:59, 9 January 2016 (UTC)

Indeed... see also User:Tsirel#Probability_theory_is_pure_mathematics. The situation seems to be changing in the 21 century. In our university (Tel Aviv) probabilists were on the statistics dept, but now we are on the pure math dept. Also, probabilists start to be awarded by most prestigiuos prices. Boris Tsirelson (talk) 08:37, 31 January 2016 (UTC)

I will respond to Mgnbar's statement of 9 January "For example, theoretical computer science has lots of theorems and proofs." That implies, by the definition of pure mathematics, that theoretical computer science is part of pure mathematics.

And to Ancheta Wis: Yes, many fields of pure math are still informed by their roots. But to the extent that they consist of rigorous reasoning (i.e., axioms, theorems and proofs), they are a part of pure mathematics.

P.S. Are people here aware that it is recommended that each commenter on a Talk page indent a little more than the previous comments? That means to use one more colon : than the person immediately above you.Daqu (talk) 15:06, 4 February 2016 (UTC)

Terry Tao and the 4 other Breakthrough Prize in Mathematics winners ought to remind us that the discovery of theorems precedes formal reasoning. This takes real labor which is firmly rooted in mathematical technique. The current stance of the encyclopedia seems to not acknowledge that there are intuitionistic insights which have to happen before any meaningful machinery of proof starts cranking. In Tao's case, he "completely obliterated the line between pure and applied mathematics" (minute 6:30 in the Breakthrough Prize video listed above). See minute 11:30, same clip, for the opinion that mathematics is discovered, not invented. --Ancheta Wis   (talk | contribs) 15:42, 4 February 2016 (UTC)

Daqu, two comments. First, you present your definition of pure mathematics as if it were indisputable. But it's obvious from Mathematics, Definitions of mathematics, their talk pages, etc. that there is widespread disagreement about such definitions.

Second, on Wikipedia talk pages you don't indent once more than previous posts. You indent once more than the post to which you are responding. See explicit examples here. Some of the posts here are correctly indented, and some are not. Regards. Mgnbar (talk) 17:17, 4 February 2016 (UTC)

Thank you for the better explanation of when to indent.

I apologize if I sounded dogmatic. But let me attempt another characterization of some areas that are pure-mathematical:

If a field contains theorems and proofs in the sense that mathematicians use those words, then at least that portion of the field containing those theorems and proofs is part of pure mathematics.

This allows for other parts of that field to not necessarily be pure mathematics. Also for other areas without theorems or proofs to possibly be part of pure mathematics. I hope that is flexible enough to inspire wide agreement.Daqu (talk) 01:05, 28 February 2016 (UTC)

External links modified

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Future of mathematics

Should Future of mathematics appear in "See also" section? Boris Tsirelson (talk) 08:32, 31 January 2016 (UTC)

No. — Preceding unsigned comment added by 212.159.119.123 (talk) 13:37, 23 March 2016 (UTC)

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Invention or Discovery

One of the longest debates is whether mathematics was "invented" or "discovered". Interestingly, the article makes use of both words in various contexts (use Ctrl+F to search), but discover seems to be used more often. What's the stance that should be taken on this topic?

Jsmith7342 (talk) 07:29, 15 May 2016 (UTC)

This issue is specifically discussed in the final paragraph of the section "Mathematics as science". And both stances are found throughout the literature. I'm not sure that it would even be desirable to try to make the terminology consistent throughout the article. But it's possible that the inconsistency is confusing to some readers? Mgnbar (talk) 12:10, 15 May 2016 (UTC)

Fortran

This is like a certain type of circular method used in discovery. Type of math actually, like calculus or algebra. It has not anything other than a supposed language named after it for computers. — Preceding unsigned comment added by 23.117.16.22 (talk) 01:43, 24 October 2016 (UTC)

Godel's Incompleteness Theorem

In the part of the article fields of mathematics logic is mentioned. There Godel's incompleteness theorem is mentioned and it is said that it shows that for any valid axiomatic system there exists "a true mathematical fact" that can't be proved. This is incorrect and misleading since if a theorem is unprovable it is not in any way a "true mathematical fact. Godel's incompleteness theorem simply shows the for any axiomatic system that the peano arithmetic axioms are derived from it there exists a property that is unprovable to be true nor false.

Remomer (talk) 21:14, 18 November 2016 (UTC)

Yes, in some reasonable (but rather formal) sense you are right. On the other hand, in another, even more reasonable (and somewhat informal) sense, the statement "Peano arithmetics is consistent" IS true but not provable in the Peano arithmetics. And of course, it IS provable in the Zermelo-Frenkel set theory. Boris Tsirelson (talk) 21:32, 18 November 2016 (UTC)

Semi-protected edit request on 1 April 2017

Defining Mathematics--- Mathematics in both practical and theoretical forms mean studying the consistency and change in the nature i.e. quantity, structure and value of both intangible and tangible sources which occupy space. It's the only thing which helps in solving queries related to time perfectly. Existence of time is fully dependent on pre-existence of "Mathematics" which sets the rules for all actions going around. It's the tool given to brain of animals only. When correctly applied by human to different forms of physical, biological and even psychological sciences mathematics can discover the facts and figures related to them which further helps in understanding the design and pattern of existing life and death circle. AnkurKatyal (talk) 07:45, 1 April 2017 (UTC)

If this is not an April-1 joke, then this should be a point-of-view, unless a number of sources will be added. Boris Tsirelson (talk) 08:28, 1 April 2017 (UTC)

Missing some critical disciplines

Any math discipline that is the root of a branch of science really belongs on this page. The one that jumped out at me was combinatorics, which is the root of statistical mechanics and thermodynamics. Others include spherical geometry, which was driven almost entirely by navigation. — Preceding unsigned comment added by 67.100.124.87 (talk) 06:44, 8 May 2017 (UTC)

Combinatorics is already mentioned in the article. Spherical geometry is a particular kind of non-Euclidean geometry, which is already mentioned in the article. I don't think either topic needs heavier treatment here. Mgnbar (talk) 12:34, 8 May 2017 (UTC)

Opening Sentence/Paragraph

Currently: "Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change.[4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.[7][8]"

Here are my thoughts.

• "There is a range of views" is weasel words; I'd recommend deleting the entire sentence.
• I'd mention addition, subtraction, multiplication, and division (or at least arithmetic), for the benefit of an elementary-aged audience.
• I'm not sure "structure, space, and change" is more understandable than "Algebra, Geometry, and Analysis".
• Should "logic" be listed as a sub-division of mathematics, or of philosophy?

Power~enwiki (talk) 06:18, 16 May 2017 (UTC)

Please understand that this intro is highly contentious, precisely because there is a range of views. We get a lot of editors saying "this is the right way to define mathematics", often neglecting sources and ignoring other definitions. Similarly, we can argue forever about whether logic is math or philosophy. I do think that "structure, space, and change" is vague, but they are actually supported by sources, and probably more meaningful to non-mathematicians than "algebra, geometry, and analysis". In short, I do not agree with your proposal. Mgnbar (talk) 12:15, 16 May 2017 (UTC)

This sentence has been discussed many many times, by many editors. You should search through the "Archives" of this talk page (listed above). Paul August ☎ 16:58, 16 May 2017 (UTC)

Yes, I understand the first sentence has been debated extensively, I'm not terribly interested in arguing about it if the consensus still holds. The second sentence is egregiously bad and I am deliberately attempting to re-open discussion. There are many things far more important about mathematics than the fact that its exact definition is vague. Power~enwiki (talk) 19:37, 16 May 2017 (UTC)

Why "bad"? We honestly inform the reader that the first phrase is somewhat controversial. Boris Tsirelson (talk) 19:44, 16 May 2017 (UTC)

Everyone knows that arithmetic is part of mathematics, that's not controversial. "The lead should stand on its own as a concise overview of the article's topic." (from WP:LEAD). I fail to see why "teaching the controversy" should be in the lead; there's a full section on it later in the article. Power~enwiki (talk) 19:51, 16 May 2017 (UTC)

The controversial claim is not that "arithmetic is part of mathematics", but that the four listed aspects cover most of mathematics. Boris Tsirelson (talk) 20:09, 16 May 2017 (UTC)

This ("egregiously bad") sentence links to "Definitions of mathematics"; there, the lead (three sentences) end with "All are controversial". Is it even more "egregiously bad"? Boris Tsirelson (talk) 20:17, 16 May 2017 (UTC)

There is a difference between an article on "Mathematics" and an article on "Definitions of mathematics". Power~enwiki (talk) 20:23, 16 May 2017 (UTC)

Sure. For that reason the former just contains a hint and the link to the latter. Boris Tsirelson (talk) 20:36, 16 May 2017 (UTC)

I would not oppose moving the second sentence to the section "Definitions of mathematics". Paul August ☎ 20:41, 16 May 2017 (UTC)

I usually agree with Paul, but in this case I don't. The move leaves a one-sentence lead paragraph, and (much worse) makes the proffered definition appear, well, definitive. --Trovatore (talk) 20:37, 19 May 2017 (UTC)

I find it absurd that Wikipedia is incapable of saying anything definitive on the subject of "What is mathematics". Power~enwiki (talk) 20:40, 19 May 2017 (UTC)

You're allowed to find it absurd, but them's the facts. There is no agreement in the mathematical community, so we can't invent one here. --Trovatore (talk) 20:45, 19 May 2017 (UTC)

That's right. As for the one sentence lead, that could of course be fixed by combining that sentence with the following paragraph. But I understand Trovatore's concern. Paul August ☎ 23:58, 19 May 2017 (UTC)

Lots of sources do say that the definition of mathematics is complicated. The first sentence of Chapter 1 of Boyer's "A History of Mathematics" is "Mathematicians of the twentieth century carry on a highly sophisticated intellectual activity which is not easily defined". The book then goes on to discuss the history of arithmetic, algebra, geometry, and analysis. I see no dispute that those four topics are mathematics, and other topics (such as music and astronomy) are not. While "the set of all mathematical facts" is ill-defined, the concept is defined clearly enough for the purposes of a lede paragraph in an encyclopedia. Power~enwiki (talk) 20:47, 20 May 2017 (UTC)

Perhaps a second-rate encyclopedia, but I would hope that our aspirations are higher than that. The problem is not that we can not identify areas that are clearly mathematics, but rather where do we stop and how fine should the distinctions be made? Courant and Robbins book What Is Mathematics? spends 566 pages attempting to do this and Reuben Hersh gives it another 334 pages in What Is Mathematics Really?. To think that this can be distilled down to a couple of meaningful sentences seems to me to be the height of hubris. --Bill Cherowitzo (talk) 21:57, 20 May 2017 (UTC)

It would take time to distill the 900 pages into a few sentences: "I would have written a shorter letter, but I did not have the time." —Blaise Pascal. I personally took a year on Imre Lakatos' Proofs and Refutations article. As Lakatos put it, "mathematicians are imperfect personifications of Mathematics". --Ancheta Wis   (talk | contribs) 09:43, 21 May 2017 (UTC)

Wow! Probably useless for this article, but quite a pleasure anyway (this phrase of Lakatos); thanks. Boris Tsirelson (talk) 16:17, 21 May 2017 (UTC)

Semi-protected edit request on 2 July 2017

hey dawg. Wanna make some repairings round here. Hope you dont mind dawg. This incorrectly written article may miseducate few other daaaawgs. Better repair it all up Jasmína Hajdúková (talk) 08:20, 2 July 2017 (UTC)

Not done: dawg this is not the right page to request additional user rights. You may reopen this request with the specific changes to be made and some dawg will add them for you, or you can wait until you are autoconfirmed and edit the page yourself. DRAGON BOOSTER ★ 08:54, 2 July 2017 (UTC)

I just realized...

This is one of the rare pages that doesn't eventually link to Philosophy according to xkcd's rule (by clicking the first link not in parentheses or brackets).

Mathematics --> Quantity --> Counting --> Finite set --> Mathematics

Hdjensofjfnen (UTC) 18:33, 22 September 2017 (UTC)

I want to add a line

In History Section I want to add the line:

After the time of Ancient Greeks, the first people whose researches wielded a wide influenced in the world march of mathematics were Hindus, in far-off India.

The reason I am telling to add this line is that Indians had Contributed a lot in the field of Maths and Indians are not mentioned in this article.

And Source for my Line is CEO of Universe (talk) 09:51, 7 October 2017 (UTC)

References

Voevodsky obituary

The NYT obituary of Voevodsky made me want to learn more, but his Wikipedia article does not even begin to connect the dots for me. For example Voevodsky's project for defining proof checking software is not covered (apparently it is related to the Langlands program). Neither is the Times' sentence quoting Thomas Callister Hales "He changed the very meaning of what the equals sign means in mathematics.". See higher category theory, homotopy type theory#The univalence axiom

I'd contribute if I could but the topics in his article's wiki links are inaccessible to me right now. Hold on, I think I might be able to help out; this paper is meaningful to me. What his obituary amounts to is a secondary source comment on his contribution to univalent foundations of mathematics. --Ancheta Wis   (talk | contribs) 13:02, 7 October 2017 (UTC)

No need to mention abbreviated forms

The solution to whether to put "maths" or "math" first is just not to mention them at all. --Trovatore (talk) 15:03, 13 November 2017 (UTC)

Agree. Paul August ☎ 15:45, 13 November 2017 (UTC)

An error

17×19607843=333333331, not 33333331. 80.98.179.160 (talk) 15:51, 24 November 2017 (UTC)

I removed it. I did not check that error, but the strange formatting of the numbers made it hard to follow, the writing otherwise needed cleaning up, but most importantly it simply did not belong in the lead as an obscure, unsourced example, breaking the flow of the existing text.--JohnBlackburne^words_deeds 15:56, 24 November 2017 (UTC)

Were there not eight 3s ? The example is famous, and a good example of why proof is needed. The formatting could be solved afterwards, I didn't want to turn everything upside down. Boeing720 (talk) 22:14, 24 November 2017 (UTC)

education

Shall we add a section about mathematics education? Benjamin (talk) 02:48, 20 December 2017 (UTC)

Why? I see no similar sections in any of top pages devoted to disciplines (Biology, Chemistry, Physics, Sociology, etc.). As a math educator myself, I am not adverse to talking about math education, but I do not see such a discussion as adding anything to the topic of mathematics. --Bill Cherowitzo (talk) 04:48, 20 December 2017 (UTC)

I thought it would be relevant. Benjamin (talk) 06:59, 20 December 2017 (UTC)

Rolled-back copyedits

@Purgy Purgatorio: would you please explain why you rolled back these edits? They're small, mostly copyedits, but I'm puzzled by the rollback. Specifically, here's what you rolled back that I find puzzling: (1) deletion of modern Greek from the etymology, where it's not relevant; (2) fixing the use of St. Augustine's "warning" as an example of a mistranslation (the mistranslations, not the original text, are the mistranslations); (3) the ordinary phrase "takes a singular verb" instead of the puzzling plural "singular verb forms". —Ben Kovitz (talk) 09:00, 17 January 2018 (UTC)

I tried to paraphrase (3) and (1) in my edit summary, by using more than a "singular verb" in "singular verb forms", and by the use of "etymologists" to refer to the linguistically interesting remarks in the alluded section, which I restored. I think that the given information is sourced, is interesting, and belongs to the topic of this article. My intentions regarding (2) were to respect the weight of St. Augustine as a philosopher and the correspondingly widespread "mistranslation" by restoring the attribute "notorious". In my perception, "condemnation of mathematicians" is a notorious "misinterpretation" of St. Augustine's statement(s) caused by too literal a translation of "condemnatio mathematici".

I am myself puzzled about the possible intentions of your edits, and believe my partial rollback is reasoned and reasonable, too. Purgy (talk) 09:37, 17 January 2018 (UTC)

@Purgy Purgatorio: Thanks for explaining, Purgy. Let's take these one at a time, starting with (2). I agree that it would be nicer to retain the word "notorious", but I couldn't think of a graceful way to do that. The current version has two errors: it says that St. Augustine's warning was itself a mistranslation; and it calls mathematici a "notion", making it appear that a concept rather than a word is at issue. How about I fix these errors and leave it to you to find a way to weave in the word "notorious" without reintroducing these errors? (If I think of a graceful way to include it myself, I'll put it in.) —Ben Kovitz (talk) 10:01, 17 January 2018 (UTC)

@BenKovitz:I apologize for not having answered your comment, but I understood your edits of the article as implementing your intentions, with which I did not want to interfere any further. Yes, I consider the notion, addressed by St. Augustine with the word "mathematici", as a concept, and therefore the word's translation to "mathematicians" is correct in its literal meaning, but is wrong in rendering the intended (by St. Augustine) notion, aka concept (Mit Worten läßt's sich trefflich streiten, mit Worten ein Gebild bereiten. Faust).

In a similar vein, I perceive a fundamental difference between "singular verbs", possibly denoting "always only one verb", and "singular verb forms", being explicit that all employed verbs are to be used in their singular form (see my earlier edit summary for multiple verbs, all in plural forms).

I stated already that I consider the content, which you removed and I restored, as "sourced, interesting, and belonging to the topic of this article". However, again, I will not interfere with your intentions beyond what I did already. Simply let me know, if you think I could answer further questions. Purgy (talk) 08:48, 26 January 2018 (UTC)

Thanks for your answer, Purgy. Unfortunately, I don't understand most of it. I hope I understood the part where you gave me the green light to go ahead with my copyedits. I'll do that next. Regarding "takes a singular verb" vs. "takes singular verb forms", please see this Ngram and this sampling of books written in English. A Ngram by itself can't settle such a matter, of course; it must be combined with experience and common sense. Hopefully sampling actual usage will help with that, hence the book search. Anyway, the phrase "takes a singular verb" is customary in English to name the kind of grammatical agreement that we're talking about; it does not imply that "mathematics" can't be the subject of a sentence with more than one verb. —Ben Kovitz (talk) 17:01, 31 January 2018 (UTC)

It's really funny how much dissent influences (factual or claimed) non-understanding of a statement, especially when it is formulated in a borderline style. But, main thing, you are right, I do not care (beyond what I did) about phrases being logically worse but more wide-spread, nor do I mind deleting content, which is "undisputed, interesting, and belonging to the topic of this article", just because some editor dislikes it; and the same holds for changing interpretations of some "transcribed" opinion of an ancient Doctor of the Church about mathematicians (in whatever meaning). So yes, go on, improve the article to your measures (and degrade it to mine). Purgy (talk) 09:36, 1 February 2018 (UTC)

Making math interesting to read and to comprehend

This is "the first" math article, or where to begin possibly. Just a lot of philosophy isn't sufficient. Interesting examples really is a good way in order to reach readers. Yes axioms are mentioned later, but that part could well have been deleted instead. Axioms are fundamental. Everything else must be derived (either from axioms or what's already proven). And at a certain level, there are assumptions. But just using words isn't helpful for our readers. I strongly believe examples are required, and as interesting as possible. And interesting at a level that reaches at least readers who have studied math at secondary school level. Lots of our "deeper" math related articles are simply just understandable to those who have studied mathematics for years at university level. But with examples would they become "within reach" for so many more. Assumptions belongs mainly at the very highest level, like that estimation of how often a prime occurs (don't remember it all), but it was an assumption which later was proven to be either far to high or far to low, regarding very high such numbers. But anyways, in this article I think that 31, 331, 3331 etc series really illustrates the importance of proof, even if assumptions also later can be proven to be correct. I assume, by the way, that most of our math-related articles just will be for the extremely few (also very few among math educated people, like engineers) if we avoid examples in hard numbers. All formulas are available at other sites, so why use Wikipedia (for math) if we don't (or won't even) offer something more ? (I have nothing against philosophy but that subjest can't be the main issue in this article) Boeing720 (talk) 22:09, 24 November 2017 (UTC)

Boeing720, I agree with you that examples accessible to a lay reader are most helpful, and that most philosophy and graduate-level mathematics are off-putting to a lay reader in a general survey article like this. The article has improved enormously over the years, but it could still use much improvement. It's a very difficult job, though, partly because mathematics is such a vast topic, it's hard to do justice to it in a brief survey, and partly because mathematics is itself difficult to explain clearly in a way that's easy to understand. I can tell you how to do it, though. You probably already know, since you've been on Wikipedia a long time, but I'll mention it for anyone else reading. The thing to do is get a few books that are general surveys of mathematics for a lay reader, find their main points and examples, and summarize them in the article. There are actually quite a few of these general-survey books published. This is a lot of work, of course, but this kind of work is the most fulfilling part of editing Wikipedia. —Ben Kovitz (talk) 18:04, 2 February 2018 (UTC)

Portions, fractions, ratios

"Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of topics such as quantity (numbers),[1] structure,[2] space,[1] and change.[3][4][5] There are many views among mathematicians and philosophers as to the exact scope and definition of mathematics.[6][7]"

Somethings missing in the basic introduction - that math is the study of portion and proportion, and done so systematically such as to provide a basis for science (and engineering). That a good portion of math is portions, which is to say holistic study - the study of whole forms and how they are divided. Math is not measurement itself, but it uses measurements to build formula upon. -Inowen (talk) 22:14, 1 February 2018 (UTC)

The introduction to this article is contentious, perhaps because the article attracts many editors with differing backgrounds. For you to convince your fellow editors of your viewpoint, you will surely need Wikipedia:Reliable sources. Then the discussion can begin. Mgnbar (talk) 02:40, 2 February 2018 (UTC)

"Ratio and proportion are fundamental to mathematics and important in many other fields of knowledge. Many phenomena can be expressed as some proportional relationship between specific variables, often leading to some new, unique entity." [4] -Inowen (talk) 04:15, 2 February 2018 (UTC)

Aren't "ratio" and "proportion" already subsumed in "quantity"?

The important thing to keep in mind is that the first sentence of this article is intentionally vague. We will never be able to give a complete, defensible demarcation between what is mathematics and what is not. But pro forma we have to put something that looks like a definition at the start of the article; it's part of the style, and it's what readers expect.

We're not going to be able to convey an awful lot of actual information there. I think it is useful that we mention "structure", because a lot of less mathematically inclined readers probably don't think of math as being about structure, and that might spur productive thought patterns for reading the rest of the article. But other than that, we mostly want to get the "definition" out of the way without doing any harm. Possible ways to do harm would be to make it seem more precise than it is, to limit it more than it should be limited, or to drag it on too long. Adding "ratio" and "proportion" would seem fine as regards the first two criteria, but the danger is in letting it drag on too long, especially if it sets a precedent for people to add other things that might occur to them. --Trovatore (talk) 05:26, 2 February 2018 (UTC)

Indeed, "There are many views among mathematicians and philosophers as to.." Portion and proportion could be mentioned briefly (with due weight) in Section "Definitions of mathematics", not in the lead. Boris Tsirelson (talk) 06:52, 2 February 2018 (UTC)

I support the views of Trovatore and Tsirel (about vagueness, inclusion of "portion, ..." in quantity, importance of structure, mentioning "portion, ..." later on), but oppose to the claim that math builds formulae upon measurement. Rather, math is eager to develop formulae, capable of predicting measurement, possibly inspired by existing measurements. Furthermore, this were only a description of the applied part of math. Maybe, it is true that the mentioning of "math being essential in many fields" is a somewhat meager denotation of the central and crucial role of math in all natural science. I am unsure, if the importance of the accentuated notions "portion, ..." matches the importance of other mathematically refined notions, which are shaping our lives, not covered by elementary math. Purgy (talk) 09:08, 2 February 2018 (UTC)

"Math builds formulae upon measurement"? Is it written in the article? I fail to find it there. Boris Tsirelson (talk) 17:02, 2 February 2018 (UTC)

Sorry for invasion: (math) "uses measurements to build formula upon" by Inowen above. Purgy (talk) 18:00, 2 February 2018 (UTC)

Tsirel, the lead says "mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects." I'm not sure if Purgy is arguing against that proposition, but it's well established fact. —Ben Kovitz (talk) 17:22, 2 February 2018 (UTC)

Sorry for invasion: You are mixing up different statements, and insinuate alien claims! Purgy (talk) 18:00, 2 February 2018 (UTC)

Thanks for the clarification, Purgy. I found "[math] uses measurements to build formula upon" too vague and ambiguous to agree or disagree with. I couldn't tell if it was a reference to the sentence in the lead, or what. I couldn't tell what you meant by "math builds formulae upon measurement", either. (No insinuations intended.) —Ben Kovitz (talk) 18:11, 2 February 2018 (UTC)

Take a look at Definitions of mathematics for a survey of some of the many competing definitions. —Ben Kovitz (talk) 12:51, 2 February 2018 (UTC)

Inowen seems to have a bee in his bonnet about "portion and proportion". The book he cites above does not even use the phrase. Of course, "ratio and proportion" are important topics in mathematics, but they are hardly the most important topics, and "uses measurements to build formula upon" is, as BenKovitz says, too vague and ambiguous to agree or disagree with. Rick Norwood (talk) 21:05, 2 February 2018 (UTC)

"disputing Oakley"

In my last two (reverted) edits I did not intend to simply dispute B. Oakley in general, but to demonstrate that the ideas, which are excerpted in the article from the two references before my edits, (1) the claim about natural language, "where people can often equate a word (such as cow) with the physical object" and (2) the idiosyncrasy that in math a "single symbol can encode a number of different operations or ideas", are not undisputed in the scientific world. BTW, her claim of "multiplication being repeated addition" is also not accepted in the erudite math world.

I gave two sources and one obvious referral to the mentioned "cow", establishing the inherent incapacity of "natural languages" to unambigously identify physical objects, and cited from the "Begriffschrift" by G. Frege, more than two centuries ago, that any intuitive understanding has to be secured by strict formalism, thereby excluding any "encoding" of different concepts in one notion.

Imho, the given refs suffice to render the transcribed ideas of Oakley in "stark contrast" to other, relevant reliable sources. I am not after calling Oakley "generally refuted". Purgy (talk) 16:53, 31 January 2018 (UTC)

In the article, there are three ideas attributed to Oakley:

1. Mathematical notation is more abstract than natural language.

2. Mathematical notation is more encrypted than natural language.

3. The greater abstractness and encryptedness are the reason why beginners often find mathematical notation daunting.

The first two seem self evidently true. The third seems highly plausible. I don't see how any of the three ideas "are in stark contrast not only to the rigor, which, in generality, all mathematicians strive for, but also to the inherent ambiguities of the natural languages." Paul August ☎ 18:45, 31 January 2018 (UTC)

I explicitly referred to the disputed ideas, subsumed under your wishy-washy points (encrypted! in natural language), and do it again:

"... natural language, where people can often equate a word (such as cow) with the physical object it corresponds to, ..."

"... meaning a single symbol can encode a number of different operations or ideas ..."

"By encryptedness, I mean that one symbol can stand for a number of different operations or ideas, just as the multiplication sign symbolizes repeated addition."

The first two claims ARE in "stark contrast" to the sources I cited, the last repeats the opinion of the second, and adds elementary level teacher's misunderstanding. Purgy (talk) 19:12, 31 January 2018 (UTC)

Purgy, I checked the sources that you provided, and they did not contrast Oakley's ideas about mathematical notation with mathematical rigor. On Wikipedia, we just summarize the authoritative sources about each article's topic; please see WP:V. The articles on requirements engineering were not even about mathematics as such. The Mathematics article is a general survey of mathematics; it should be a summary of authoritative surveys of mathematics. —Ben Kovitz (talk) 20:15, 31 January 2018 (UTC)

By the way, I'm not sure that we should even be mentioning Barbara Oakley by name here. The salient points are just that modern mathematical notation is more rigorous and abstract than ordinary language, and that this rigor and abstractness often presents difficulties for beginners. The claim that the "encryptedness" of mathematical notation is greater than that of ordinary words sounds dubious, and the word choice is strange; normally we would say that mathematical notation is "equivocal" or "ambiguous". I haven't checked the sources about this, though. Are facts about Barbara Oakley (as opposed to mathematical notation) salient here? And does the claim that mathematical notation is more equivocal than ordinary words fairly represent scholarly consensus? —Ben Kovitz (talk) 20:15, 31 January 2018 (UTC)

I hadn't actually read what Oakley meant by "encryptedness". I agree that "encryptedness" is a strange choice for meaning that "one symbol can stand for a number of different operations or ideas"; "ambiguous" would be better. And thinking about it with that meaning in mind, her claim 2 does now seem questionable. Paul August ☎ 20:43, 31 January 2018 (UTC)

When Oakley says mathematical symbols can stand for a number of different operations or ideas, what she really means is that mathematical symbols can encode or symbolize a number of different operations or ideas. She isn't claiming mathematical symbols are more ambiguous than ordinary words (although I can see how the sentence quoted in the article, without the context of the surrounding paragraph, gives that impression). To illustrate the encryptedness of mathematical symbols, she gives the example of multiplication (e.g., the succinct 5 × 5 encoding the more complicated 5 + 5 + 5 + 5 + 5). This is not the best example, as Purgy pointed out, because multiplication can only represent repeated addition in a rather limited context; explaining the multiplication of fractions or negative numbers as repeated addition would be rather tricky, for instance. A much better example of how mathematical symbols are more highly encrypted than regular words is the prime symbol (') used as a differential operator for single variable functions, as described by User:Wcherowi in this discussion I had with him. A couple other examples of encrypted mathematical symbols I can think of off the top of my head are 5! encoding 5 × 4 × 3 × 2 × 1, and 2⁶ encoding 2 × 2 × 2 × 2 × 2 × 2. Basically, Oakley is saying that mathematical symbols can have a number of different operations or ideas packed into them, and that this helps explain why mathematical language is more difficult to process than natural language. Lord Bolingbroke (talk) 00:13, 1 February 2018 (UTC)

It does help to have the full context from the source available. Paul August ☎ 01:10, 1 February 2018 (UTC)

Do you think the current wording of the article regarding the encryptedness of mathematical symbols needs to be clarified at all? If people such as you and Mr. Kovitz are being mislead, I don't know if the average reader will fair much better. Lord Bolingbroke (talk) 01:12, 1 February 2018 (UTC)

First, an apology having misspelled the name above.
As already stated, I do not care very much about the content of this article, only if I get -by chance- confronted with it. So I also will not mind any further, if you leave untouched the obviously inconsistent formulations by Oakley (ambiguity in math notation, superiority of natural language to avoid ambiguity) as a leading idea in the disputed paragraph. Oakley is certainly on to something with the formalism and abstractness of math, making math hard to comprehend for beginners, but the current three sentences and the given citations cannot express the reasons in a concise (mathematical???) way. Partly, this is induced by the unlucky term "encryption", which she has a hard time herself to interpret, and ends in an inappropriate claim of ambiguity. Maybe she should have used "compressed" instead of "encrypted". Concise, strict, rigorous, abstract, compressed, formal, even unintuitive, all being not very sexy attributes, are acceptable reasons for beginner's difficulties, but encrypted and less attached to a well defined meaning are not.

If you mind comparing these three sentences to the content of the following paragraphs in this section, you will see a demonstration that it is not math to be accused of equivocation, but exactly Oakley's c-o-w. These paragraphs give a way more consistent description of reasons for perceiving math as difficult than Oakley's idea of "encryptedness", which, imho, just serves to appeal to the mystic impression math has in the general public ("I'm a rational person, I've never been good at math, and PROUD of it").

Considering that the citations of Oakley start with unfounded conjectures (no human evolution), continue with banalities (math being abstract), and end in obvious wrongness (well formed math notation is ambiguous), I suggest to remove wholesale the last three sentences of the first paragraph, starting with the editorializing "According to Barbara Oakley ..." Purgy (talk) 10:50, 1 February 2018 (UTC)

BTW, on 22. Oct. 2017 I left the following on Lord Bolingbroke's TP as an additional reply to his attempt to "further illustrate" Oakley's ideas:

---

While stalking the talk page of Wcherowi I noticed your intent to illustrate the claim of B. Oakly that "mathematical symbols were more highly encrypted than regular words". By referring to the mentioned "cow" I claim that this notion is by far "more highly encrypted" than the notion of "addition". Comparing the plethora of properties involved in identifying something as "cow" (this is a cow, and that also, yes, this too, ...) to the few -admittedly- abstract axioms making up the "addition", makes it obvious to me that Oakly is carried away by the rigorous abstractness of this notion, and involves a new term, encryption, which is imho not appropriate. It is not true that "cow" would not exist as a fully abstract notion, as the cow-in-itself; and it exists in an enormous variety as concrete animal, chewing grass on a meadow, within a, possibly big, herd, made up of, all of them, cows. On the other hand, the "addition" is not only an abstract notion, but has real manifestations, too: adding a dash of salt to some soup "adds" the number representing the mass of the dash to the number representing the mass of the soup (both in the same units, neglecting mass deficits of chemical reactions), putting together a number of fruits from one basket to a number of fruits from another basket adds these numbers to the total number of fruits, and infinitely many other instantiations. The essence of mathematical addition is to embody the addition-in-itself, disregarding any concrete realisation. Maybe, we cannot phrase (axiomatize) a "cow-in-itself", but math works on phrasing "addition-in-itself". Imho, with respect to addition, Oakly is right, when talking about "abstraction", wrong, when denying "physical analogs", and quite meaningless, when mentioning "encryption". Therefore, I object to any illustration of this thought.

---

Just to make interests more clear. Purgy (talk) 11:29, 1 February 2018 (UTC)

@Lord Bolingbroke: In answer to the question you asked above: "Do you think the current wording of the article regarding the encryptedness of mathematical symbols needs to be clarified at all?" Yes I think so. Paul August ☎ 12:00, 1 February 2018 (UTC)

I agree with Purgy's suggestion about removing the sentences about Barbara Oakley opinions, which are taken from A Mind For Numbers. If we quote or paraphrase Oakley's opinions in her own language this is confusing; if we try to interpret them this is speculation; and these opinions are based mostly on her own personal experiences anyway. Her book is interesting, but should not be given undue weight in this article. Gandalf61 (talk) 15:20, 1 February 2018 (UTC)

I also concur that the article's explanation of "encryptedness" is ambiguous to the point of being misleading (misleading one to think that it means ambiguity!). Possibly the whole passage on Barbara Oakley's ideas should be removed. I'm not at all sure that it reflects scholarly consensus, but I haven't looked into it enough yet to know. I'm happy to read some of Oakley's book and search for other sources on the same topic if no one else gets to it before I do. I probably won't have time until the middle of next week. —Ben Kovitz (talk) 13:08, 2 February 2018 (UTC)

@Purgy Purgatorio: I tried to clarify this in my previous message, and I'll try to do so again now. Oakley doesn't claim that math notation is especially ambiguous. I'm not sure where in the text you find her making claims that "well formed math notation is ambiguous" or about the "superiority of natural language to avoid ambiguity". As I mentioned above, the wording "one symbol can stand for a number of different operations or ideas" does make it sound like she's saying math notation is ambiguous; considered in context, however, it is obvious she's saying math notation is compressed (i.e., that multiple operations or ideas are embedded in just a few symbols). For this reason, I agree with you that the term "compressed" would probably be a better term than "encrypted" to get Oakley's message across. I'm open to removing the in-text attribution of Oakley and to rewording the article to clarify what she's talking about (perhaps by adding an example of compressed math notation such as exponents or factorials as I discussed above); I just hope we can do so without attributing positions to Oakley that she's not actually taking. Lord Bolingbroke (talk) 06:55, 3 February 2018 (UTC)

@BenKovitz: I don't think the whole passage on Oakley's ideas should be removed. I'm inclined to agree with Mr. August that two of the three ideas attributed to Oakley (that mathematical notation is more abstract and more compressed than natural language) are pretty much common sense. Of course, "common sense" shouldn't be the criterion for the inclusion of content in Wikipedia, given how nebulous and subjective it is. I'm confident, however, that sources can be found for these claims (Oakley herself cites a few, as I recall). I think sources could also be found supporting Oakley's claim that the abstractness and compressedness (?) of mathematical notation may be why it more difficult to process than natural language.

At this point, it seems like there's something close enough to consensus that I'd like to offer a few concrete suggestions:

• Remove the in-text attribution of Barbara Oakley.
• Remove the term "encrypted" from the passage, along with Oakley's citation supporting it. (This specific citation seems to be the one that's causing the most controversy.) Instead, use the term "compressed" to describe what Oakley is trying to communicate, and possibly include an example of what this term means.
• Keep the rest of the wording the same for now, but search for more sources to see whether there is any disagreement among scholars about the claims Oakley is making. If there is disagreement, this discussion can be restarted to see how we should proceed.

Any thoughts? Lord Bolingbroke (talk) 07:51, 3 February 2018 (UTC)

Well, I received your ping (not required in a discussion), read your remarks and acted according to the statements as of then. I did not know then about your addiction of keeping popular rubbish like "encryptedness" (= exclude access to non-in-the know) of math within the article, and also not of your attempts of making new suggestions to save a (recently used) "bee in your bonnet". Imho, it does not help to defend Oakley by simply substituting in your suggestion my coinage of "compressed" for her -by prevailing opinion- misleading formulation. As of now I stop at my sole discretion commenting on this article until further notion. Purgy (talk) 08:42, 3 February 2018 (UTC)

Purgy, I'm actually not that attached to this specific source by Oakley. As I've come to see through this discussion, the wording she uses is far from ideal. I do think the basic ideas she's trying to communicate are important though. What do you think of this suggestion: I will remove all references to Oakley from the article (citations, in-text mentions, the whole caboodle), but take a shot at rewording the material attributed to her in order to clarify what she's trying to say. As I stated earlier, I'm confident other sources can be found to substantiate the claims she's making (or something close to them). And really, it's these claims that I'm interested in seeing in the article, not Oakley's specific description of them. Do you mind if I take a shot at this? If you and other editors sill want to remove the new wording in light of future sources or further discussion, I won't object too vehemently. It is, after all, just three sentences that we've been discussing this whole time. Lord Bolingbroke (talk) 09:31, 3 February 2018 (UTC)

For what it's worth, the wording of the article before I added the material sourced from Oakley's book went like this: "Modern notation makes mathematics much easier for the professional, but beginners often find it daunting. It is compressed: a few symbols contain a great deal of information." This second sentence on how mathematical symbols are compressed is basically the same thing Oakley was trying to communicate about mathematical symbols being encrypted; it's just slightly different terminology. In the reword I'm thinking of, I'd have a sentence along these lines, and then add another sentence about how mathematical notation is more abstract than natural language. I think I would leave out the claim that these things are what make mathematical notation difficult for beginners, at least for now. Again, I'm open to having this new wording changed per sources and discussion. Do you have any objections? Lord Bolingbroke (talk) 09:47, 3 February 2018 (UTC)

I substantially support all of Lord Bolingbroke's suggestions. Paul August ☎ 13:00, 3 February 2018 (UTC)

Lord Bolingbroke, here are my thoughts. (1) Remove in-text attribution of Oakley: yes. (2) Remove "encrypted": yes. (3) Regarding the word "compressed": How about "terse"? That's ordinary English for the same concept. I don't think there's any need to invent jargon here. (4) More sources: yes, another source or two would probably help a lot. (5) I'm actually not convinced that mathematical notation is more abstract than natural language. Is "+" more abstract than "plus"? At least, the notion of 'abstraction' probably needs to be broken down to indicate what sort of abstractness the source is talking about. (6) Even if we haven't settled every detail, go ahead and edit. Sources and further editing by other editors to fine-tune wording or anything else should improve this part of the page pretty quickly, without extended discussion. If some new problem comes up, we can discuss it then. —Ben Kovitz (talk) 14:58, 3 February 2018 (UTC)

I concur with Ben Kovitz' points. Schmandt-Besserat, cited above, points out that the use of clay tokens (the precursors of writing) of ownership pre-dates numerals, which predate writing. The clay containers for these tokens of ownership were marked by embossing symbols for the tokens, which in fact are the direct precursors of writing on clay tablets. Thus the symbols, far from encrypting the number of sheep in a flock, aided the ownership of, and trade in, wealth. --Ancheta Wis   (talk | contribs) 15:17, 3 February 2018 (UTC)

Suggest citing Schmandt-Besserat

@User:Lord Bolingbroke, rather than Oakley, might I suggest Schmandt-Besserat. See Denise Schmandt-Besserat's From Accounting to Writing which shows that clay tokens were a concrete representation of things such as chattel, in the fertile crescent, where clay was abundant. Thus these tokens encoded the notion of 'the size of my flock of sheep', and enumeration of 'kinds of things', before development of the general concept of 'number'. Hence according to Schmandt-Besserat, the notion of number appeared thousands of years before writing. These abstractions evolved gradually through usage over thousands of years. But after their formulation these notions spread rapidly via trading across long distances. --Ancheta Wis   (talk | contribs) 15:40, 3 February 2018 (UTC)

Ancheta Wis, I took a quick look at "From Accounting to Writing". Its main point seems to be that phonetic writing grew out of inscribed symbols for accounting, the impetus for the shift being a religious ritual that required the names of the dead to be spoken aloud. It doesn't seem to be a source primarily about mathematics, and I don't think that it makes the points that number concepts predate writing or that the earliest number-words referred to specific types of things counted rather than fully abstract quantities (though I could have missed something). If that's right, it would be WP:SYNTHESIS for us to pull those conclusions from this source. However, I think these points are made elsewhere in sources that make broad surveys of mathematics—the ideal kind of source for this article. It's been a while since I looked at it, but I think the first chapter of Number Words and Number Symbols: A Cultural History of Numbers by Karl Menninger discusses these same facts explicitly. That book is widely considered a classic, so it's probably one of the best sources we could go to for this article. By WP:BALASPS, the fact that these facts are in such a source, even given some prominence, suggests that they probably belong in this article.

One slight basis for doubt, though. I'm not sure that number-words began tied to specific kinds of objects being counted in all languages. Menninger's book was written in 1934, and IIRC it reasoned on the basis of the grammar of some American Indian languages. It would be nice to check against recent scholarship (even if it's not published in a book that makes a broad survey of mathematics, of course).

—Ben Kovitz (talk) 17:00, 3 February 2018 (UTC)

Ben Kovitz, Schmandt-Besserat wrote a lot. What I recited came from a Scientific American article "The Earliest Precursor of Writing" by Denise Schmandt-Besserat. Scientific American. June 1977, Vol. 238, No. 6, p. 50-58. which did not tie the clay tokens (10,000 years ago) to rites (5,000 years ago), but to accounting. In her web page Denise Schmandt-Besserat 'The Evolution of Writing' I refer you to section 1: "1. Tokens as Precursor of Writing". --Ancheta Wis   (talk | contribs) 19:45, 3 February 2018 (UTC)

Semi-protected edit request on 3 February 2018

Please change "Mathematics [...] is the study of topics such as quantity (numbers) [...]" to "Mathematics [...] is the study of quantity (numbers) [...]", removing the "topics such as". The current wording including "such as" is not mentioned by the cited sources and is editorializing. 58.167.81.248 (talk) 02:37, 3 February 2018 (UTC)

The sources do not agree on any exact list. See this page, especially this section. Some wording like "such as" is needed to avoid saying that mathematics is limited to exactly those four topics. The list is imprecise; "such as" or some equivalent is needed to indicate that. I would favor "such topics as" over "topics such as", since the latter suggests that mathematics is a grab bag of topics, whereas the former suggests a little better that there is some kind of unity to the topics of mathematics even if people can't agree on what it is or put their finger on it precisely. That is indeed what the sources indicate. —Ben Kovitz (talk) 03:42, 3 February 2018 (UTC)

Well put. Lord Bolingbroke (talk) 07:55, 3 February 2018 (UTC)

I suppose your suggestion is a little better. The current wording doesn’t particularly define anything except to say "these four things are a part of mathematics, but there are many other things that aren’t listed here". 1.129.109.81 (talk) 08:43, 4 February 2018 (UTC)

I worked on this article extensively when the "quantity, structure, space, and change" formulation was agreed upon. I didn't like it, preferring the definition "mathematics is that body of knowledge discovered by pure reason", but I lost the argument. Dictionaries tend to agree with the "quantity, structure, space, and change" formulation, or some subset thereof. For example, Merriam-Webster says "the science of numbers and their properties, operations, and relations and with shapes in space and their structure and measurement".

The "quantity, structure, space, and change" formulation was a compromise which most of the large number of people working on the article at the time could accept. It is now incorporated in a great many Wikipedia articles, and to change it would require changes in all of those articles as well. Since many other sources pick up material from Wikipedia, a Google search of "quantity, structure, space, and change" (in quotes) returns 212,000 hits, and a book published by Springer in 2013 is titled "Mathematics, The Study of Quantity, Structure, Space, and Change". So, like it or not, trying to change that definition now would prove extremely difficult. Rick Norwood (talk) 12:38, 4 February 2018 (UTC)

I remember the many long discussions involving that formulation. Many editors for whom I have great respect participated. A lot of careful thought when into those discussions. In my opinion, the formulation that we arrived at is a good one. This is born out, to some extant, by its apparent adoption elsewhere. (And, as an aside, I think it's something we can all feel proud of.) Paul August ☎ 17:45, 4 February 2018 (UTC)

It's a shame that those four broad subtopics of mathematics have been taken as an authoritative definition. While I think it's a good compromise for a general reference work such as Wikipedia, no one should find it satisfying as a true definition of the topic. The sources certainly do not support that. The sources support that no definition yet proposed is satisfactory. That's why we use an ostensive definition rather than the usual definition by genus and differentia. The "such as" ought to indicate that it's only a rough, ostensive definition, but evidently that's not enough to convey that the definition is nonstandard and unsatisfactory. I recall that we used to have clear wording about this: not the mealy-mouthed "many views", but a plain and direct statement that there is no consensus about the definition. I'll see if I can find it and put it back in, or write something straightforward. Feel free to have a go at it yourself, of course, if you get an idea first. —Ben Kovitz (talk) 14:34, 11 February 2018 (UTC)

Sorry, it's not a shame, but rather speculating with the existence of some authoritative definition of mathematics is a shame. Perhaps, may I point you to the linguistic side of this problem, via Wittgenstein (... thereof we must remain silent), or to the more formal aspect of incompleteness of anything sufficiently strong to fix arithmetic, via Gödel? Clear wordings, outside of formal models just appear as such to the uninitiated, and those looking for being deceived. Sorry, I felt provoked; nevertheless, happy editing. Purgy (talk) 15:00, 11 February 2018 (UTC)

Actually, I think a sound definition is possible. Mathematics is that body of knowledge arrived at by pure reason. Science is that body of knowledge arrived at by reason, observation, and experiment. So, definition is possible, just not practical in the context of Wikipedia. Rick Norwood (talk) 12:13, 12 February 2018 (UTC)

This isn't the place to argue about it, but as long as you've brought it up, I'm going to say I disagree with that definition. It both includes things it shouldn't be included (such as natural theology) and excludes things that ought to be included (such as experimental mathematics). --Trovatore (talk) 19:56, 12 February 2018 (UTC)

Where is Linear Algebra?

It seems to me that linear algebra is missing from the different links to mathematical topics. — Preceding unsigned comment added by 97.102.177.26 (talk) 13:02, 8 February 2018 (UTC)

We typically add new comments to the bottom of our talk pages (unlike many other sites on the web), so I have taken the liberty of repositioning yours here. As to your comment, look at the section titled Algebra under Pure Mathematics. --Bill Cherowitzo (talk) 20:32, 8 February 2018 (UTC)

The IP poster does raise an interesting point here, though. Should we subsume linear algebra under (abstract) algebra? Linear algebra is studied by a lot of people who will never learn what a group is. And a lot of them will come across it via very "applied" routes. I'm not sure we're serving these people best by shoving the only mention down in the middle of the second paragraph of a subsection of "pure" that they won't even read. --Trovatore (talk) 20:15, 12 February 2018 (UTC)

I didn't think that the IP had raised that point, but now that you have, I do think it is a good point to raise. First, I did make a mistake above, the section title is Structure not Algebra (but the hatnote points to that as the main page), but that is inconsequential to the question. I don't know how, without vast amounts of repetition, to deal with topics that are very applicable in areas outside of mathematics proper. The question about linear algebra could be asked about any of these. The pure vs. applied dichotomy has always left me cold and I view these things more like fuzzy sets with a time dependence–a concept that is very tough to convey in a stripped down article such as this one. So, while I believe that the point is a good one, I am baffled about how to address it. --Bill Cherowitzo (talk) 21:51, 12 February 2018 (UTC)

mathematics is a tool of logic based on it

mathematics is a tool of logic based on it — Preceding unsigned comment added by 2A02:2149:887F:EC00:913:9FEF:9923:68 (talk) 19:49, 23 February 2018 (UTC)

More than just a tool of logic. Paul August ☎ 19:55, 23 February 2018 (UTC)

First known written numerals by Egyptians vs Sumerians in the 3rd millennium BC

The Summerians ability to do base 60 astronomy math calculations without writing anything down is amazing.

Per Google, https://en.wikipedia.org/wiki/Mathematics states, "the first known written numerals were created by Egyptians in Middle Kingdom" and https://en.wikipedia.org/wiki/Sexagesimal states, “Sexagesimal. Sexagesimal (base 60) is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used…” 2001:558:6025:6E:153F:C57:13B8:34E2 (talk) 00:23, 25 February 2018 (UTC)

The Babylonian and Egyptian numerals are roughly contemporary, circa 2000 BC. I do not know if there is strong evidence that the Egyptians came first. If nobody provides it, I'll include the Babylonian numerals in this article. Rick Norwood (talk) 23:07, 26 February 2018 (UTC)

Edit request, 5 August 2018

From the last section: "A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. A solution to each of these problems carries a $1 million reward, only one of which (the Riemann hypothesis) is duplicated in Hilbert's problems."

The way this is structured, the reward is treated as several things of which only the Riemann hypothesis is duplicated in Hilbert's problems. Also, the passive "is duplicated" is weird here, because Hilbert's list was earlier.

My proposal: "A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Only one of them, the Riemann hypothesis, duplicates one of Hilbert's problems. A solution to any of these problems carries a $1 million reward." 2.24.117.46 (talk) 16:51, 5 August 2018 (UTC)

I agree. It's done. Mgnbar (talk) 17:42, 5 August 2018 (UTC)

Intro

The article is about a topic, which is an idea, which has a name, and both the name and the idea are ancient and quite commonly understood. So the proposal that mathematics 'has no generally accepted definition' is weak, and has only the basis that its sourced to the typically overspecialized or unremarkable type of math person. Like doctors arguing that 'medicine' is 'too broad to define'and 'there is no clear definiton,' when everyone knows what medicine is; it's the science of human health. The sources are also less than high level, one being an old article and not a foundational one, and the other being a biographical article. -Inowen (nlfte) 03:48, 22 August 2018 (UTC)

It seems, you know what exactly is mathematics. Please let us know, and then we'll see. Boris Tsirelson (talk) 04:52, 22 August 2018 (UTC)

To editor Inowen: If you can supply the article with a better definition and cite a reputable, dependable source for it, we would love to have it in the article—assuming it passes consensus, of course.—Anita5192 (talk) 06:01, 22 August 2018 (UTC)

I am not a mathematics expert, so I will yield the request to someone else, perhaps even multiple contributors, who can work together to lay out the basics. Obviously, you should start with the obvious - what a layman or non-mathematician professional knows:

Math is the scientific language of numbers and consistent expressions, that combines numbers (symbols of countable form) of well-built form (real form), and operations (+,-,×,÷..) of exact consistent form, to precisely transform individual measurements or estimates into endless possible theoretical projections. The simplified or canonical form of such calculations is called a formula, and the output of formula are called expressions or solutions. Mathematics is regarded the fundamental tool at the heart of sciences such as engineering, physics, and chemistry. At the base of mathematics is a principle that countability of objects is a real property of nature which is universal and uncontestable and that a mathematical proof must similarly extend without flaw from the core of universally-accepted ideas (cf. mathematical truth).

-Inowen (nlfte) 01:43, 23 August 2018 (UTC)

This presentation comes across as dogmatic and creates a barrier which makes any new (unfamiliar) concepts unreachable to laymen. The new ideas aren't even that hard if one is patient or humble. You are describing what I would call the Moore method (and yes, I even spoke to R. L. Moore, once. In his words .. "I like to keep them guessing.", which is the reason he didn't use a book in his classes. ..). In my view, you are leaving out important things, such as the significance of little words such as "a", "the", "some" .. in precise English. I especially object to the word "must" above. And the "core of proven ideas" are what Moore's students each would discover for themselves. --Ancheta Wis   (talk | contribs) 02:43, 23 August 2018 (UTC)

More important than these specific criticisms, in my view, is the fact that content on Wikipedia should not be based on "what a layman or non-mathematician professional knows" but rather on reliable sources (see Wikipedia:Common knowledge). Until sources are provided demonstrating that Inowen's definition is anything close to an end-all be-all definition of mathematics, there's not really any need to critique specific elements of it. Lord Bolingbroke (talk) 03:01, 23 August 2018 (UTC)

Of course, Lord Bolingbroke is right; my specific critic below is unneeded. And nevertheless I want to ask Inowen: what about (say) Graph theory? Is it a part of mathematics? According to your definition, it is not. Boris Tsirelson (talk) 04:59, 23 August 2018 (UTC)

Obviously, the common understanding about the name and the idea under discussion is by no means covered under one specific POV, insinuated to be the obvious - what a layman or non-mathematician professional knows. Obviousness or simplicity is in the eye of the beholder. Purgy (talk) 06:42, 23 August 2018 (UTC)

"My definition" has many different elements. No single source will back up all of those elements together. So each part needs checking. The first two things I delivered above are that:

• math is scientific - https://undsci.berkeley.edu/article/mathematics
• math is a language - http://www.ascd.org/publications/books/105137/chapters/Mathematics-as-Language.aspx

Each continued element can be sourced, or not, as well,

• math uses numbers -
• math uses operations -
• math combines numbers and operations -
• numbers are well built -
• operations are regular -
• math transforms measurements and estimates in precise way -
• the idea of countability is fundamental -
• from the simple idea of countability comes the greater idea of mathematical truth -

Etc. -Inowen (nlfte) 02:33, 24 August 2018 (UTC)

But you did not address my question (above): is graph theory a part of mathematics? Even more: is geometry a part of mathematics? Numbers are an important but small part of mathematics. Boris Tsirelson (talk) 04:21, 24 August 2018 (UTC)

I've read through the proposal and while I wouldn't be too quick to reject it out of hand, I agree that it is dogmatic. The opening sentence of the lead currently reads:

• Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change. It has no generally accepted definition.

While this is suitably vague and imprecise allowing for wider scope of understanding, I think the proposing editor struck a reasonable chord with the suggestion that the opening sentence mention every day life application. Therefore a less imposing alteration might be:

• Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes the study of such topics as quantity, structure, space, and change. It overlaps with many fields of research and engineering and owing to its wide scope it has no generally accepted definition.

Edaham (talk) 05:00, 24 August 2018 (UTC)

The basic proposition I made was that the idea of 'no agreed definition' is weak, and really not true. Honoring the idea of mathematicians squabbling over what to include or not is not the right thing to do, as there is no such debate in the public at large. Debates in the context of specialization are irrelevant to the greater discussion. And the word 'numbers' has a meaninig that underlies all of mathematics, and that includes graphs, so the question about the inclusion of graph theory was misplaced. -Inowen (nlfte) 05:09, 24 August 2018 (UTC)

Then, I do not understand, what do you mean by "definition". Can a small part of something be enough for the definition of the whole thing? "Great Britain is basically London"? Numbers are an important but small part of mathematics; and moreover, formulas manipulation (elementary algebra) is a small part of number-related mathematics. Numbers underlie graphs? Well, no more than they underlie nearly everything (science, engineering, accounting, ...), but not everything is mathematics. Boris Tsirelson (talk) 05:27, 24 August 2018 (UTC)

Comment I complained about this last year here. It's clear that arithmetic, algebra, geometry, and calculus are mathematics, while astronomy and music are not; saying there is "no generally accepted definition" is somewhere between bad writing and misleading. I'm not sure Edaham's version is a significant improvement, though. power~enwiki (π, ν) 05:12, 24 August 2018 (UTC)

Reply to comment I don't like that "no accepted definition" statement either. My opinion about this piece of text is this: it doesn't matter. If something has fuzzy edges and is difficult to define, why bother remarking that the definition is elusive. Just talk about what the sources say it is and leave it at that. With that in mind, maybe this would be better:

• Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes the study of such topics as quantity, structure, space, and change. The study of mathematics has many applications in real world tasks, which overlap with many fields of research and engineering

Or something like this. You know, as an editor I look at the current version and with a bit of a wry smile look at that "no accepted definition" remark and I think: I bet there's been some no-consensus argument on the talk page of this article a while back. I think even a shrewd reader might get that impression from what we've written. Edaham (talk) 06:19, 24 August 2018 (UTC)

Well there seems to be some agreement on the matter of 'no accepted definition.' And though Boris seems to disagree, he also admits that he does'nt understand what I mean by 'definition.' The word "definition" simply means 'a short and sufficiently whole-form description of the meaning of a word.' The argument for defining something, describing something with a short description, is important. The argument against a single definition seems to be an argument against a short description, but then that is an argument against all definitions, in any subject, in such a way as to throw away the idea of a dictionary, or the idea of being clear in article introductions here. The idea that 'no short description is sufficient' comes from a certain type of critic, let them be named so we can identify them. In spite of the critics, short descriptions seem to be popular and necessary. -Inowen (nlfte) 06:37, 24 August 2018 (UTC)

No objection to Edaham (from me), basically. But I guess, the phrase "no accepted definition" is just a precaution against someone who will say: but first of all we need a definition, don't we? Inowen speaks about short description, but in fact proposes something quite long (and still not enough)... Boris Tsirelson (talk) 06:43, 24 August 2018 (UTC)

Regarding the need for definitions: I think that giving a few broad examples of what constitutes math subjects and their offshoots (which are definitely encompassed by or close to the definition) and also inferring that the summary is not exhaustive is sufficient. It's tempting to edit the article text based on what seems to be an emerging consensus, but I'll let a few other editors chime in before editing the article Edaham (talk) 06:48, 24 August 2018 (UTC)

@Boris. But then because people ask for a definition, we give them one, which one editor, regardless of their ability, cannot do alone: 'math is the scientific language of numbers and precise number transformation, which goes on to include abstract ideas of entity and quantity, and sophisticated ideas of transformation..' -Inowen (nlfte) 06:51, 24 August 2018 (UTC)

I definitely prefer Edaham's approach. Numbers as the central point and the starting point of the whole mathematics is just POV of Inowen (and discriminates geometry, at least). Great Britain is not "London and more"; and math is not "numbers and more". What is better: no definition at all, or a bad, controversial, unstable definition, chosen arbitrarily from many (equally bad) possibilities? Boris Tsirelson (talk) 08:50, 24 August 2018 (UTC)

My opinion has not changed very much since 11 February 2018:

Speculating with the existence of some authoritative definition of mathematics is a shame. May I point to the linguistic side of this problem, via Wittgenstein (... thereof we must remain silent), or to the more formal aspect of incompleteness of anything sufficiently strong to fix even arithmetic, via Gödel? Clear wordings, outside of formal models just appear as such to the uninitiated, and those looking for being deceived.

I sense a great discrepancy between the interpretations of "definition" by editors, favoring more vs. less rigor in this non-technical article. I oppose to Inowen's efforts for the above reason, I am not bothered by there explicitly being "no generally accepted definition", and I can easily accept Edaham's suggestion of "... includes the study of bla, bla, ..." Purgy (talk) 09:02, 24 August 2018 (UTC)

Ive altered the opening sentence as follows: Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes the study of such topics as quantity, structure, space,[1] and change. The study of mathematics has many applications in real world tasks, which overlap with many fields of scientific research, analysis and engineering. In my mind it now looks like a sentence in an encyclopedia entry and not the result of kids being unable to resolve a debate. That was my main issue with it before. I think it also briefly explains that the field is broad and has wide reaching applications. Having thus been explained it is tautologous to add the fact that there is no accepted definition for such a nebulous subject. Edaham (talk) 10:38, 24 August 2018 (UTC)

I support Purgy's comments and also have no problem with "no generally accepted definition". For a mathematician a definition supplies a name for a concept or object and also serves the function of being the litmus test for deciding whether or not something is that which is being defined. We regularly are involved in discussions of whether or not a definition is good, and this has nothing to do with names, only function. A definition becomes important only in the gray areas, where the distinction between what is and what is not mathematics is blurred. I strongly agree with Boris, attempting to tie the subject to a generalized concept of number is totally inadequate. Better nothing at all than that approach. I am also not happy with the current second sentence. This article is about mathematics, and while many hold the belief that what is important about mathematics is its applications, I find that POV to be akin to the statement that, "Chemistry is an important subject since it can be used to improve toilet bowl cleaners." Applications are treated, with respect, in the last paragraph of the intro and I think that is where this material belongs, not in the second sentence.--Bill Cherowitzo (talk) 19:18, 24 August 2018 (UTC)

I do not join your likening all the applications of math to only improving toilet bowl cleaners. Well, I've look at "Physics" and "Chemistry", and... yes, indeed, I see that applications are not mentioned in the first paragraph (the more so, in the first sentence) of the lead. Hmmm... Boris Tsirelson (talk) 20:17, 24 August 2018 (UTC)

And by the way, in "Biology" I did not find applications at all! Probably, its usefulness is uncontroversial, while usefulness of math is most controversial (among these four)... Boris Tsirelson (talk) 20:23, 24 August 2018 (UTC)

As long as we're talking about math and its applications, let me raise a point about the first two paragraphs. I have rated each sentence P or A, where A sentences are about applications and P sentences are about math narrowly and "purely". And my ratings go:

• First paragraph: P, A
• Second paragraph: P, A, P, A, P

Is this interleaving intentional? I think it's bad writing. Some of the A sentences are redundant with the fifth paragraph, too. Mgnbar (talk) 20:49, 24 August 2018 (UTC)

There is some name-calling going on that might not be helpful or might be helpful. On the one hand I and others are calling the usage of the language 'no agreed-upon definition' to be weak and incorrect, given such a major topic, and its universality. On the other hand, the other side (Boris, etc.) is calling something which is cobbled together collaboratively to be "bad, controversial, unstable, and chosen arbitrarily, from many( equally bad) possiblities." While I and others are criticizing the current version, Boris is criticizing a version that hasn't even been written yet! He also dislikes the idea that math has anything to do with numbers. He might back off from that a little and say that numbers are a 'rudimentary' part of mathematics, but then how does one exclude something of a 'rudimentary' part of a fundamental topic like numbers excluded from mathematics, or medicines excluded from medicine? Rather than accept Boris' rigorous handwaving, we should ask him to write a defense of the current version. For collaborative work, I suggest using a draft page at Mathematics/Draft and transclude it here with a transclusion tag {{:Mathematics/Draft}} and work on it collaboratively. There should also be an edit page link inside of the draft. -Inowen (nlfte) 20:37, 24 August 2018 (UTC)

That post does not fairly summarize Boris Tsirelson's viewpoint. He does not "dislike the idea that math has anything to do with numbers". Rather, he correctly points out that math is about much more than numbers. And this is why the reliable sources mention not just "quantity" but also "structure", "space", etc. This is a serious flaw in your proposed intro. Mgnbar (talk) 20:49, 24 August 2018 (UTC)

Math may be about "much more than numbers," but it starts with numbers, and so why reject the idea of talking about math ←→ numbers in the introduction to the root article? This idea of saying in the "x is much more than [fundamental part]" is so high-level it doesn't touch the ground, and though pretenses can be made, never got off the ground in the first place. -Inowen (nlfte) 21:00, 24 August 2018 (UTC)

The current intro sentence already addresses this issue by mentioning "quantity". Most importantly, it does so based on reliable sources.

I look forward to seeing how your draft develops. Regards. Mgnbar (talk) 21:26, 24 August 2018 (UTC)

The draft ideally would be set up in main space and not just my user space, and as such would be open to collaborative editing, which it is still, its just things in user space don't appear as open to editing. -Inowen (nlfte) 21:32, 24 August 2018 (UTC)

@Tsirel, sorry about that. I was going for the visual image rather than the strength of the metaphor. Applications are of course important and they are what makes most people want to learn mathematics, but I felt that it needed to be said that they are themselves not mathematics, rather, mathematics is the tool being used to solve the application problems. The article would not be complete without discussing several applications, but mathematics would still exist (as an art form) even if it had no applications at all.--Bill Cherowitzo (talk) 23:57, 24 August 2018 (UTC)

"How does the mathematician—closer to the artist than to the explorer—by turning away from nature, arrive at its most appropriate descriptions?" (The last point in: Mark Steiner "The Applicabilities of Mathematics", Philosophia Mathematica 3(2):129--156 (1995), see page 154.)
"It is positively spooky how the physicist finds the mathematician has been there before him or her." (Steven Weinberg 1989, quoted by Mark Steiner on the first page.)
Thus, another definition: Mathematics is the spooky art of arriving the most appropriate descriptions of nature by turning away from it.   :-)   Boris Tsirelson (talk) 08:12, 25 August 2018 (UTC)

I do like that very much. I wish, but know better, that we could use it. --Bill Cherowitzo (talk) 17:48, 25 August 2018 (UTC)

Draft

Math is the scientific language of numbers and number transformation, which goes on to include abstract ideas of number (countable entity) and quantity, and sophisticated ideas of transformation. Mathematics combines numbers, variables, and constants of well-built form (real form) with operations (addition, subtraction, multiplication, division..) of exact consistent form, to precisely transform individual measurements or estimates into endless possible theoretical projections. The simplified or canonical form of such calculations is called a formula, and the output of formula are called expressions or solutions. Mathematics is regarded the fundamental tool at the heart of sciences such as engineering, physics, and chemistry. At the base of mathematics is a principle that countability of objects is a real property of nature which is universal and uncontestable and that a mathematical proof must similarly extend without flaw from the core of universally-accepted ideas (cf. mathematical truth).

Individual parts

• math is scientific - https://undsci.berkeley.edu/article/mathematics
• math is a language - http://www.ascd.org/publications/books/105137/chapters/Mathematics-as-Language.aspx
• math uses numbers -
• math uses operations -
• math combines numbers and operations -
• numbers are well built -
• operations are regular -
• math transforms measurements and estimates in precise way -
• the idea of countability is fundamental -
• from the simple idea of countability comes the greater idea of mathematical truth -

Missing

• quantity - Mgnbar

No, this isn't going to fly. I don't really see any point in going into it in detail. It isn't going to go anywhere. --Trovatore (talk) 21:37, 24 August 2018 (UTC)

So you say; do you have anything to contribute to the discussion, on the main point, which is the problem of using weak language like 'no agreeable definition?' -Inowen (nlfte) 23:02, 24 August 2018 (UTC)

I think the problem people will have with that proposal is that it is unduely limiting to the point of being draconian. Numbers are a way of talking about lots of math things but they aren’t the “science” behind math. Numbers are particularly ill-suited to a number of areas of mathematics, which are expressed using other means. To use your language analogy: Math isn’t a language, it’s a topic and numbers are but one language you can use to talk about this topic. Other expressly non-numerical means have been devised for communicating mathematical concepts and those are languages too. Edaham (talk) 23:37, 24 August 2018 (UTC)

Trovatore is quite right, this is not going to fly. There is way too much OR (and here I am being polite and not calling it what it really is) in this draft. Just to highlight two of the most glaring examples. Mathematics says absolutely nothing about the countability of objects in the physical universe, that's physics. If I made the claim that mathematical truth flowed from the concept of countability, I would be forced to give up my membership in the American Mathematical Society.--Bill Cherowitzo (talk) 23:40, 24 August 2018 (UTC)

That’s right. A further analogy would be to say, our article on computer programming doesn’t say that printed letters are the science behind computer programs. A cellular automaton fits the definition of a set of computational instructions without using any particular language. You can build one out of wood. I tried it. There’s a bigger point at large here which also needs to be addressed. The purpose of this article is not to mollycoddle involved editors who care about the outcome of this debate, but to let our readers know that they have stumbled across a huge, sprawling subject and give them some idea of its scope, point out the impossibility of giving an exhaustive list and provide some history and useful leaping off points. It does that quite nicely at the moment. Cluttering the lead with any awkward attempt at definitions (or comments about the lack thereof) is a bad move. This article is a hub and needs to quickly get down to the business of signposting To historical and contemporary areas of study. Usefulness to our readers is the primary issue here. Edaham (talk) 23:55, 24 August 2018 (UTC)

A number of us agree that the language of 'no clear definition' is weak and seriously beneath the level of a well-written article. The draft was created in article space as it is intended for others to edit. It was moved to my user space by an editor, presumably under some rules that drafts should be in user space. It is for anyone to edit, particularly those who agree that 'no clear definition' is poor form. -Inowen (nlfte) 01:00, 25 August 2018 (UTC) @Bill, "mathematics says absolutely nothing about the countability of objects in the physical universe, that's physics." Is the idea of one and then two, being universally different, and on which the ideas of counting, adding and subtracting are based, which I am calling "countability", something "that's physics" and not math? -Inowen (nlfte) 01:06, 25 August 2018 (UTC)

I don't know. What do the reliable sources say? Mgnbar (talk) 02:26, 25 August 2018 (UTC)

If the concept of not having a clear definition appears weak to some, then perhaps we should be attempting to expand and strengthen it. Definitions in the literature run the gamut from Engels', "Mathematics is a science whose subject matter is spatial forms and quantitative relationships of the real world" to Hilbert's "Mathematics is what competent people understand the word to mean." (Both quotes can be found in Ya. Khurgin's little book, Did You Say Mathematics). My favorite, however, is the statement in Davis & Hersh, The Mathematical Experience (p. 8), "The definition of mathematics changes. Each generation and each thoughtful mathematician within a generation formulates a definition according to his lights." I, for one, enjoy the flexibility of not having clearly demarcated boundaries. When someone starts to spout off about the mystical powers of pyramids, I like to be able to say, "that is not mathematics" without having to put too fine a point on it.--Bill Cherowitzo (talk) 04:29, 25 August 2018 (UTC)

@Bill, both of those quotes are grandiose and philosophical. Not suitable for a clear introduction. The book excerpt "the definition of mathematics changes. Each generation and each thoughtful mathematician within a generation formulates a definition according to his lights," is nice, but non-definitive, and again a bit grandiose. Do the authors propose that there is no similarity between the math of one generation and the math of the previous? To the contrary math is to a great deal about preserving a worldwide scientific heritage of inquiry into truth itself, by way of the use of numbers and operations and seeing what they express. -Inowen (nlfte) 10:07, 25 August 2018 (UTC)

@Inowen Please note there are people who have already done the work. No sense in reinventing the wheel or rebuilding the Pyramids. Rather than using applied mathematics or one's personal history of instruction in mathematics, consider using the foundations of mathematics — one could just as well use

1) a constructivist's solution for constructing numbers: Church numerals, which arose in the 1930s. It's more elegant as well, as infinity is built-in. You don't need a lot to go very far.

or 2) a formalist approach with axioms etc ala Principia Mathematica or geometry. (But there are problems)

or 3) a category theory/Univalent foundations approach using types as the objects, and now we are no longer restricted to numbers, and computerized proof assistants become feasible.

The list goes on and on, with as many foundations as there are mathematicians ...

It should be clear that no static definition of mathematics suffices; an act of definition requires both a foundation and an approach to the mathematics, based on our natural biases. So "no generally accepted definition" in the article doesn't strike me as weak. Rather it's realistic. --Ancheta Wis   (talk | contribs) 09:25, 25 August 2018 (UTC)

@Inowen Ancheta Wis makes a very good point. The quotes I gave were meant to show the disparity in what is available in the literature, I was not suggesting that they be used in the article. You are also reading more into the Davis and Hersh statement than they are saying. Perhaps you would be more inclined to follow the advise inherent in this excerpt from Morris Kline's Mathematics for the Non-mathematician (p. 3)

... consider what mathematics is. Unfortunately the answer can not be given in a single sentence or a single chapter. The subjects has many facets or, some might say, is Hydra-headed. ... Because it is impossible to give a concise and readily understandable definition of mathematics, some writers have suggested, rather evasively, that mathematics is what mathematicians do. ... A variation on the above definition which promises more help in understanding the nature, content and values of mathematics, is that mathematics is what mathematics does. If we examine mathematics from the standpoint of what it is intended to and does accomplish, we shall undoubtedly gain a truer and clearer picture of the subject.

Kline, whose audience consist of non-mathematicians, goes on to say that "Mathematics is concerned primarily with what can be accomplished by reasoning." Notice that numbers do not play the fundamental role that you wish to assign them in his approach. --Bill Cherowitzo (talk) 17:41, 25 August 2018 (UTC)

An opening sentence with the phrase which goes on to include is a complete non-starter, and I'm not sure that At the base of mathematics is a principle that countability of objects is a real property of nature which is universal and uncontestable and that a mathematical proof must similarly extend without flaw from the core of universally-accepted ideas (cf. mathematical truth). is accurate or meaningful. The The simplified or canonical form of such calculations is called a formula sentence isn't great either. power~enwiki (π, ν) 19:58, 25 August 2018 (UTC)

I summarize. The Inowen's number-centric approach to (the definition of) mathematics is criticized by me, power~enwiki, Purgy, Bill Cherowitzo, Mgnbar, Trovatore, Edaham and Ancheta Wis, and supported by Inowen only. Right? Thus, it is evidently a Inowen's misconception, not worth to be discussed further. Right? Boris Tsirelson (talk) 05:38, 26 August 2018 (UTC)

I agree that the number-centric approach proposed above is probably not the way to go here. Paul August ☎ 11:39, 26 August 2018 (UTC)

The language regarding 'no agreeable definition' was removed, as per my original request. The writing still seems abstract, and while the topic may be abstract, that does not mean abstract writing is good writing. Also, the topic may be rather abstract at a high level, but at a basic level it is rather simple. There is an idea that math is simple and consequently also sensible. So can it be improved? -Inowen (nlfte) 19:38, 26 August 2018 (UTC)

The language regarding 'no agreeable definition' was removed from the lede, but I returned it to the body of the article. Paul August ☎ 19:47, 26 August 2018 (UTC)

@Inowen The phrase in the article is 'no generally accepted definition'. The act of using synonyms is an inconsistency and humans do this naturally, but machines (like compilers) have to expend resources to get there, so practitioners avoid synonyms as a matter of hygiene. Can we please take a little care with this? I admit it's a discipline, but please. --Ancheta Wis   (talk | contribs) 21:05, 26 August 2018 (UTC)

• Oppose- Even when already tired from repeatedly reading wrongly cited arguments against Inowen's suggestions, I want to make explicit that, besides my already stated positions, I adhere to more or less all arguments brought up against this simplistic view of a complex matter, and I see not a single, unrefuted sensible opinion in favour of the suggestion. The avoidance of the unbeloved phrase of there being no generally accepted definition is just a minor detail and no argument to accept an unacceptable definition. I already deny the premise that math were simple. It is "simple" only for the simple minded. I also deny the statement -presented as conclusion- that there must be a definition for things like math. Finally, and specifically, I deny the monomaniacal view on math per numbers only; even when one might cite a famous german mathematician with "Alles ist Zahl." This is no currently valid statement anymore. Purgy (talk) 12:51, 27 August 2018 (UTC)

"Mathematics includes.."

The opening sentence "Mathematics [..] includes the study of such topics as quantity, structure, space, and change," is weak. It says what mathematics "includes" but not what it is. It does not even state what math "includes" exclusively, such that doesn't problematically overlap with philosophy (quantity), engineering (structure), space (physics), and change (physics). -Inowen (nlfte) 02:08, 30 August 2018 (UTC)

It is absolutely on purpose that the definition does not say what mathematics is not. That's a feature, not a bug. It's the way it should be. --Trovatore (talk) 03:30, 30 August 2018 (UTC)

Let me try to say something very very preliminary (far from being proposed for the article).

Physics studies change of something specific (of the coordinates of a body, of the strength of a field etc); for mathematics these are only examples, special cases.

Physics studies specific spaces (the three-dimensional space we are embedded to, the Hilbert space of quantum states etc); for mathematics these are only examples, special cases.

Engineering studies structure of something specific... and so on.

Philosophy studies quantity as such? I doubt it. Relations between quantity and quality - maybe. But first of all, philosophy is oriented toward epistemology, not ontology. Relations between object and subject, not object itself. Boris Tsirelson (talk) 04:46, 30 August 2018 (UTC)

But, on the other hand, the elusive boundary between mathematics and non-mathematics can be roughly approximated by object and method (togeteher); the approximation by object only is too bad anyway. Boris Tsirelson (talk) 05:07, 30 August 2018 (UTC)

Second try: Mathematics provides unified theoretical description, via mathematical models and theorems, for objects of various kinds, in such aspects as quantity, structure, space, change and some others.

"Some others" include, for instance, connectivity (treated by graph theory and topology).

I am reluctant to say "Mathematics is unified theoretical description...", since this formulation covers a large part of math, but probably not everything. Boris Tsirelson (talk) 09:17, 30 August 2018 (UTC)

We have a Blind men and an elephant case here. There are even mathematical models of the case using posets or topoi. It may be more fruitful to wait patiently for other suitable topics: "Whereof one cannot speak, thereof one must be silent." It is possible this could take thousands of years to answer. That isn't so long for an encyclopedia. --Ancheta Wis   (talk | contribs) 11:26, 30 August 2018 (UTC) There is even an English word for this situation, waiting for our biases toward our personal subjects of study [quantity, structure, space etc] to be mathematized: partiality. There could even be a metric: weakness! 11:51, 30 August 2018 (UTC)

Let me mention here that the formulation "quantity, structure, space, and change" was arrived at after thousands of words of discussion, is a compromise between two strongly conflicting points of view, was accepted to avoid an endless "revert" war, and was not thought by either side to be ideal. However, it is now incorporated in many Wikipedia articles, and any change here would require changes in all of those other articles. Rick Norwood (talk) 11:58, 30 August 2018 (UTC)

@Inowen: As Trovatore has witten above, the lack of an attempt to give a precise definition in the lede is intentional. Please see the section "Definitions of mathematics", in particular the first paragraph:

Mathematics has no generally accepted definition. Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science. A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. Some just say, "Mathematics is what mathematicians do."

References

Paul August ☎ 14:02, 30 August 2018 (UTC)

This is NO blindness:

The opening sentence ... is weak. It does not say ... what math is. It does not ... state what math "includes" exclusively, such that math does NOT overlap with philosophy, engineering, and physics.

transcribed by Purgy (talk)

This rather reminds of Palmstrom's

• For, he reasons pointedly
  That which must not, can not be.
  • „Die unmögliche Tatsache” “The Impossible Fact” (1910)}} by Ch. Morgenstern

The expenditures brought forward by R. Norwood compared to the perceivable improvements via other suggestions makes me suggest to close this case for the time being. Purgy (talk) 14:23, 30 August 2018 (UTC)

Perhaps the second sentence in the lede could be: "A global definition of mathematics remains elusive, although partial definitions abound." or just restore the "no generally accepted definition" as it was. --Ancheta Wis   (talk | contribs) 16:04, 30 August 2018 (UTC)

mathematical reasoning

Be careful. This article in mathematica [5] states there is only three. — Preceding unsigned comment added by 159.100.67.82 (talk) 09:57, 25 August 2018 (UTC)

I tried translating the citation, but the text is unicode. How about resubmitting in plain text? --Ancheta Wis   (talk | contribs) 16:02, 25 August 2018 (UTC)

"Simplicity, conciseness, and clarity" —(Paul Hudak (2000),The Haskell School of Expression Cambridge Univ Press) are hallmarks of mathematical thinking. Perhaps they might become an influence in the article? --Ancheta Wis   (talk | contribs) 12:55, 31 August 2018 (UTC)

Science of number transformation

The Aristotilian definition is important, and even though it has been said above, presumably paraphrasing others, it has not been and cannot have been truly replaced as it has lasted for so long 'up until the 18th century.' Let's look at it: "Mathematics is the science of quantity." The term "science" is accurate; its sophistication and importance rises to a level of being a science unto itself. The word "quantity" is often transformed to "numbers," as "number" simply means the 'symbolic notation of quantity.' I suggested in my draft section above that 'math is the science of numbers and number transformation' (the "..numbers and.." part can be dropped) which I suggest is close to Aristotles, with only the modern update of referencing numbers instead of quantity, and getting to the point that math is really number transformation, and all other ideas of math start there. -Inowen (nlfte) 00:11, 12 September 2018 (UTC)

Please see Wikipedia:Identifying reliable sources. Mgnbar (talk) 01:20, 12 September 2018 (UTC)

Your contribution resembles Rewriting systems, but that article does not claim all the objects of mathematics. --Ancheta Wis   (talk | contribs) 19:12, 23 September 2018 (UTC)

Philosophy loop

Mathematics no longer leads into Philosophy, breaking my favorite Wikipedia game of all time. It makes reasonable sence for math to lead to philosophy, but it no longer does. Thoughts?Calumapplepie (talk) 22:28, 24 March 2018 (UTC)

Restructuring a page so it “leads to philosophy” does not benefit the encyclopedia, and is considered disruptive. Please don’t. Just plain Bill (talk) 23:04, 24 March 2018 (UTC)

No need to restructure; just follow the citations. --Ancheta Wis   (talk | contribs) 09:05, 25 March 2018 (UTC)

What? Shenanigans such as rearranging the text of an article to move wikilinks around, or adding internal links whose only purpose is to further some meta-topology game, amount to a terrible idea, as noted below. Just plain Bill (talk) 12:55, 25 March 2018 (UTC)

This is a terrible idea. The philosophy loop was interesting when it occurred naturally. To force it makes it just boring. Rick Norwood (talk) 11:37, 25 March 2018 (UTC)

Indeed. Paul August ☎ 19:19, 25 March 2018 (UTC)

I personally think some people don't like the idea of mathematics being "under" something and have "forced it" away from reaching philosophy. The first sentence is written incorrectly in order to get mathematics away from feeding to philosophy. The manual of style states, "The first sentence should tell the nonspecialist reader what, or who, the subject is. It should be in plain English," however the first sentence of this article gives a list of examples. It should be changed for THAT reason. I suggest either a mathematician construct a better first sentence or use something akin to the Webster's definition, " Mathematics is the science of numbers and their operations (see OPERATION sense 5), interrelations, combinations, generalizations, and abstractions and of space (see SPACE entry 1 sense 7) configurations and their structure, measurement, transformations, and generalizations." At this point science should be the first link and it does NOT lead to philosophy currently as it gets stuck in a loop in the reality article. Nevertheless the current first sentence is poor according to the style manual.167.88.240.5 (talk) 15:36, 23 October 2018 (UTC)

The opening sentence has been discussed over and over again in very fine detail, and changes to it should be made with caution. In the case of your suggestions, there are two big problems. First, it is controversial to say that mathematics is a "science". This issue is discussed more fully in the article. Second, mathematics is not exclusively about numbers. This point has been discussed recently on this page. --Trovatore (talk) 18:02, 23 October 2018 (UTC)

Adding pattern, and structure

Here is a citation for mathematical structure: Corry, Leo. Synthese Vol. 92, No. 3 pp. 315-348 (September 1992) "Nicolas Bourbaki and the Concept of Mathematical Structure" --Ancheta Wis   (talk | contribs) 23:05, 25 October 2018 (UTC)

References

Highlighting the notion of pattern

I had tweaked the first sentence of the lead to include pattern among the topics of study included within math. But Paul August has reverted my edits with the request that I "please discuss, and gain consensus, for these proposed changes. In particular note that the rest of the article uses the 'quantity, structure, space, and change' description."

(First a quick bit of meta. I did ponder whether to query here on the talk page before proceeding, but in the end I judged that the overriding consideration was WP:BB. So I have a question, addressed mostly to Paul August: Is it your sense that prior consensus would have been preferable? EndMeta:ResumeSubstance)

As for me, I subscribe to the perspective that pattern is the single broadest characterization of the objects of mathematical investigation. For instance, in math even quantity is not really what we study, but rather such things as the properties that quantities may possess and the relationships among quantities. We search out regularities and irregularities. All of this is pattern.

I do also subscribe to the concern to maintain consistency between the lead and the rest of the article, so if there is consensus that pattern should indeed be added, I'd be happy to do a scrub to address that.

Thoughts?

—PaulTanenbaum (talk) 14:49, 26 October 2018 (UTC)

As to your "meta" question, directed at me, about "prior discussion" the short answer is yes. The first sentence is the result of literally thousands of words of discussion, among dozens of serious editors, many of them professional mathematicians (You're welcome to have a look through the talk page archives) hence the comment at the end of the first sentence: "Please do NOT change the opening sentence without discussion; much time and discussion have been invested in its current form." Paul August ☎ 15:57, 26 October 2018 (UTC)

@PaulTanenbaum There seems to be a hidden sense within mathematicians (This is going to be controversial.): which is that mathematicians can detect and explicate pattern, and structure, which is "invisible" to others. Amid the subtleties, which are currently restricted to the topics in the lede sentence, are hidden away patterns, etc., which are also topics of study by mathematicians. If this seems vague, please see, for example motivic of Vladimir Voevodsky. It's a practical question: there are currently computerized proof assistants which get overwhelmed by memory leaks that human mathematicians skip right past. It is also clear that we are waiting for someone to ask the right question. --Ancheta Wis   (talk | contribs) 16:33, 26 October 2018 (UTC)

To corroborate what Paul August said: Being bold is usually good for Wikipedia, but on highly contentious articles being conservative is more productive. The hidden comment in the lede is a sign that this article is contentious. This article continually attracts new editors who make massive changes, with good intentions but harmful results. So please take it slowly, with lots of support from reliable sources.

Which isn't to say that the article can't be improved or that pattern shouldn't be prominent. :) Mgnbar (talk) 16:49, 26 October 2018 (UTC)

See-also to science tourism

@Drbogdan: regarding this edit. There aren't any exact criteria for what makes a good "see also", but could you explain your reasoning on this one? Why is this more appropriate to show in this section than just any random science-related article? (Just on the "tourism" aspect, it occurs to me that I'd be more interested in a link to Museum of Mathematics, but on that one I should point out that I know the founder, so I shouldn't be the one to add it.) --Trovatore (talk) 22:35, 12 November 2018 (UTC)

@Trovatore: Thank you for your comments - and observations - this very recently created "Science tourism" article seems relevant to the science(s) (and mathematics?) in general - for my part, "Museum of Mathematics" seems relevant to the article I would think - nevertheless - it's *entirely* ok with me to rv/rm/mv/ce the edit of course - hope this helps in some way - in any case - Enjoy! :) Drbogdan (talk) 22:49, 12 November 2018 (UTC)

BRIEF Followup - seems "Museum of Mathematics" has already been added to the "Science tourism" article, as "National Museum of Mathematics" - iac - Enjoy! :) Drbogdan (talk) 22:55, 12 November 2018 (UTC)

Given the comments above, I do not understand Drbogdan removing the link to science tourism from the article. It seems to me a useful link. User:Rick Norwood (talk) 12:42, 13 November 2018 (UTC)

@Rick Norwood, Paul August, and Trovatore: Yes - agree - also - to be clear - another editor, not me, removed the "Science tourism" wikilink from the article - restoring the link is *entirely* ok with me of course - iac - Enjoy! :) Drbogdan (talk) 14:46, 13 November 2018 (UTC)

Well, I was the one who removed the "See also" entry for science tourism (without having seen this discussion), since it didn't seem to me to be particularly appropriate. Paul August ☎ 14:52, 13 November 2018 (UTC)

And now I see that Rick Norwood has restored the entry. I don't care that much, and Trovatore of course can speak for himself, but I read his comment above as mildly disapproving. Paul August ☎ 15:49, 13 November 2018 (UTC)

He did it with edit summary "restore the link to mathematical tourism"; but no, the link is to "Science tourism"! Why? The link to "National Museum of Mathematics" is relevant; that article does not link to "Science tourism". As for me, this is woeful violation of a natural monotonicity; clearly, "Science tourism" is much closer to "National Museum of Mathematics" than to "Mathematics". It is quite enough if a short chain of links lead from here to "Science tourism", and further, to "Tourism" (but for now "Science tourism" does not link "Tourism", why?). Boris Tsirelson (talk) 18:06, 13 November 2018 (UTC)

Ah, I hadn't looked at the edit summary, so maybe there is some confusion involved here? Perhaps Rick will tell us. Paul August ☎ 18:29, 13 November 2018 (UTC)

The technical name is "a mistake". I meant to type "science tourism". Rick Norwood (talk) 13:06, 14 November 2018 (UTC)

Ok:-) Paul August ☎ 14:35, 14 November 2018 (UTC)

As Paul correctly understood, I do not think the link to science tourism makes sense as a see-also from this article. It might make sense as a see-also, or even a direct link, from Museum of Mathematics.
As I say, there aren't any exact rules as far as I know, and I don't even know how there could be. See-also is a bit of an odd bird. If something is very related to the topic of the article, then it will be linked from the article itself, and if it's not related at all, then why mention it? So it's inherently for things that are in some sort of in-between state.
Still, in this case I think the link is just too tenuous. --Trovatore (talk) 16:04, 14 November 2018 (UTC)

I'm surprised that such a minor matter has caused so much controversy. The link will take interested people to information about museums of science and mathematics, and to museums of just mathematics. What's so bad about that? Rick Norwood (talk) 13:11, 15 November 2018 (UTC)

I agree that whether the link stays or goes is a minor matter. What is a less minor matter is the principle involved. That is, what is the best use of the "see also" section? In my view the spirit (if perhaps not the letter) of WP:UNDUE applies here. And since I think there are probably dozens (hundreds?) of more deserving see also-links, including this link without the others gives undue weight to the article "Science tourism", while including all the other, in my view more deserving links, would make the section unusefully large. Another way to to state the question is do we believe that the recently created "science tourism" article (by the way is that really a notable thing?) is one of the nine most important articles we should be linking there? I don't think so. Paul August ☎ 14:00, 15 November 2018 (UTC)

Right. I mean, you could also have a see-also link to dinosaur, if you wanted — there's probably something mathematical to say about dinosaurs, and who can object if readers go learn more about them? People should know more about dinosaurs. But the link just doesn't seem natural.

It's a subjective assessment, of course. I don't think there's any need to prove there's not a more deserving link, just to add a link — then it would be very hard ever to add any links at all. But in my subjective judgment, this one comes up short. --Trovatore (talk) 15:59, 15 November 2018 (UTC)

I also agree that this specific link is a minor matter, but the more general discussion of what should or shouldn't be in a see also section is worthy of consideration. Without strong guidelines (and I am not sure that these would ever exist) editors will produce quite a wide spectrum of possible links, some of which will no doubt be objected to by other editors. My own rule of thumb in these matters is to apply WP:SURPRISE and possibly WP:EASTER. Viewing the section as providing links to articles that either elaborate on or introduce material central to the topic of the article but not sufficiently dealt with in the article, if I have to delve fairly far into the link to see a connection, I don't consider it a good link. In the present case, I agree with Paul and Trovatore that this link is too tenuous and also redundant since we already link to MoMath. --Bill Cherowitzo (talk) 19:05, 15 November 2018 (UTC)

The length this thread has arrived now at, lets me ask how many tourists are assumed to exist as travelling within a year for a "math as science" touristic endeavor (not counting congresses with ladies activities)? I support the skeptics on including the link "science tourism" with "see also" of "Mathematics". Purgy (talk) 19:38, 15 November 2018 (UTC)

I don't have exact numbers, but here is one number: MoMath's traveling Math Midway exhibit alone attracted 750,000 visitors, so I think the answer would be in the millions for everyone interested in finding a math museum. How many go to Wikipedia to find a math museum? My guess is, all of them. :) Rick Norwood (talk) 12:41, 16 November 2018 (UTC) And, yes, the article "Science Tourism" does mention MoMath. It comes up first when I google Math Museum. On the other hand, when I search Wikipedia for "Math Museum" is asks me "Do you mean "Match Museum". (Below that it does suggest MoMath.)Rick Norwood (talk) 12:46, 16 November 2018 (UTC)

I don't really understand how these remarks are supposed to bear on whether we should have a see-also to science tourism in this article. --Trovatore (talk) 22:03, 16 November 2018 (UTC)

I think it's a response to Purgy Purgatorio's post immediately before it, which appears to ask how many math tourists there are. Mgnbar (talk) 02:21, 17 November 2018 (UTC)

Ah, good catch. Standard indenting would have made that clearer. In any case, do we have a rough consensus that the link should not appear in see-also? --Trovatore (talk) 03:06, 17 November 2018 (UTC)

To make both my question and my intention more obvious: I want to know about the fraction of "math tourists" within the "science tourism", and I object to include the link "Science Tourism" within the article "Mathematics". Yes, I do expect this fraction to be rather small, compared to "soft sciences" interest (architecture, history, archeology, languages, sociology, religion, nutrition, ...) Purgy (talk) 08:25, 17 November 2018 (UTC)

I vote against the link to "science tourism", given that we have already the much more relavant link to "National Museum of Mathematics". The link to "science tourism" should be moved thereto. Boris Tsirelson (talk) 08:33, 17 November 2018 (UTC)

Re-word to avoid Eurocentricism: "Rigorous arguments first appeared in Greek mathematics..."

The phrase "Rigorous arguments first appeared in Greek mathematics..." begining the 3rd paragraph strikes me as Eurocentric. We could dicuss the importance of the Greeks without implying that they were the first to think rigorously, perhaps with this phrasing: "Greek mathematics, most notably Euclid's Elements, are the oldest surviving written rigorous arguments." Thoughts? — Carl (Seaplant (talk) 06:17, 28 November 2018 (UTC))

Haven't you been warned beforehand that WP might contain more or less precise spacetime coordinates about specific events? Bad luck that there might be evidence for some notable events being –horribile dictu!– eurocentric. Maybe you could have a look at centroid for calculating coordinates of (including spatial) centers. Purgy (talk) 07:24, 28 November 2018 (UTC)

I'm not concerned by Greece or Euclid being located in Europe! Eurocentrism isn't a geographic or spatial concern at all, but an ideological one. "Greece" is a fine way to describe the centroid of the locations of the early Greek mathematicians, but not (as the current sentence seems to imply) the centroid of the locations of the only mathematicians to begin to make rigorous arguments. The current sentence discounts the many cultures that developed rigorous thinking without any influence from the Greeks. — Carl (Seaplant (talk) 08:02, 28 November 2018 (UTC))

I think the change is fine. Alternative, (since I don't like covering up the logic): "Greek mathematics contain the oldest written logical arguments, notably Euclid's Elements Crazynas ^t 08:53, 28 November 2018 (UTC)

Such assertions need sources. Paul August ☎ 12:03, 28 November 2018 (UTC)

I think "first appeared" implies "first appeared in writing". Of course people everywhere can think logically, but we have no records of thoughts. Only writing (and other artifacts) "appear". If, however, you do make the change suggested by Crazynas, be sure to write "Greek mathematics contains ... ." since "Greek mathematics" is a collective singular noun. Rick Norwood (talk) 12:48, 28 November 2018 (UTC)

I won't be editing the article soon, but I have it on my watchlist and plan to work on it someday (finally cutting my teeth on a Level-1 article). I just wanted to chime in because I think Seaplant makes a good point, and especially to second Crazynas. I personally don't think there's any problem singling out Euclid with the catch that the sentence should be very clear that "rigor" here means "logic".

My main reasoning is that there's a not-half-bad argument that ancient Chinese mathematics reached a similar level of sophistication around the same time. What's tricky is the surviving Chinese sources do sometimes discuss in detail why the math works, but rather than deductive logic, they rely on something more akin to constructivism, arguing from demonstration and commentary that techniques are comprehensive. It's also not always clear when the detailed arguments were added in as commentary either.

If anyone with access to a good library wanted to perform due diligence, you could probably get pretty far with any of the following sources:

• Volume 3 from Joseph Needham's Science and Civilisation in China
• The section on China from Carl Boyer's history
• A translation with in-depth commentary for The Nine Chapters on the Mathematical Art
• Any recent monograph on reconstructing the technical sections of the Mozi

I personally wouldn't try debating what does or doesn't qualify as rigor though; on top of arguing over eurocentrism and Chinese revisionism, you might wind up with a constructivist vs. traditionalist knifefight on your hands. That said, I think the article's history section does have a China-shaped lacuna in it, not a big one, just a sentence or two in the ancient paragraph and maybe another to fill out the medieval paragraphs.

I've done a little research into history of math for projects IRL, nothing professional-grade though (so my reading is still limited). But if anyone is interested, I have a few more thoughts on gaps in the history section (or if you're willing to wait a few months/years, I'll eventually try them out in my own edits). Zar2gar1 (talk) 23:12, 28 November 2018 (UTC)

I didn't know that about Chinese mathematics! It would be great to see that added in at some point. — Carl (Seaplant (talk) 02:41, 29 November 2018 (UTC))

Paul August, in rephrasing this sentence I wasn't trying to claim anything more than the current sentence (less, actually), but I agree that it's useful to look at the source material. As I see it, this sentence is summarizing this from the History section: "Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. [Source: Heath] Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof. [Source: Boyer]" This is in contrast to the "practical mathematics" described in the previous sentence of the lede, and specifically is referring to deduction, as described in History of Mathematics#Greek: "All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them. [Source: Bernal]" Maybe it would be truest to these sources to phrase the sentence like "Greek mathematics, notably Euclid's Elements, contains the oldest surviving deductive arguments developing the subject in its own right." We could add refferences Heath and Bernal. — Carl (Seaplant (talk) 02:41, 29 November 2018 (UTC))

I'm afraid this is all a bit beyond my ken;-) However, I think the move away from "Rigorous arguments" toward "deductive reasoning" is probably good. And a qualification something like "in its own right" is probably needed. As for whether the sources provided are adequate, I don't know. Digging in a bit, here is what I see:

The sentence sourced to Heath: "Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics."

I've spent some time looking in my copy of Heath, but I can't find where he says anything like this, page numbers anyone?

The following two sentences: "Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof. His textbook Elements is widely considered the most successful and influential textbook of all time."

Here's what Boyer says on page 119: "The Elements of Euclid not only was the earliest major Greek mathematical work to come down to us, but the most influential textbook of all time. It was composed in about 300 B.C. and was copied and recopied after that." So Unfortunately, no mention of the axiomatic method, but I suppose, since this is certainly the common wisdom, this is ok?

The sentence (from History of mathematics) sourced to Bernal: "All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them."

I don't have ready access to Shank's book, but looking at Bernal article originally published in Isis, Vol. 83, No. 4 (Dec., 1992), pp. 596-60 (JSTOR 234260), I have yet to be able to find support for this assertion. Again page numbers anyone?

Paul August ☎ 13:59, 29 November 2018 (UTC)

References

International Mathematical Olympiad

I inserted the below sentence in "Awards" section. It was reverted and I and was instructed to discuss in talk page:

The International Mathematical Olympiad is one of the most prestigious mathematical competitions in the world. It is an annual mathematical olympiad for pre-college students, and is the oldest of the International Science Olympiads.

I would like to understand why this statement is inappropriate. Arman ^(Talk) 10:55, 8 January 2019 (UTC)

References

It doesn't fit under the "Awards" header for one thing; as Purgy noted, IMO is a competition, not an award like the Fields Medal or the Abel Prize. Lord Bolingbroke (talk) 17:16, 8 January 2019 (UTC)

Among other arguments, specifically it has been mentioned that the IMO is not an award that can be mentioned in a reasonable manner together with the awarding of the Fields medal or the Abel prize, and that, as an undergraduate, pre-college competition, it has no adequate place in an article "overviewing the entirety of mathematics", and that the details of "how many observers go with each IMO team, or the % of world population and so on" do not fit here.

I wholeheartedly support these opinions, and I expect that there exist rules in WP which support this, even when taking IMO's age, its repetitiveness and "prestigiousness" in account. Purgy (talk) 09:03, 9 January 2019 (UTC)

Semi-protected edit request on 4 February 2019

Could you merge the last two sentences of the introduction? "application in mind, but practical applications" 208.95.51.53 (talk) 13:21, 4 February 2019 (UTC)

On an unrelated note, could you remove Encyclopedia of Mathematics from the external links? It's a link to a Wikipedia article, so it should be put into the see-also section, or it should be removed entirely. 208.95.51.53 (talk) 13:25, 4 February 2019 (UTC)

I do not see any advantage in combining the two sentences, but I have fixed the link to the Springer Encyclopedia of Mathematics. Rick Norwood (talk) 15:48, 4 February 2019 (UTC)

 Done, along with a little wording tweaking to make it read a little easier still. –Deacon Vorbis (carbon • videos) 17:39, 7 February 2019 (UTC)

Nomination of Portal:Areas of mathematics for deletion

A discussion is taking place as to whether Portal:Areas of mathematics is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The page will be discussed at Wikipedia:Miscellany for deletion/Portal:Areas of mathematics until a consensus is reached, and anyone is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines.

Users may edit the page during the discussion, including to improve the page to address concerns raised in the discussion. However, do not remove the deletion notice from the top of the page. North America¹⁰⁰⁰ 12:38, 26 March 2019 (UTC)

Why was the external links section removed?

On 7 February 2019, User:Deacon_Vorbis removed the external links section, justifying his edits by saying "None of this is really what external link sections are for." I have conformed with WP:NOTLINK, there was no good reason to remove the external links. I am new to editing Wikipedia, so there might be something I'm missing out, but as far as I can conclude, the external links section should be brought back. Is that right? Ambuj Shukla 15:50, 5 May 2019 (UTC)

The external link section deserves to be brought back only if there are external links that pass WP:ELNO and are useful for the article. If you think that some of the removed links belongs to this category, list them and explain why do you think that they must be added again. So we could discuss whether there is WP:consensus for that. If a consensus is reached for some of these links, then they will be added in a section "External links". Otherwise this section is not needed. D.Lazard (talk) 16:17, 5 May 2019 (UTC)

'Definitions of mathematics': section's repeated line.

In the first paragraph, the sentence "Benjamin Peirce (1809–1880) called mathematics "the science that draws necessary conclusions".[33]" is almost identical to the fourth paragraph's "An early definition of mathematics in terms of logic was Benjamin Peirce's "the science that draws necessary conclusions" (1870).[38]" I suggest keeping the second instance of the sentence because it contains a better reference and it is more vital to the paragraph. Pabsoluterince (talk) 04:41, 17 May 2019 (UTC)

@Pabsoluterince: I've gone ahead and removed the first because the context doesn't really require it to be there. the reference is incase anyone would use it in the future. (Oops i forgot to sign myself) --NikkeKatski [Elite] (talk) 15:11, 17 May 2019 (UTC)

References

No mention of realism?

Prompted by my response in the previous section, I searched the article to see how the term "intuitionism" was used h:ere, to see if it needed work, and I came across this sentence:

Three leading types of definition of mathematics are called logicist, intuitionist, and formalist, each reflecting a different philosophical school of thought.[37] All have severe problems, none has widespread acceptance, and no reconciliation seems possible.[37]

Now, what jumps out at me here is that realism (Platonism) is not mentioned some people seem to think that logicism is a form of realism, but this makes no sense to me. In fact the word "realism" does not appear in the article at all, and "Platonism" shows up only in the external links.
I have to say this seems like a flaw. I'm not sure the right place to mention realism (or indeed the other schools) is in a sentence about definitions, but it's pretty weird not to mention it at all. Ideas for improvement solicited. --Trovatore (talk) 00:47, 16 December 2018 (UTC)

See the book 18 Unconventional Essays on the Nature of Mathematics and chapter one deals with platonism (and I think it makes the argument that if its accessible to intuition, it must therefore be platonic). Chapter two claims that math is an oral tradition passed from professor to student. After that things spiral out of control. Now, I'm not sure if it's just me, or if others feel this way, but whenever I read "Popper says XYZ", I always manage to think "wow, this Popper guy sure is wrong." Should I be mildly miffed, or is there a cult of Popper, or am I just a jerk? OK, the latter, but what's in the kool-aid? 67.198.37.17 (talk) 04:29, 13 January 2019 (UTC)

The book is available here. Boris Tsirelson (talk) 05:50, 13 January 2019 (UTC)

I understand mathematical realism as a philosophical theory about mathematics, not a definition, i.e. not an attempt to distinguish mathematics from everything else. I do think that the realist/fictionalist controversy merits a mention. We have a section titled "Foundations and philosophy", which currently contains no philosophy. Definitions of mathematics are really part of the philosophy of mathematics—AFAICT, the main part. Perhaps, then, a good place for a quick summary of Platonism, etc. would be the "Definitions" section, perhaps summarizing the literature on how the competing definitions relate to the competing theories of what mathematical propositions correspond to? —Ben Kovitz (talk) 19:43, 9 June 2019 (UTC)

Why isn't there any external links section for this article?

For an article rated B-class, with this level of accuracy, its really not good to see no external links. What's the point of this article for people looking for a serious overview. I've never created an external links section and I have no idea of the guidelines for adding external links, need help with this case. — Preceding unsigned comment added by 106.201.30.102 (talk) 14:03, 5 July 2019 (UTC)

For having an external link section, one must have external links to link. See WP:External links for knowing what could appear (or what must not) in this section. Apparently, the editors of this article (myself included) do not know any relevant external link that passes the criteria given in this guideline. This is the answer that I can give to your question, as it makes no sense to have en empty section. D.Lazard (talk) 15:09, 5 July 2019 (UTC)

Fuzzy beginning of the article

I think this article should start "Mathematics is a scientific method modelling reality to understand and describing reality. This applied from children’s counting of toys to Einstein and quant physics. There are differences if the math is a part of the reality itself, due to strong correlations or an invented scientific language to describe the world. Mathematics is used in most sciences as tools in understanding and describing the reality."

--Zzalpha (talk) 17:43, 9 June 2019 (UTC)

That would count as application of mathematics, but not as creation of new mathematics by its practitioners, unfortunately. --Ancheta Wis   (talk | contribs) 17:49, 9 June 2019 (UTC)

This is a possible definition of mathematics, although very few living mathematicians would agree with it. Even among mathematicians and philosophers, there is no consensus for a definition of mathematics. Therefore, per WP:NPOV, every definition that is given in Wikipedia must be attributed to a recognized author. This is not the case for the definition the you propose.

By the way the relationship between modern mathematics and physical reality is not understood, even by the best mathematicians and philosophers. As a witness of this, I know of a well known mathematician who was strongly antimilitarist, and said that his choice of research field (modular functions) was motivated because the results that can be obtained in this area cannot be used for military purpose. Alas, a few years, applications to high energy physics were found, and the subject became useful for military purpose. Such unexpected applications of mathematics are rather common. So, the relationship between mathematics and reality cannot be described in a single sentence. Moreover, as it is an open philosophical problem, Wikipedia is not the place for trying to solve it. 18:22, 9 June 2019 (UTC) — Preceding unsigned comment added by D.Lazard (talk • contribs)

Zzalpha, please look over the literature on philosophy of mathematics, applied mathematics, and/or definitions of mathematics. You can probably find a better formulation than what we have. Please keep in mind that on Wikipedia we only summarize the literature (and provide sources); Wikipedia is not a place to publish original thought. —Ben Kovitz (talk) 20:03, 9 June 2019 (UTC)

1. The first sentence of any article should state what the subject of the article is, not what it does.

2. The idea that math has no agreed upon definition appears to be an original assertion.

Derwos (talk) 11:58, 9 August 2019 (UTC)

Your two objections correspond to the two sentences of the opening paragraph. Your second objection is handled by the references at the end of the second sentence. Then, the fact that there is no agreed-upon definition explains why the first sentence is written how it is.

If you wish to improve this part of the article, then please propose new text here, on this talk page, with Wikipedia:Reliable sources supporting your text. Mgnbar (talk) 12:14, 9 August 2019 (UTC)

Mathematics has no generally accepted definition?

This is false. Mathematics is the science of number and number is the measure of a quantity.

This entry is laughable. You don't get to redefine the meaning of mathematics. Of course we all know that Wikipedia is the world view according to the morons who run this site, but spreading misinformation will eventually backfire on you!

65.127.45.210 (talk) 13:22, 6 November 2019 (UTC)

Straightedge and compass construction has no need of numbers. Just plain Bill (talk) 14:35, 6 November 2019 (UTC)

The claim that mathematics has no generally accepted definition is supported by two sources. Additional sources are cited, that give conflicting definitions, further bolstering this claim. Your claim, that it has a generally accepted definition, is not supported by any sources yet. In fact, this objection has been raised repeatedly on this talk page, but I have never seen the objector actually follow through on supporting her/his claim. Mgnbar (talk) 15:04, 6 November 2019 (UTC)

Templates

The addition of the {{Algebra}} template was reverted, which makes sense considering how many other major mathematics templates exist. How about choosing a dozen or so of the major templates and displaying them in a navbox cage similar to the 'Founding Fathers and their related articles' navbox cage template at United States Founding Fathers. Just the common math topics that general audiences would recognize (Algebra, Geometry, etc.) would then cover many of the topics readers would be searching. Randy Kryn (talk) 13:53, 9 January 2020 (UTC)

Modern Mathematics

Hi! I am asking a question for a class assignment. Should more modern mathematics be added to the article? Some schools use Common Core and while that might not be great for the kids, it is a development in math. --Vadams1996 (talk) 00:31, 27 January 2020 (UTC)

Your question seems to be about mathematics education, whereas this article is focused on mathematics research (for reasons that are admittedly not clear). You might try at that other article's talk page. However, be aware that Wikipedia talk pages exist to improve articles, not to serve as general forums for discussing topics. Best wishes. Mgnbar (talk) 01:58, 27 January 2020 (UTC)

New lead

I have rewritten the lead. My main motivation was that, as a mathematician, I do not recognize mathematics in the description of the preceding lead. Here are more details on the motivations of my edits.

For the first paragraph, I have added the fact that the object of study of mathematics is abstract. As this can be taken as a definition of mathematics, I have modified th elast sentence of the paragraph into "It has no generally accepted precise definition, and its status as a science is sometimes disputed." The fact that, presently, mathematics is considerd almost universally as a science must appear here. A witness of this is the fact that all science funding agencies, such as National Science Foundation, include mathematics into their funding areas.

For the second paragraph, I have removed the dubious considerations on the psycology of mathematicians, and the reference to patterns, as these are rarely encountered in mathematical texts. I have replaced them by fundamental term such as theorem, proof, mathematical problem, that are, in some way the essence of mathematics, and are encountered everywhere in mathematics.

For the remainder of the lead, the changes are relatively minor, and consist mainly in a more accurate presentation, and changing some dubious assertions such as "Applied mathematics led to entierely new fields of mathematics". D.Lazard (talk) 16:59, 31 January 2020 (UTC)

Here is a diff of the proposed lead --Ancheta Wis   (talk | contribs) 11:25, 1 February 2020 (UTC)

D.Lazard, while I really would have preferred that you had proposed the changes on the talk page first, I'm not unalterably opposed to all of them. But I think we should go back to the stable version while we discuss it, in the spirit of WP:BRD, and I have accordingly reverted.

I agree that mathematics studies abstract objects and structures. I am concerned that your first sentence implies that all study of abstract objects and structures is mathematics, which I don't think is the case.

More problematic is the claim that mathematical truth can be established only by deduction and proof. This seems to me to be biased towards Euclidean foundationalism (and even, to some extent, formalism).

So very very much effort has been spent on the first sentence of this article. I am not enthusiastic to re-litigate it. But I think any major changes to it need to be very carefully discussed, as little as I really want to do that. --Trovatore (talk) 17:20, 31 January 2020 (UTC)

In my experience, the claim that "mathematics is considerd [sic] almost universally as a science" is wrong. For a tiny example, the acronym is STEM rather than STE. Inconsistency and disagreement really do exist. Mgnbar (talk) 19:50, 31 January 2020 (UTC)

I also do not consider mathematics a science. The sciences are (at least mostly) about the behavior of the physical universe. Mathematics is about principles that can be proved in the absence of physical experiment.—Anita5192 (talk) 21:48, 31 January 2020 (UTC)

I think we might be rabbitholing on that a little. D.Lazard's recent changes had only one reference to "science", and it was in the short description, which most people don't see anyway. If we're concerned about the word "science", I think a higher priority would be the hatnote (which, as an aside, should not mention the abbreviation "math". Neither "math" nor "maths" should appear in this article at all, not even once. Burn them and then burn the ashes. But that's not important right now).

I would like to see more discussion of the points that D actually changed, in visible text. --Trovatore (talk) 03:47, 1 February 2020 (UTC)

I agree with the revert back to the stable version while we discuss things here. With Trovatore, I would also emphasize the considerable amount of work, the many many long and careful discussions and compromises, by dozens of mathematicians and others, that have gone into crafting the current lede. It should be changed only with great care, and with the appropriate considertion of past discussions. Paul August ☎ 15:14, 1 February 2020 (UTC)

There are so many issues in the stable lead, that the discussion must be divided in several topics. So, I'll open several subsection for separate the different points, beginning by thoses of first paragraph. D.Lazard (talk) 18:19, 1 February 2020 (UTC)

"Accepted definition"

The stable version asserts: "It has no generally accepted definition". This is true for intensional definition, but clearly as written, as the Mathematics Subject Classification is an extensional definition that results from a consensus elaborated by all mathematical societies around the world. I do not know any reliable source that disputes this extensional definition. This is the reason for which I have replaced "generally accepted definition" by "generally accepted precise definition". Clearly, "extensional" would be more accurate than "precise", but it is too technical here.

The formulation can certainly be further improved, but the sentence of the stable version is clearly misleading. D.Lazard (talk) 18:19, 1 February 2020 (UTC)

I think adding "precise" here is fine. --Trovatore (talk) 19:32, 1 February 2020 (UTC)

@D.Lazard: I think the distinction you are making here is correct, but I'm not sure it's needed. The same reader for whom the intensional/extensional distinction is too technical will also likely wonder how a "precise definition" differs from a "definition". (By the way in the last sentence I think you meant to say "intensional".) Paul August ☎ 19:55, 3 February 2020 (UTC)

Short description

There's a current minor conflict over whether to include the word "science" in the article's short description. I agree that the use of "science" in the short description is problematic, given that it's controversial whether math is a science. (I generally would call it a science, but I can see the other point of view, and I think that if anything it's more common to consider it something distinct from science sensu stricto.)

But I think we can trim it even further, or perhaps remove it entirely, and that this would be still better. Participants should first understand what short descriptions are for, in the first place.

At Wikipedia:Short description#Content, we find

• The short description may be used for several purposes, including as a disambiguator in searches and as an annotation in outline articles.
• The short description should be as brief as possible. A target of 40 characters has been suggested, but this can be exceeded when necessary.
• The short description should focus on distinguishing the subject from similar ones rather than precisely defining it.

[end of quoted text]

The canonical use case is to give a user of the mobile app enough information to decide whether to click on a link, by distinguishing it from other articles that might come up in the same search. I think, for that purpose at least, there is no huge value in having a short description for this article at all. Almost all users are going to know the word "mathematics". I suppose there's a chance that someone might have been looking for Mathematics (producer). To help such a user, a short description just saying Field of study seems perfectly adequate. There are other uses, such as annotated links, but I don't think an elaborate short description is going to be very helpful for those purposes either.

So I propose to change the short description to {{short description|Field of study}} or possibly even the empty {{short description}} (an empty short-description template is recommended when there is no useful short description for an article). --Trovatore (talk) 23:24, 17 February 2020 (UTC)

"Field of study" works for me. Paul August ☎ 00:09, 18 February 2020 (UTC)

"Field of study" works for me, too. I agree with Trovatore. Even though mathematics is difficult to define, most people at least have an intuitive understanding of what it is and do not need a short description. If necessary we can attach a comment to the short description to alert future editors in case they feel that "Field of study" or an empty description are not adequate.—Anita5192 (talk) 00:53, 18 February 2020 (UTC)

Request for simple language

Hi, May You please add some of the more complicated words You know dumbed down in parentheses fo me and others I'm on the younger end Please and Thank You So Much !!!! ✖️➗➖➕ 69.124.24.51 (talk) 04:32, 22 February 2020 (UTC)

Hi 69.124.24.51. I've taken the liberty of removing the template you used, which is supposed to be for when you know exactly what change you want to see, but you can't do it yourself because the article is protected. Could you be a little more specific about where the article is giving you trouble? --Trovatore (talk) 04:50, 22 February 2020 (UTC)

Hello! Could we have more beginner facts and detail.

Hello! Could we have more beginner facts and detail, such as maybe having a section of of math that talks about normal mathematics with detail and spelling that more people on the younger side reading Wikipedia can read sorta easily? Just asking because I’m on the younger side and me and my friends do use Wikipedia a lot and sometimes don’t get what Wikipedia is saying!

To be a bit more clear, I’m on the younger side and sometimes Wikipedia uses more bigger words that when I read the definition I still don’t know what there talking about. Thank you so much! 😊 — Preceding unsigned comment added by 24.14.6.51 (talk • contribs)

You might wish to visit simple:Mathematics. El_C 01:24, 2 March 2020 (UTC)

Removed original synthesis in "math as science" section

The paragraphs detailing how organizations name their departments were entirely inappropriate, bordering on original synthesis. We can't conclude just from the names whether they consider mathematics to be a science or not. The section properly treats what mathematicians, scientists, and philosophers have said about the relationship, when they were considering it explicitly. I have removed those paragraphs. --Trovatore (talk) 17:04, 6 April 2020 (UTC)

Hi Trovatore, I agree with your editions.James343e (talk) 17:23, 6 April 2020 (UTC)

Suggestion; the Philosophy game

Clicking the first main link in any Wikipedia article body, and repeating this for every new article, almost always ends in Philosophy. Try it - it's fun. However, some articles will terminate in a cycle involving Mathematics. Since Mathematics is a branch of Philosophy, it would be apropos if the first link in the Mathematics article were to Philosophy. E.g. "A branch of Philosophy which includes the study of..." — Preceding unsigned comment added by 24.4.91.20 (talk) 08:11, 11 April 2020 (UTC)

Mathematics is not a branch of philosophy! D.Lazard (talk) 08:52, 11 April 2020 (UTC)

And Wikipedia is not a game! Paul August ☎ 11:10, 11 April 2020 (UTC)

Semi-protected edit request on 18 April 2021

2600:100C:B0DE:D1EA:E428:74AE:2064:2EBF (talk) 18:29, 18 April 2021 (UTC)

Math was not invited, it was discovered

What you want is not clear.—Anita5192 (talk) 18:32, 18 April 2021 (UTC)

Semi-protected edit request on 1 May 2021

Maths is rubbish 2A02:C7F:716D:8C00:5C1E:80D2:CD30:1A4A (talk) 13:38, 1 May 2021 (UTC)

Not a request. D.Lazard (talk) 13:55, 1 May 2021 (UTC)

Some miscellaneous

The wellknown series 0+1=1, 0+1+2=3, 0+1+2+3+4=10 and so on has a remarkable fact because there appears this list: 0 1 3 (1x3) 6 (2x3) 10(2x5) 15(3x5) 21(3x7) 28(4x7) 36(4x9) 45(5x9) 55(5x11) 65(6x11) 78(6x13) 91(7x13) ...

1001 can be devided by 7, 11 and 13 and is the least common multiple.

108, 1008, 10008, 100008, 1000008, 10000008 and so on ara all divisible by 12. You get respectively 9, 84, 834, 8334, 83334, 833334 and so on. — Preceding unsigned comment added by 82.170.17.19 (talk) 13:11, 4 May 2021 (UTC)

Semi-protected edit request on 9 September 2020

Rakesh Yadav Math- https://sarkariok.com/rakesh-yadav-7300-maths-book-pdf/ 2409:4063:2384:DC7:A533:CF95:F534:EE53 (talk) 08:31, 9 September 2020 (UTC)

 Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. Cannolis (talk) 08:39, 9 September 2020 (UTC)

Semi-protected edit request on 31 July 2020

i want to put more imortant info — Preceding unsigned comment added by 75.132.49.54 (talk) 00:46, 31 July 2020 (UTC)

Declined. It is not clear what you want.—Anita5192 (talk) 01:02, 31 July 2020 (UTC)

Brainstorming / what does the article need?

Before editing the article in the coming year, I just wanted to ask what everyone thinks it needs most. I've always worked on more focused topics where improvements are relatively clear, but what specifically would move this one closer to FA status? Is there anything that stands out to the veterans in particular?

I've skimmed the article and come up with my own breakdown of possible changes, but that may not line up much with what everyone else agrees is important. I can discuss my proposed changes here first too since I imagine editing needs to be incremental here. Zar2gar1 (talk) 19:19, 8 December 2018 (UTC)

Yes incremental changes, and discussing proposed changes here first, are both very good ideas. Paul August ☎ 19:49, 8 December 2018 (UTC)

If nothing jumps out at anyone, I'll start by bringing up some smaller notes to discuss...

• I really like mentioning Aristotle where the definition section starts, but I wonder if it should convey a little more continuity with what follows. Aristotle definitely focused on quantity & magnitude more than today, but he also commented on how it relied on a sort of abstraction ("separability"): Physics II.2 (done)
• I noticed that the article (rightly, I feel) mentions the cognitive "moves" people use in math throughout (e.g. deduction, counting, etc.). However, synthesis & analysis in the mental/philosophical sense are never really brought up. If that would be a positive change, I don't know what the best way to massage them in would be, but I did a little experiment using find in my browser just to have some data...
  • "synthesi(s/ze)", "assemble", and "combine" never appear in the article at all
  • "build" only appears in historical discussions, never as an intuitive act
  • "construct(ion)" does pop up several times, but only in this sense around the paragraph on intuitionism and maybe the discussion of Gödel's incompleteness theorem
  • "analy(ze/sis)" obviously appears several times as part of subfield names. Otherwise, except for maybe two instances (one in footnote 59 for a source on set theory and the other near the mention of Newton), the word is just used as a synonym for study
  • Other synonyms, like "divide/division", "split", "break down", and "decompose" never appear in this sense either, if it all; the one use of "reduce" near another discussion of Gödel's theorem may be the only exception.
• Finally, without overemphasizing it and biasing the article towards an intuitionist POV, it might be worthwhile to mention the role of intuition and creativity a little more directly. The "Inspiration..." section seems especially fitting for a couple sentences, but perhaps just namedropping & linking one of the words in the lead's second paragraph wouldn't hurt either. Zar2gar1 (talk) 14:23, 15 December 2018 (UTC)

This is a digression, so I'm putting it in small type, but just so you know, you might want to be careful with the word intuitionism, which does not really mean what I think you think it means. The defining feature of intuitionists has little to do with intuition; it has to do with their rejection of excluded middle. The term "intuitionism" for this has a historical basis in Brouwer's personal intuition, but it does not have much to do with whether your foundations are based on intuition. Unfortunately the lead of our intuitionism article is misleading on this point and really ought to be corrected. --Trovatore (talk) 21:52, 15 December 2018 (UTC)

Oh, no worries. I'm aware intuitionist logic is pretty much what people usually mean by the word nowadays. My impression's always been that the different philosophical outlook is still there in the background though, even if nobody obsesses over it like Brouwer did, but I could be mistaken. Since the above changes all touch on more philosophical & mental things, I just wanted to let everyone know I was aware about it and wasn't going to use any edits to make math look like Romantic poetry or something. I really appreciate the feedback though and would be interested on what you think about the changes themselves. Zar2gar1 (talk) 00:45, 16 December 2018 (UTC)

Oh, absolutely, the import is philosophical, not just formal. But the point is that intuitionists are not the only people who place a high value on intuition. For example Gödel (Platonist) proposed that truths about underlying mathematical reality were directly accessible to intuition. --Trovatore (talk) 00:50, 16 December 2018 (UTC)

I like Zar2gar1's suggestion that there be a small section discussing how mathematicians seem to think about how they obtain results. I feel I got good at math only when I learned how to make "cognitive moves", but I never know how to explain that to someone who does not know what it means. However, the terms "synthesize", "build", "construct", "analyze", "divide", "decompose", "split" "reduce" are all far more mechanical -- that is what I do when I'm not particularly inspired or awake ... its necessary but sometimes tedious make-work to split, construct, analyze, synthesize. Without these steps, you can't quite gain the required knowledge, but they're the least-fun part of math .. the "cognitive moves" being the most fun (for me). It seems that suitable articulations are necessarily philosophical, metaphysical, or appeal to psychology, sociology or have MD's place mathematicians into MRI machines. Here is a physics paper that asks: "how can assemblages of atoms (described by equations, taking the form of humans) come up with ideas and communicate them?": "Agent Above, Atom Below: How agents causally emerge from their underlying microphysics" by Erik P Hoel https://fqxi.org/community/forum/topic/2873 67.198.37.17 (talk) 19:43, 18 April 2019 (UTC)

This is a continuation of the preceding discussion. However it has to do with the way of presenting mathematics, and this belongs to the answer to the initial question. So, I do not put it in small characters. What follows is somehow WP:OR, as I have never seen it published in an academic paper. However, it is based on a long career of professional mathematician, and I do not know any mathematician that will fondamentally disagree with me.

The modern mathematical discourse has two parts, an intuitive part (that is called either "intuitive explanation" or "context" in WP articles), and a "formal part". The formal part consists of formal deduction and proofs. If completely developed, it is, in principle, verifiable by a computer. The "intuitive part" of the discourse is the explanation of the relationship between the theory and the physical (or mathematical) experience of the audience. Until the end of the 19th century, the distinction between the two parts was clear only in geometry, where one needs a figure for understand a proof, and a proof is correct if one can verify it without referring to any figure. With the introduction, at the beginning of 20th century, of axiomatic theory, emphasis was given on formal rigor, and the intuitive discourse was often completely discarded. This culminated with Bourbaki's treatises and Dieudonné's presentation of Grothendiek's Éléments de géométrie algébrique. Meanwhile, some mathematicians tryed to develop some purely formal theories, and it appeared (at least to people in charge of evaluating them) that if a theory is developed without the aim of solving specific problems, and without any application outside itself, this theory reduces eventually to trivialities and problems that are impossible to solve. Both parts of the mathematical discourse are essential, and a mathematical theory cannot be really understood without mastering them. Using computer science terminology, one can say that the intuitive discourse it the semantics, and the formal discourse is the syntax.

I know that what precedes is too WP:OR for being included directly in a WP article, but I thing that we must find a way for introducing these ideas in the article. In fact there is a consensus on them between professional mathematicians, but it seems that thing are much less clear for amateurs and teachers. D.Lazard (talk) 15:11, 6 November 2019 (UTC)

Thanks for the feedback, everyone. It sounds like discussing mathematical intuition a bit more, possibly even in its own subsection, would be a popular addition. I didn't realize it before, but someone further below also mentioned that the article leans heavily towards mathematical research vs. common use and teaching. So that might be another topic that could use some expansion.

I went ahead & put in the note on Aristotle since it was straight-forward. Apparently though, I cleaned out the draft notes I wrote back in 2018. Doh! I may have put them on a backup I left with family before a move though. Either way, I'll try to work a bit more on the article in my free time later this year. Zar2gar1 (talk) 02:11, 14 July 2020 (UTC)

Changes in regard to Fundamental Thm. of Algebra

(a) Sorry, the statement of the FTA is such a nonsense that it needs to be removed immediately. Take the equation in one complex variable:

exp(z)=0

That is an equation in one complex variable, but it cannot be solved since exp(z) is always non zero. The FTA is about such equations as

z^5 + b z^4 + c z^3 + d z^2 + e z + f = 0

a polynomial equation for which, in general, no formula for the solution exist, but a complex solution IS always guaranteed by the FTA. That's a very strong statement about IC. (algebraic closure)

(b) IR is actually invented to have limits of rational approximations of Sqrt[2]. Or similarly, Pi as the area of the unit circle. Continuous properties can also be studied in IQ which has a metric (distance). This part of the article is only semi-correct.

(c) I moved the statement about FTA closer in the writing where IC is introduced. In the previous version, it seemed lost context-wise where it was.

(f) I find it good that the symbols IN...IR..IC are introduced even for laymen. I introduced them to resume the discussion after the statement of FTA.

LMSchmitt 21:58, 30 October 2020 (UTC)

As to point (f), please see Wikipedia:Manual of Style/Mathematics#Blackboard_bold. My view is that blackboard bold is primarily for blackboards (though I have used a blackboard bold numeral 1 in a published paper). Bbb is not banned, but introducing it de novo in a high-profile article has the potential to be contentious, particularly when it requires using inline <math> tags, which still do not render very gracefully. --Trovatore (talk) 22:21, 30 October 2020 (UTC)

Scutoid § Appearance in nature

The mathematical shape Scutoid#Appearance in nature occurs not only for biological life-forms, but also for geological shapes.

hexagonal prisms, and more

The Devils Postpile in California includes not just hexagonal prisms, crystals that are up to 100 feet long, and pentagonal prisms, but also scutoids, on the face of it. A glacier polished the top of the Postpile, exposing the geometrical cross-sections of the prisms. I bring a question up on this talk page because this group may have an opinion whether some illustrations of the Postpile are appropriate in the scutoid article, Scutoid § Appearance in nature.

hexagonal prisms, as well as a distribution of other shapes

Or do we wait for a naturalist to provide an observation of a scutoid at the Postpile. Or perhaps a beekeeper will present a picture of a curved honeycomb showing that scutoids might also appear, as well as prismatoids, and the familiar hexagonal prisms.

pentagonal prisms

--Ancheta Wis   (talk | contribs) 04:28, 21 December 2020 (UTC)

Maths

I recently edited this article saying that "maths" is a common term for this subject, but it was reverted and dubbed as incorrect. Can someone explain this to me, please? Maths even redirects to this article. GOLDIEM J (talk) 01:12, 15 January 2021 (UTC)

This is a convention enforced by the editors. No other reason. --Ancheta Wis   (talk | contribs) 01:15, 15 January 2021 (UTC)

There have been a few discussion, viewable in the archives here. --John (User:Jwy/talk) 04:28, 15 January 2021 (UTC)

I agree that this does not belong in the wp:lead, let alone in the wp:first sentence, as this fact(oid) is hardly ever discussed or even mentioned in the literature. It is casually mentioned at the end of the Mathematics#Etymology subsection, and I think that is just about sufficient. - DVdm (talk) 14:01, 15 January 2021 (UTC)

As far as I know, the abbreviations are rarely used for refering to the subject of the article (an area of knowledge). They are generally used in education for referring to the courses (and their content) about mathematics. So, a mention could be worth in a section about mathematical education, if such a section would exist. D.Lazard (talk) 14:56, 15 January 2021 (UTC)

I have never seen mathematics abbreviated to maths in any textbook or paper, nor have I heard the colloquial term maths used in casual speech. I don't even see how anyone would try to pronounce it in casual speech.—Anita5192 (talk) 16:42, 15 January 2021 (UTC)

"Math" is used in the USA (and elsewhere) and "maths" is used in the UK (and elsewhere). The question is whether either one should be explicitly mentioned in the lede. Personally I agree with DVdm that the treatment in etymology is sufficient.

However, do we need to mention them in the lede for the sake of obeying Wikipedia:Redirect? My opinion is "no", because almost all readers searching for "math" or "maths" will know/realize that they are short forms of "mathematics". No serious risk of astonishment. Mgnbar (talk) 16:51, 15 January 2021 (UTC)

My thoughts: math and maths should be mentioned early partly due to WP:BOLDSYN, but also because someone who enters the term unfamiliar to them (like Anita if she entered 'maths') will see immediately the two are equivalent. Restricting discussion to things "in the literature" seems to me overly formal for what Wikipedia is. I don't quite understand the vehemence of those who do not want the terms in the lead, but long ago decided that my interest in the topic was not up to defending my position beyond a statement like this. --John (User:Jwy/talk) 08:44, 16 January 2021 (UTC)

Semi-protected edit request on 16 July 2021

Algebra was way before from the Greeks, the arabs just pirated and stole as china then published and sold gyp gypsy "books" claiming their "idea" , pirated rights claimed infringement , as usual for china arab ghandi gyp gypsies intellectual copyright , pirating and infringement as usual 2600:1702:FA0:B360:B47C:34A2:ADB0:DE81 (talk) 18:28, 16 July 2021 (UTC)

 Not done: please provide reliable sources that support the change you want to be made. ScottishFinnishRadish (talk) 18:38, 16 July 2021 (UTC)