Talk:Mathematician/Archive 1

(Untitled discussions)
Hi I think Demographics section is too vague. Maybe one should include statistics on demographic changes after World War II. Cheers --Riccardo

I added some statistics on doctoral degrees in mathematics in the United States. Since most mathematicians have some type of degree in mathematics I figured these statistics would be a good indicator of demographic information of mathematicians in the US. The information is a bit outdated (2000) but the AMS has some reports with more recent information, including undergraduate and masters degree statistics. I'll try to bring the information more up-to-date over the coming week.

Worldwide statistics would also be useful so if anyone knows of resources for international statistics, please leave a note here.

TooMuchMath 00:46, 2 February 2006 (UTC)


 * for the time being, i guess it is better to have a separate page called "statistics on doctoral degrees in mathematics in the United States" and an external link to it. i think it does not make sense to have a page called "mathematicians" with a particular section like what you have added. of course a section on worldwide statistic will be useful. derham 8april2006.

The Physicist page organizes people by the century they lived in. I find that helpful. Should we do it on our page also? --AxelBoldt

If we do this, then we should do it properly, arranging them by order of birth, rather than mixing alphabetical and chronological order as is done with the physicists. However, I'm not sure this is really better than an ordinary alphabetical listing. Ideally we should have both, but that's probably too difficult to maintain. Zundark, 2001-08-11


 * Maybe at one point we will have a Mathematical timeline just like Computing timeline and that would take care of the chronological order. --AxelBoldt

Wouldn't it be advisable to use only one alphabetical list? What's the point of listing living and dead mathematicians separately? What happens if a hitherto living mathematician dies? Maths is supposed to be timeless -- that's one of its greatest charms ;). -- Piotr Gasiorowski

I agree, the division between living and dead is not important. If we give dates of birth and death, then the living ones can be easily identified by not having a death date yet. --AxelBoldt

Is it correct to use characters as Č, Š and Ž herein or should I put them away? I don't know how, for example, Slovene persons are listed in English sources. We don't use trancriptions for names as it is done for Russian names. I can't use swaps as Ch, Sh or Zh.

Best regards. XJamRastafire


 * I would use &#268;, etc., (as we have been doing for Stone-&#268;ech compactification). Unfortunately, some people won't see them correctly, but they should be OK for most people. The main alternative is just to drop the accents, but I don't like to do that. --Zundark, 2002 Feb 25


 * --Thank you very much Zundark for your encouraging words. I am glad that the most important Slovene mathematicians could find their places among the world's ones. I shall use in my articles of Russian people their original names with latinic transcription as for example in ( &#1070;&#1083;&#1080;&#1072;&#1085; &#1050;&#1072;&#1088;&#1083;&#1042;&#1072;&#1089;&#1080;&#1083;&#1081;&#1077;&#1074;&#1080;&#1095; &#1057;&#1086;&#1093;&#1086;&#1090;&#1089;&#1082;&#1080; )
 * I hope this would clarify some undistinctnesses of their names. I am also pleased that your native language is English, so you can correct the most us who don't speak English 100 % --XJamRastafire (2002.02.25)

It's funny situation here. Zundark you sort the list in English alphabetical order. This seems to be OK. But its funny for example for me. To search Zhukowski (Slovene = #381;ukovski) under Z and not Ž it takes time for nonEnglish users. Because of these things English version looses something. Ordering of something is almost an art. Some banal ASCII code "screwed" all it up. I think Windows 95 had solved this quite well but bitter taste remains. These kind of (and specially of mathematicians and people) really bother me. We won't be able to make such transformations as:

[Sorting A] -(whatever)-> [Sorting B]

very succesfully. But it would be very desired. I wonder how these things are arranged elsewhere. XJam 3 Wednesday (2002.02.27)

Adding huge quantities of Slovenian mathematicians to this page is unacceptable - it completely distorts the page, and is likely to encourage someone else to do the same for their own favourite country. I suggest a separate page for Slovenian mathematicians, which can be linked from the bottom of this page. It can even use Slovenian alphabetical order, since it will only contain Slovenian names. --Zundark, 2002 Feb 28


 * Yes, Zundark a great idea. I shall implement it as soon as I would be able. Or someone else who has some knowledge about the subject //Slovene mathematician| Slovenian mathematicians// According to my knowledge of English language adjective Slovene is the same as Slovenian. Please correct me if I am wrong if you know something on it. Why useing two different words for the same thing. One of my acquaintances said English language is so non - explicit, but I haeavy disagree with this opinion. Just think on programming and for reserved words as for instance in C. --XJam 4 Thursday (2002.02.28) (0,1st ed.)


 * As far as I know, there is no distinction between "Slovene" and "Slovenian" in English. I don't know which is best. Wikipedia seems to use "Slovene" more than "Slovenian" at the moment. --Zundark, 2002 Feb 28


 * Perhaps another approach is that those Slovene mathematicians remains in the world's list just to keep track on them. These are just the most prominent mathematicians of 20th and 21st century from Slovenia and some from earlier. Another thought is: does anywhere in the world exist the perfect list of all mathematicians of all times. Just think of Asimov's list of scientists. Or on Sloane's famous enumeration of integer sequences. On my home PC I have my own enumeration which is derived from TeX macros and shurely won't fit in Wikipedia, but who knows. My list contains over 1200 mathematicians and over 1600 astronomers from all over the world and from all times. So *.dvi preview of this list shows for example [ 1624 ] Zhukowski as the last one in it. I am looking for ZZ Top's kind of name of certain mathematician to have surname with the property to be &Omega; liked. Any help for this? Another list which can be simply derived from alphabeticall order is of cource the timeliked list. In this it would be [ 1624 ] The youngest world's astronomer, (mathematician, ...) but questions remains at what time one comes a mathematician. When he graduates, when he first publishes his results of certain researches, when he first with LaTeX writes his high-school textbook, when he gets Field's medal, when he dies in a Galois duel, ...? --XJam 4 Thursday (2002.02.28) (1->,2nd ed.,3rd ed.)

There is a big list of mathematicians [on the MacTutor site]. We shouldn't try to list all mathematicians in the Mathematician article, only the most famous. Keeping all the Slovenian mathematicians here is not an option, which is why I suggested a separate page. (Any who are sufficiently well-known that they are on the MacTutor list can also be listed in the Mathematician article, of course.) --Zundark, 2002 Feb 28


 * Yes. MacTutor site is one of the best I've ever seen. But unfortunately I haven't found yet some of the most important Slovene and well known mathematicians as Josip Plemelj is. Also their article about Jurij Vega is also unworthy of such prominent University. I wonder what Winchester University got to say on it. I tried to correct this directly by sending some adds to MacTutor but obviously I haven't come in a row hitherto or it is just because I am just one unfree copywriter or happy wikipedian. I hope here in Wikipedia I won't be sacked out of it... One drop of guilt goes perhaps to DMFA S, Slovene Society for Mathematicians, Physicist and Astronomers of Slovenia. --XJam 4 Thursday (2002.02.28) (3->4th ed.)


 * Could add more jokes but shouldn't there be jokee'pedia for that?

The article says that "a misconception that everything in mathematics is already known is widespread among persons not learned in that field". I have not encountered anyone who thinks that. Examples, statistics, source? --Ian Maxwell 16:08, 2004 Nov 11 (UTC)


 * I would be surprised if there were any formal studies of this. On the other hand, basically every person I've met that is not a mathematician, scientist, or technically-minded academic of some kind, thinks this.  And I am not alone.  My fellow graduate students (at least the one I've discussed this with) all have had the same experience.  I've been involved in numerous discussions related to this on sci.math and I've found other posters have had this experience.  It also seems that whenever I read articles about math education the author who is either a math educator or research mathematician believes that the average person believes "everything in mathematics is already known".  I can only conclude these people believe the same as me because they've had the same experience.


 * You are indeed a very lucky person, Ian, to never have had this experience. --C S 00:29, Jan 2, 2005 (UTC)


 * I have not had this experience, but a related one: "So HOW do you do research in math?" The question isn't based on the idea that everything's been discovered in math, but rather a misconception of how research works: most people think of research as a process of experimentation, as in the physical sciences. Being in combinatorics, it's easy to pose simple mathematical questions which are unanswered, or only recently answered. --Dcclark 04:09, 10 May 2005 (UTC)

Some inner aspects
User:DigitalCharacter wrote a new section:
 * Achievements of mathematicians may vary. A mathematician with great achievements is considered as genius. Geniuses are extremely rare. This is one of the reasons they get a lot of attention and admiration (and critics) from ancient times. All broadly known mathematicians are in fact geniuses in field of mathematics and abstract thinking.


 * Glory plays an important role in whole history of mathematics. It is a key factor of motivation. There is no patent over theories and theorems (except some algorithms in computer science), so money that can be made in mathematics is not much and glory is almost the only prize.

I find this horribly biased and distorted, particularly the material about "glory". The material about "genius" uses a notion of genius I don't believe most mathematicians would agree with. It also seems irrelevant to this article. There are geniuses in every subject. Pointing this out is well, pointless. --C S 00:34, Jan 2, 2005 (UTC)

Because of the reasons I've stated right above, I've rewrote the section, and in addition I've retitled it "Motivation" -- this gives it more focus. I feel the result is much fairer and accurate than before. --C S 14:24, Jan 2, 2005 (UTC)


 * I think the current version is still very POV, but in the opposite direction. The comment about not being motivated by "monetary greed" is emotive and insulting to anyone whose goal is to earn money.  There are other examples too, but I'll have to go back through this.  I agree with the other editor in the discussion who said that there is quite a bit to be done here.  I will edit the emotive "greed" stuff out now, and put a quality tag (and possibly a POV tag) on the article.  capitalist 07:37, 7 December 2005 (UTC)

is this all?
Boy, this article needs some work. Disjointed, cryptic, and bland. To be honest, it kind of stinks at the moment.

enough jokes
Enough with the jokes. If you want to have fun with them, make a new article.

math
is there any more information that i can have on leonhard eluer and some examples of his work


 * This is not the place to ask this sort of question. I recommend reading the relevant Wikipedia pages, or googling. --Dcclark 04:11, 10 May 2005 (UTC)

Removed TIMSS stuff
This is an article about mathematicians, not a comparative article about the primary educational systems of various countries and their effects on elementary school students' test scores. I understand that the heavily European and European-American focus of a lot of the biographical mathematics articles might be seen as minimizing contributions from Asian countries, but misusing statistics is not a remedy for that. (See notes above on Slovenian mathematicians.) I recommend picking up a copy of EDM (the Japansese Encyclopedic Dictionary of Mathematics), which tends to rank these contributions more highly, and creating some new Wikipedia articles on Asian mathematics based on its material to balance things out. Cheers.

138.88.101.14 4 July 2005 19:22 (UTC)

Total Number of Mathematicians
Is it correct that the United States has the largest number of career mathematicians in the world? Also, can someone give an estimate of people in U.S. and E.U. whose understanding of mathematics goes beyond abstract algebra, topology, et cetera?

--66.81.21.224 09:41, 17 December 2005 (UTC)


 * I tried a few Google searches but haven't found any statistics by country yet. capitalist 04:03, 18 December 2005 (UTC)

Famous mathematicians
I just finished a 4th year history of mathematics course - I would be happy to enter in some of the most notable mathematicians (such as Archimedes, Euler, etc) - ones regarded as the most important within the field of mathematics, and generally recognized for their brilliance (Archimedes, for instance, is known to have been studying a rudimentary for of the integral around (I think) 600 BC - just a few years before Newton's calculus came along!). But, it will have to wait for the New Year, as the holidays are family time for me, and I'm limiting my Wikipedia time to monitoring a few pages and a couple talk page entries......DonaNobisPacem 07:58, 28 December 2005 (UTC)
 * I think that would add a lot, and will try to contribute when I can. I just read a book about the Riemann Hypothesis, and the author felt that Gauss was one of history's greatest mathemeticians.  Eventually there could be subsections for each period/geographic region too.  I would do more on this article because it's my priority on Wikipedia now, but I'm trying to finish work on a commercial website, and it's taking forever.    capitalist 04:44, 29 December 2005 (UTC)


 * I certainly think that three of necessary mention are Archimedes (identified as greatest of antiquity, and possibly of all recorded history), Euler, and Gauss; there is also Thales of Miletes, traditionally regarded as the founder of Mathematics, Pythagoras and his school (although Plato's Academy was arguably great, Plato was a neo-Pythagorean in many regards); Newton and Liebnitz for their work on calculus; and there are certainly a few of note in the 20th century.DonaNobisPacem 06:24, 29 December 2005 (UTC)

Articles already exist for all the mathemeticians mentioned above, see Archimedes, Gauss, Euler, Thales, Pythagoras, Plato, Newton, and Leibnitz, see List of mathematicians for lots more. Paul August &#9742; 05:11, 31 December 2005 (UTC)


 * Sorry - I should clarify - I wasn't trying to say that a complete description should be given of these mathematicians, just that they be mentioned in this article as the most famous examples.DonaNobisPacem 08:17, 31 December 2005 (UTC)

Differences
"Mathematicians differ from philosophers in that the primary questions of mathematics are assumed (for the most part) to transcend the context of the human mind; the idea that "2+2=4 is a true statement" is assumed to exist without requiring a human mind to state the problem. Not all mathematicians would strictly agree with the above."

This is not only doubtful about mathematics; it is also doubtful about philosophy: analytic philosophy, at least, is founded on the idea (from Frege) that the truth-values of propositions can be determined independent of psychological context. This should probably be removed, or at least revised; there are more important differences between mathematics and philosophy.


 * I would think that the entire reference should be removed, since it belongs in an article about the philosophy of mathematics. This article is about mathematicians; the people, not the subject they study.  capitalist 04:28, 31 December 2005 (UTC)

jokes
are the jokes encyclopedic? Not sure they belong here. JamieJones talk 21:45, 30 January 2006 (UTC)

I agree so I just deleted the jokes section. TooMuchMath 22:29, 1 February 2006 (UTC)

Einstein a mathematician?
Einstein a mathematician
 * A Poster of Albert Einstein · Mathematicians born in the same country."
 * "Albert Einstein - Mathematician, Physicist,Spiritualist?"
 * "Albert Einstein was born in 1879 in Ulm, Germany. He was a keen mathematician"
 * etc...

See http://en.wikiquote.org/wiki/Talk:Albert_Einstein for arguments that Einstein was not a mathematician.

The MacTutor website with biographies of mathematicians includes Einstein, but this doesn't mean he was. That website has biographies of Maxwell and Lorentz too, and they are certainly physicists, not mathematicians. They weren't proving theorems in mathematics but were practicing physicists. I am sure the vast majority of mathematicians and physicists consider Einstein solidly as a physicist, not a mathematician. (Some may be both, but not Einstein.) The MacTutor biography site even has the Einstein quote "Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore." &mdash;The preceding unsigned comment was added by 137.99.17.121 (talk • contribs).

"For instance, Albert Einstein, whose ideas had a significant impact in geometry"

The above quote is simply wrong. It was Riemann, not Einstein, whose ideas had a significant impact on geometry. &mdash;The preceding unsigned comment was added by 70.81.11.209 (talk • contribs).

"(Redirected from Mathemagician)"
Why does Mathemagician redirect here?

Are mathematicians smarter than the rest of us?
So I have frequently heard the claim that one reason to study math is that it makes you vastly smarter in every day life. On Jonathan Hayward's webpage, for example, I see the claim, "Thinking logically and abstractly is an important discipline in life and in other academic disciplines that consist of thinking--it has been said that if you can do mathematics, you can do almost anything. The main reason mathematics is valuable to the non-mathematician is as a form of weight lifting for the mind. Even when the knowledge has no application, the finesse that's learned can be useful."

Surely there must be tons of peer reviewed research on this subject, right? Alex Krupp 05:29, 6 April 2006 (UTC)


 * I searched in all the math, cognitive science, neurobiology, psychology, education, and math education journals, plus Google & JSTOR. I was using the phrases "math" + "cognitive development," and also "studying math" + "intelligence" (math + intelligence returned too many results, all useless) but found no relevant results. Again, I am looking for evidence for the claims that studying higher math makes you smarter at solving every day problems. It seems that mathematicians are all full of it though. Alex Krupp 05:50, 8 April 2006 (UTC)


 * Is this a claim that's made in the article? I didn't see it in there, but I just skimmed through and may have missed it.  At any rate, if it's not substantiated then you can certainly remove it from the article until it is.  capitalist 02:28, 9 April 2006 (UTC)


 * The claim isn't made in the article. However, I have heard many people make this claim in general. Alex Krupp 02:57, 9 May 2006 (UTC)


 * Oh. You may want to review Talk_page_guidelines, specifically this excerpt:


 * "What talk pages may be used for
 * Talk pages are not for general chatter; please keep discussions on talk pages on the topic of how to improve the associated article.
 * Talk pages are also not strictly a forum to argue different points of view about controversial issues." capitalist 02:42, 15 April 2006 (UTC)


 * Well I was thinking that these claims could potentially be included in the article. For example, here is a former US president making this same basic claim about the thinking of mathematicians. I think it might be worthy for inclusion into the article, no?


 * "And so I say that all that you are doing in using higher mathematics (and I approve of your using them) is to train the human mind to such processes of precision as will correct that loose-jointed, wabbly, incorrect, indiscriminate reasoning to which we are naturally inclined; which will make it demand processes clearly connected with premises, and make it impatient of conclusions that do not flow from the premises. We are trying to rid the human mind of its tendency to accept vague propositions." --Woodrow Wilson, Jan. 9th, 1909. Printed in High School Teachers Association of New York Volume 3 1908-1909 (n.p., n.d.), pp. 19-31. Alex Krupp 02:57, 9 May 2006 (UTC)
 * Good quote! I'd have no problem with that being in the article as long as it fits into some logical place.  Any suggestions? capitalist 02:30, 14 August 2006 (UTC)

Mathematicians don't teach/tutor??
Why exactly was this removed? I think of myself as a mathematician, and part of what I do is teach. As well as being a student of mathematics. Not saying it is the be all and end all of mathematics (heck no!), but it certainly is an important aspect of it. Mathmo


 * According to the first paragraph, "In other words, a mathematician is a person who contributes new knowledge to the field of mathematics, i.e. new theorems." Taking this approach, someone who simply applies mathematics to their job (i.e. a teacher) is not strictly a mathematician.  This distinction between the field of mathematics and fields that simply apply mathematics is also in the first paragraph.  I didn't remove the material in question, but I can understand why it was removed.  Saying "Some mathematicians also work as teachers" is like saying "some biologists also work as zoo-keepers."  That may be true, but while they're administering the zoo, they're not making new discoveries in biology and thus do not presently hold the job title of "biologist".  A math teacher may have a PhD in math, but presently holds the job title of "teacher" not "mathematician".  Maybe the solution is to add the field of "teaching" to the list of examples of fields that use applied mathematics at the end of the first paragraph. capitalist 02:51, 15 April 2006 (UTC)
 * I'll point out to you that there are two part to the statement at the start: "A mathematician is a person whose primary area of study and research". The second part is the research, which from coffee produces new theorems etc... However, the first part is the *study* of mathematics. And teaching mathematics is most certainly all about the study of mathematics!! Mathmo 19:24, 16 April 2006 (UTC)
 * But it says "study AND research" not "study OR research". Both are necessary (but not necessarily sufficient) conditions.  The point of contention seems to be which qualifications are necessary for a person to claim the title of "mathematician."  I study mathematics all the time, and apply it all the time in my work, but that still doesn't make me a mathematician.  If anything, I would consider myself an "amateur mathematician" but I don't think that's what this article is about.  It's about actual professional mathematicians; not teachers of math, students of math, users of math, lovers of math or anything else.  If anything, I would prefer to add the following to the definition of a mathematician: "a person who has a post-graduate degree in mathematics and is employed in a position for which that degree is a basic requirement." capitalist 04:06, 17 April 2006 (UTC)
 * That seems like an extremely narrow definition of a mathematician, what next going to say certain areas are not mathematics as well?? Excluded people who study cellular automata?? Perhaps this narrower definition would be better off under a different article (or subsection) entitled something like "professional mathematican researcher"?? Mathmo 13:43, 22 April 2006 (UTC)
 * If by "narrow" you mean that my definition is very precise, I would have to agree. Now that you mention it, the definition has an almost "mathematical precision," which is a very important element in a definition.  Without precise definitions, everybody and his pet gerbil could be considered a mathematician and the word could mean anything at all.  Thank you for your support in pointing out this major advantage in the definition that I proposed.  capitalist 02:13, 23 April 2006 (UTC)

A definition being narrow has nothing at all to do with being precise. "Precise" means there is no ambiguity in interpreting the definition; "Narrow" means few objects fit the definition. A definition like "a mathematician is a person who has taken a mathematical undergraduate course" is very precise but not at all narrow. Anyway, Ramanujan does not, as far as I am aware, fit your latest definition. Would you not consider him a mathematician? -- Meni Rosenfeld (talk) 17:08, 5 May 2006 (UTC)


 * I would consider him an accountant, because that was his profession. Ramanujan was not a professional mathematician.  He was certainly an interesting and prodigal AMATEUR mathematician however.  But your point is well taken that my definition would exclude historical mathematicians who were commissioned by royalty to do their work and so forth, because obviously many of them would not have "post-graduate" degrees.  My definition would have to be applied only to contemporary cases.  Anyway, I'm not proposing that we use that definition in the article.  However, I'm trying to err far over to the exclusionary end of the spectrum to balance out people who want to extend the definition too far.  Granting the title of "Mathematician" to anyone who happens to use math in their job or teaches high school calculus inflates the definition so much that it loses its value.


 * As far as narrowness vs. precision, wouldn't the number of objects that fit the definition be a funtion of the definition's ambiguity or lack thereof? In other words, the "narrowness" is proportional to the precision, or N=kP.  At the very least, N=f(P), so I would have to disagree with your conclusion that the two values have "nothing to do with each other."  capitalist 03:31, 6 May 2006 (UTC)

capitalist 03:23, 6 May 2006 (UTC)

Well, I would consider Ramanujan, and contemporary individuals with resemblance to him, to be mathematicians. I consider "amateur mathematicians" and "proffesional mathematicians" to be subsets of the larger "mathematicians" set. So your definition may be suited to define a "proffesional mathematician", but I don't think it should be used to define a "mathematician". But that's just my point of view here.

And I still don't agree about the Narrow\Precise issue. Perhaps the following table of various definitions can clear my point:

Especially note the vague & narrow one: It is nowhere near precise, since it isn't clear what "doing math" means. But it is extremely narrow : arguably, there isn't a single person who fits the definition - for example, if eating is not considered as doing math. -- Meni Rosenfeld (talk) 15:58, 6 May 2006 (UTC)


 * If Ramanujan were alive today and applying for a job at the NSA or Microsoft, I think it would be unethical for him to put "Mathematician" on his resume, since he was actually an accountant. On the other hand, Hardy considered him to be a mathematician because he produced theorems (though in an unorthodox way), and it is certainly true that an amateur mathematician is a mathematician.  What about reworking the article so that it makes a distinction between professional and amateur mathematicians and provides a definition for each?  A professional mathematician would be defined as I suggested, and an amateur mathematician would have the definition that is currently used in the first paragraph of the article (which Ramanujan fits).  Math teachers, engineers and accountants still wouldn't qualify as amateur mathematicians though unless they meet the criteria of advancing knowledge in the field, i.e. "turning coffee into theorems."


 * On the Narrow/Precise issue I think you've got a contradiction in your argument. Looking at the "vague and narrow case", on the one hand you claim that we don't know what doing math means, but on the other you claim that we know that it doesn't mean eating.  Both can't be true.  If you claim that it isn't clear what "doing math" means, then it could mean anything.  We could take the Pythagorean view that "all things reduce to number" (or whatever) and make the argument that all human acts, including eating a sandwich, are mathematical acts.  Thus "a person who does nothing but math" could include everyone who ever lived for all we know.  It's not narrow, it's extremely wide.  It's extremely wide because it's vague.  Again, wideness (or inclusiveness in a definition) is a result of vagueness while narrowness (exlusion from a definition) is a result of precision.  The more vaguely you define something, the more objects there are that could be included under that definition.


 * Also, notice the top line of your table. You have both of these marked "Wide" but I would claim that the set of people who "have taken math classes" is a subset of the people who "sometimes do math."  Therefore, the group on the right is narrower than the group on the left.  They aren't both "Wide" as you show.  The group on the right is narrower because the definition is more precise.  Again, the functional relationship holds.  QED!  LOL      capitalist 03:15, 7 May 2006 (UTC)


 * I thought of another approach to the explanation as well. If you look at the article on Accuracy and precision you will see how these terms are used by scientists in discussing measurements.  If you take repeated measurements, accuracy refers to how close they are to the actual value, while "precision" refers to how close they are to each other.  Let's stick with precision.  If our measurements are all close to each other, we say that they all fall within a NARROW range, or that they are within a WELL DEFINED area which indicates a high degree of PRECISION.  If the measurements are scattered over a WIDE range, we say they have LOW PRECISION.


 * You may say, "But measurements have nothing to do with definitions of words.", but in fact they do. Measurement is the comparison of some individual thing with a standard (like a length of pipe to a ruler).  In language, definitions are our standards, and we compare specific things to those definitions in order to determine what they are.  I'm guessing that this is where the term "measure up" comes from.  We look at a person and ask if they "measure up" to the definition of "mathematician".


 * Another thought. When we refer to a person as "focused" we think of a very NARROW tight beam.  This person is very precise in their thought patterns and definitions.  On the other hand a person who is "scatter-brained" makes us think of someone whose thoughts are all over the place and whose definitions are very WIDE and imprecise. capitalist 03:57, 7 May 2006 (UTC)
 * I suppose your suggestion regarding the article is good.
 * About narrow\precise: It is true that "doing math" could be interpreted as including anything. This way, the definition in question can be said to include everyone. But who would actually interpret it this way? My guess is, not too many people. In my opinion, if almost everyone would consider this definition to include almost no-one, then it is safe to say that the definition is narrow. The same holds for any defintion that is not precise: Interpreted strictly, it can include nobody; Interpreted loosely, it can include anybody. For precise definitions, however, there is no such duality: the definition "a mathematician is a person who publishes at least 0 mathematical articles daily" will include every person on earth no matter how you interpret it (note that this one is precise and extremely wide), while the definition "a person who publishes at least 9999 mathematical articles daily" will include nobody no matter how you interpret it.
 * How, then, would we (at least theoritically) quantify these ideas of precision and narrowness? With statistical methods. Suppose X is a random variable, generated by the following experiment: we pick a person at random, and ask him, according to his interpretation of the definition, what proportion of the population satisfies the definition (assuming he has a way of finding out how many people do). Then the mean of X is related to wideness - The wider the definition, the greater the proportion will tend towards 1. The dispersion of X is related to vagueness - a precise definition will get similar (or, if completely precise, identical) results from different people, making a small dispersion; A vague definition will generate different results depending on each person's interpretation, contributing to a large dispersion. So, taking the "does nothing but math" example, an overwhelming majority of experiments will generate 0 as the result, making the mean low (hence "narrow"), but there will be those with a more liberal interpretation, generating higher results, possibly 1, contributing to a (relatively) high dispersion (hence "vague"). -- Meni Rosenfeld (talk) 12:07, 8 May 2006 (UTC)


 * You are using "precision" in the sense of "multiple measurements which are close to each other". I introduced that idea above to make a point about how the words "well defined" are often used in relation to the word "precision", but you have taken that example and tried to extend it beyond its intended use. The warranty on that example has expired.  :o)


 * The word "precision" has several senses depending on context. Precision in the sense used in measurement involves taking several measurements as in your statistical example, but we aren't taking several measurments here.  We are attempting to define a single term correctly.   I am using the word in the sense that it is used in the term "precision bombing" in which "precision" means "include the correct targets but exclude all others".  In this sense of the word, a "precise definition" of a mathematician is one which includes all people who are really mathematicians while excluding all those who aren't.


 * A definition is composed of a genus (like "people" in this case) and a set of differentia (like "who are breathing", who know how to add", "who sometimes use math" or "who have published 10 or more new theorems"). The genus is like the "target area" (the set of all people) while the differentia are the instructions that are supposed to tell us PRECISELY where to look within that target area to find our targets (mathematicians).  In this way, we will find PRECISELY what we're looking for without including any elements from the target area that we aren't looking for.    This is the sense of the word "precise" as I'm using it in relation to definitions.


 * You said that your example, "a mathematician is a person who publishes at least 0 mathematical articles daily" is precise and wide. In the sense in which I'm using the term, this is not a precise definition because it does not point to the precise group of people who are mathematicians.  It's imprecise because it's too wide.  It hits too many "non-targets".  It's not surgical.


 * The other editor's claim that my definition was "narrow" is correct. It includes only real professional  mathematicians and exludes all others as it should.  This would be like complaining that the target area of a PRECISION bomb was "too narrow" because it hit only the bad guys and didn't blow up the rest of the neighborhood.  capitalist 04:05, 9 May 2006 (UTC)


 * I suppose this can be summed up by saying that you and I have a different idea of what a "precise definition" means. It is therefore futile to try to convince each other what is precise and what isn't. But my problem with your interpretation is that it assumes that at the outset we "know" what a mathematician is, and are trying to find words to describe it. But, at least according to the mathematically techincal sense of the word "definition", you can't know what an object is before you have defined it, can you? That's exactly what a definition does - it defines, or sets, which objects belong to a group, and which don't. You can't ask, let alone know, if a matrix is regular or not before you have defined what a regular matrix is. Similarly, you can't know whether a person is a mathematician or not before you have defined what a mathematician is, and you can't say a definition is imprecise because it doesn't correctly identify the set of mathematicians (which, again, does not exist prior to the definition). What you can say is that a definition does or does not agree with your intuitive concept of what a "mathematician" should mean. This is indeed a desirable quality of a definition, but this intuition inevitably differs from person to person, so I can't see how you can measure precision by it. So, I'll agree that your definition is more "sensible" than the "at least 0 aricles" one, as it better describes what both of you and I (and probably, everybody else) feel a mathematician should mean, but I believe they are equally precise - which again, as far as I am concerned, means that the process of determining whether an object satisfies the definition is completely technical, without any personal judgement or interpretation involved. -- Meni Rosenfeld (talk) 10:56, 9 May 2006 (UTC)


 * I'll sum up the summation this way: You're saying that we must know an object's definition in order to determine what the object is.  I'm saying that we must know what an object is in order to determine its definition.  Ultimately, it's the subjective/objective debate about whether Reality or Consciousness is primary.  I take the Objectivist view that Reality is primary and that objects exist independently of their definitions, but that definitions do not exist independently of their objects. capitalist 02:28, 10 May 2006 (UTC)

Flagging mathematicians, dead or alive
Hi -

a new category (Category:Jewish_mathematicians) of mathematicians was created recently; all biographical pages seem to have been gone over - a link at the bottom of the page now flags the mathematician in question as a person whom the creator of the category seems to deem worthy of inclusion in the said category. (Type in the name of your favourite mathematician (or your own?) to see whether he/she/you make the cut.)

It seems to me that this makes even less sense than, say, "British mathematicians" - it is more along the lines of "vegetarian painters" or "Aryan restauranteurs". See Category_talk:Jewish_mathematicians.

I have proposed this category for deletion. Supporting (or contrary) statements can be made at Categories_for_deletion/Log/2006_May_4.

Mind you - a little browsing makes it evident this is a classification by descent, not by confession. Of course, a classification by confession would serve hardly any good purpose either. (There is no (other) classification of mathematicans by confession as of yet, for what that is worth.) Hasdrubal 21:32, 4 May 2006 (UTC)

Assessment comment
Substituted at 15:21, 1 May 2016 (UTC)