Wikipedia talk:WikiProject Mathematics/Archive/2007/Dec

photos of mathematicians
There is an interesting collection of photos of lots(!) of mathematicians at http://owpdb.mfo.de/. It seems that the institute is willing to grant WP the right to publish it here, see the discussion at the German Wikipedia http://de.wikipedia.org/wiki/Portal_Diskussion:Mathematik#Biographien_und_Fotos. Apparently the German Wikipedians don't want to take it under "Fair Use" license. I'm not that familiar with these license issues, but it is worth a look. Jakob.scholbach 14:47, 1 December 2007 (UTC)


 * (Note: I haven't read the German discussion.) Fair use is not a license, but quite the opposite: it means that we decide to use an image claiming it is fair use under US law, whether the owner wants it or not. If what they mean is that they would give some sort of exclusive license to Wikipedia, I don't think that would be allowed by Wikipedia policies. It would have to be under a free license which allows everyone, not just Wikipedia, to use, modify, and distribute the images. --Itub 14:58, 1 December 2007 (UTC)


 * I think the best thing we can do right now is wait for the results of the discussion on the German Wikipedia. The chances that the photos to which MFO actually has full rights (those with "Source: MFO") will be put under a sufficiently free licence to put them on Creative Commons seem to be by no means negligeable. Someone has contacted MFO already. If this fails, there might still be a chance to use some of the photos under fair use rules. The German Wikipedia does not accept fair use pictures (probably for legal reasons), but of course that doesn't restrict us. --Hans Adler 17:03, 1 December 2007 (UTC)


 * I managed to justify fair use for a portion of one of the photos in this collection. Knowing the copyright holder is already helpful, as it is an important ingredient in the fair use rationale. Geometry guy 17:17, 1 December 2007 (UTC)

So as I understand it, the reason that non-English Wikipedias usually won't use fair-use stuff is that fair use is a concept of American law, not valid in (say) Germany. Even if there's some similar notion in German copyright law (I don't know whether there is or not), it isn't the same, so the arguments that something is fair use under American law may not carry over.

Now, does anyone think that makes any sense at all? The servers are in Florida, not in Germany. Lots of people read -- and contribute to -- English WP from Germany; if German law is at issue, then it's as problematic for en.wiki as for de.wiki, except maybe numerically, insofar as one might expect a higher proportion of accesses from Germany to be on de.wiki. And I'm sure there are also lots of de.wiki users in the United States. How is the language of a WP even relevant to the legal question? --Trovatore 02:23, 4 December 2007 (UTC)
 * It isn't German law. German Wikipedia doesn't use nonfree images because they don't want to. We use them because there is no consensus on English Wikipedia to get rid of them. The Wikimedia foundation allows each project to decide individually. &mdash; Carl (CBM · talk) 02:28, 4 December 2007 (UTC)

Independent Component Analysis page
The ICA page is somewhat of a mess, with the first definition on the page not being a true definition, and no examples or common uses. Does this page fall within the boundaries of the Mathematics project? I assumed so, so I'm posting a request here that it be the "article to be fixed of the day/week/month" so that a few people can check it out and fix it up. Thanks! -- eykanal talk 01:53, 3 December 2007 (UTC)

Is information theory part of mathematics?
Currently Category:Information theory is not in the list of mathematics categories, and mathbot does not add its articles to the list of mathematics articles. Prompted by a question by Michael Hardy on my talk page, I wonder, should we consider this category as part of mathematics? If yes, mathbot will add all the articles in this category to the math articles list. (I for some reason thought that information theory was more comp sci and engineering, or either way that it strays too much from mathematics, but I am not an expert.) Oleg Alexandrov (talk) 06:22, 3 December 2007 (UTC)


 * I'm surprised. Information theory is a part of probability theory.  Shannon's paper "A Mathematical Theory of Communication", published in 1948, is one of the most famous scholarly papers ever published, and doesn't say much about computing (but it has many applications to computing). Michael Hardy 06:38, 3 December 2007 (UTC)


 * sounds like mathbot needs an update. :-) Mct mht 06:51, 3 December 2007 (UTC)
 * Well Talk:Information theory says its within the scope of WikiProject Mathematics, so I guess it is! --Salix alba (talk) 09:25, 3 December 2007 (UTC)


 * Hang on a minute, everyone: we are not talking about the article Information theory here, we are talking about the entire category Category:Information theory and (to be logical about it) all of its subcategories. If Mathbot's code is changed then all of these articles will routinely be added to the list of mathematics articles, including articles such as Journal of Multimedia, K Video Compression Dynamics, and Proxy server.
 * Information theory may be a spectacular application of probability theory that in turn has had a profound impact on probability theory itself, but that does not make it (in its entirity) a branch of mathematics any more than theoretical physics is. Some information theory is part of mathematics, but not all of it. If we go too far, here, everything in life becomes applied mathematics, because, after all, we all need to be able to count. Geometry guy 10:31, 3 December 2007 (UTC)


 * is about Error-correcting codes with feedback which was in both Category:Information theory and Category:Error detection and correction. At least the latter seems mathematical to me - and it's a subcategory of Category:Coding theory which also seems mathematical. PrimeHunter 13:44, 3 December 2007 (UTC)


 * MathBot has a more complicated system, so it would be possible to include a category but not all its subcategories. If you just start with Category:Mathematics and go down, you can get to lots of articles that are clearly not mathematics, like Google Answers. &mdash; Carl (CBM · talk) 14:09, 3 December 2007 (UTC)
 * Right, so we can include only Category:Information theory and just some selected subcategories. The question is which, if any, subcategories (and if the parent itself) should be adopted under the umbrella of our project. Oleg Alexandrov (talk) 15:49, 3 December 2007 (UTC)
 * Of 10 top level subcategories, I'd say Algebraic information theory, Algorithmic information theory, Detection theory, Entropy and information, Information theorists and Quantum information theory are probably within the scope of this project; Coding theory, Data compression and Network performance probably aren't (at least not with all subcats), and I'm not too sure about Error detection and correction. What do others think? -GTBacchus(talk) 17:46, 3 December 2007 (UTC)

Could we be specific here? Which things in information theory do not belong either to probability theory or coding theory? Which articles? Name some examples. Michael Hardy 16:05, 3 December 2007 (UTC)
 * Which things in probability theory do not belong to either Combinatorics or Measure Theory? As Shoenfield said, "the Fundamental Theorem of Calculus can be expressed in Symbolic Logic but the proof would be a mile long". That said, the information content of a bitstream is equivalent to the entropy of a system, so there are connections to both Ergodic Theory (which is in line with Probablility's connections to Measure Theory) and to Thermodynamics (which really is just sytstems of PDEs so we should replace Physics with a subcategory of Analysis :-). But yes, I'd be interested also in articles that pertain to Information Theory but not in any way to any Mathematics. Electronics Engineers might point to something but really I advocate embracing the infinite interconnectivity of scholarship. Coding Theory is mostly done by combinatorialists but obviously it overlaps with computer science, but computer science can be interpreted as Mathematics Engineering :-) Information theory is shared among math, CIS (the "I" stands for "Inforamation"), EE, physics... but we can all contribute to every part of it, even video compression. Take a look at some of the codes that do video compression and you will see math. The Tree of Knowledge is not Totally Ordered. Pete St.John 17:16, 3 December 2007 (UTC)

Michael, an example of a subcategory of Category:Information theory that is not mathematical: Category:Information theory > Category:Data compression > Category:Compression algorithms > Category:Lossy compression algorithms > Category:MP3 > Category:iPod -GTBacchus(talk) 17:30, 3 December 2007 (UTC)


 * My feeling is that in that chain, you've already crossed the line from math to computer science in the first step to data compression. —David Eppstein 17:46, 3 December 2007 (UTC)

Help organize the "list of inequalities"
Look at List of inequalities. There's a section titled "Pure mathematics" and another one titled "Probability theory". "Pure mathematics" is in effect being used as a catch-all---a "none-of-the-above" category (except that in this case it's below rather than above). Can it be organized into sections? Michael Hardy 16:22, 3 December 2007 (UTC)
 * I'm working on that, in alphabetical chunks. If someone could review my work when I'm done, that would be great. -GTBacchus(talk) 18:14, 3 December 2007 (UTC)
 * Ok, I sorted them all. There were some iffy cases (I'm not certain the various generalizations of the Arithmetic/Geometric mean inequality should be grouped together under "Analysis" as they are, and the inequalities under "Linear algebra" could probably be sorted differently), and I listed a couple of inequalities twice: Weyl's inequality, because there are two covered in the article; and Triangle inequality, which I put under "Geometry" and also under "Linear Algebra" (although I guess it's not true unless you're in a normed vector space, which is getting towards analysis). Corrections and improvements are more than welcome. -GTBacchus(talk) 18:49, 3 December 2007 (UTC)

Constant move
The Constant page was moved to Numerical constant. I'd argue that the former name is better. Comments? Oleg Alexandrov (talk) 04:59, 30 November 2007 (UTC)
 * The justification that Randomblue gave for the move was: "I don't want to the article to be too general, so as to add in other constant object such as constant functions, constant matrices, constant mappings, etc. Numerical constant is I think what people expect from". I agree that that's what most people will expect. But I am not sure moving the article was the best way to deal with this. Constant now redirects to Numerical constant. Perhaps the idea was that now constant can become an article about the general concept, or a disambiguation page? I don't like the idea much. I think constant should be what most people expect, and it should have a short paragraph mentioning that in mathematics other things than numbers can be constant as well, referring to an extra article on this if/when there is ever more material on this. In the current situation, when you enter "Constant" because you are interested in the origins of the name, you are redirected to "Numerical constant", which offers a link to disambiguation. This kind of thing is confusing for most of our users. So yes, Oleg, I agree, although of course there might still be other things that I haven't seen. --Hans Adler (talk) 10:08, 30 November 2007 (UTC)
 * On one hand, this does look like a fix in search of a problem, unless someone actually was planning to add lots of material to the constant article about advanced math. On the other hand, in the current setup constant does redirect to the correct place, so readers are unlikely to be surprised. So I don't think it's worth spending a long time discussing at the moment. In the future, if other articles are written, then it may be necessary to rearrange titles. &mdash; Carl (CBM · talk) 13:04, 30 November 2007 (UTC)
 * I agree with Carl. I am planning on completely rewritting the article focussing on what "intuitively" one thinks as a constant, not what "technically" a constant is. Because 5.68745 is indeed a constant, so is f(x)=12, but these are not very interesting ones. People expect (and I indeed find it more natural) to have an article on "universal constants", those that crop up all the time. Randomblue 16:35, 30 November 2007 (UTC)
 * But please keep in mind that there are other common uses of the word "constant", especially "constant array of small ints", but also as a first name and as a last name. The paragraph about disambiguation makes no sense in an article called numerical constant, but because of the redirect from constant it cannot be removed. That's why I would have been more happy with the situation before the move. But it's not a big thing, and you are certainly right about the way the word is normally used. Btw, I think this article has a lot of potential. I am glad somebody is working on it. --Hans Adler 16:52, 30 November 2007 (UTC)


 * We also have articles Mathematical constant and Physical constant, and I'd be in favour of having simple sections here, referring to these as the "Main articles".
 * As is not unusual on Wikipedia, the most elementary maths articles are the worst.
 * "Numerical constants are fixed numbers or values": are there any numbers or values that are not fixed?
 * "When specified, they represent mathematical or physical invariants": anyone care to reveal what the invariant is represented by the Euler-Mascheroni constant?
 * "When unspecified, constants indicate classes of functions all equal up to a constant": what is that supposed to mean? In the problem statement: "What is the volume of a cone of height h whose base has an area A?", what is the class of functions indicated by h?
 * "Emphasis will be given to those that appear both in mathematics and science": Like which ones? 0 (number)? The appearance of mathematical constants in physical formulas simply reflects the use of mathematical models such as Euclidean space.
 * --Lambiam 21:39, 30 November 2007 (UTC)


 * I fixed some really bad things, such as a statement that "the metre is only defined to a certain amount of significant figures, and any increase in the precision of the measurement of the speed of light would refine its definition". But I have a major problem with the move. I don't think that the physical constants, such as the speed of light or the Planck constant, are numerical constants. We use numbers to specify their values in given units of measurements, but the numerical values are just as arbitrary as the choice of the units, except for a few dimensionless quantities, and these numerical values are not the physical constants.
 * The term "numerical constant" is used in diverse contexts, without being tied to what we think of as mathematical constants (or physical constants), for numerical values for parameters in a class of models giving a good fit. See for example these uses:, , , and .  --Lambiam 22:59, 30 November 2007 (UTC)
 * Shame on me for giving weak arguments why the move was a bad idea and never once thinking about the physical constants in the article. In this light I must say that I would prefer the article to be moved back. --Hans Adler 23:51, 30 November 2007 (UTC)
 * I noticed that many links to Constant were not at all about numerical constants, and so I've moved it back to Constant. I've also expanded Constant (disambiguation) (please review, revise and expand), and made Numerical constant for now redirect to that. The article Constant, if it is kept at all (why not a redirect to Constant (disambiguation)?), should be completely rewritten and not attempt to cover all possible quite disparate uses of the term "constant"; most of the material that is worth keeping at all should be treated in more specialized articles such as Mathematical constant. --Lambiam 13:42, 1 December 2007 (UTC)
 * Thanks for taking the initiative. By the way, does this make any sense: "A mathematical constant is a quantity [...]"? That's what Mathematical constant claims. I am familiar with quantities in physics, but I have no idea what it's supposed to be in mathematics. And the article on Quantity (which applies the term to mathematics) doesn't help, either. The editor who first used this word seems to come from the natural sciences side. Has this been wrong for 5 1/2 years? --Hans Adler 14:25, 1 December 2007 (UTC)
 * Thank you guys for discussing my actions. I'm quite new to wikipedia and didn't expect such a response! Lambiam doesn't seem very happy with what I have done so far. What do you others think? Please comment here or in the constant article talk page. Randomblue 16:30, 4 December 2007 (UTC)

Template:WikiProject Mathematics
This is currently a redirect to maths rating. I think it should be deleted - it encourages 'flag planting' instead of actually rating articles. There's no need to tag talk pages since the List of mathematics articles already lists all the math articles. &mdash; Carl (CBM · talk) 15:59, 4 December 2007 (UTC)


 * I agree. I guess it was created (recently) for consistency with other WikiProjects. Instead they should be encouraged to adopt the "rating" approach :-) Geometry guy 21:16, 4 December 2007 (UTC)

Visualization project
At the suggestion of Sj, I am exploring the possibility of creating a Wikipedia Visualization Project to allow Wikipedia to take advantage of the Wolfram Demonstrations Project resources and similar Internet resources for scientific and mathematical visualization. Wikipedia already makes extensive use of MathWorld which is hosted on the Wolfram Research website.

Sj, who is also associated with the One Laptop Per Child project, communicated with Theodore Gray at Wolfram Research and persuaded the company to change its license to allow screenshots and some related materials on the Wolfram demonstrations project to be GFDL-compatible. As is noted on my Wikipedia entry, I consult for Wolfram Research.

The Wolfram Demonstrations Project is a professionally published site with an editorial screening process. The site already contains over 2,000 demonstrations created using Mathematica, on such topics calculus, physics, biology, astronomy, and such.

Are there other similar GFDL-compatible sites that should be added to the scope of such a visualization project? Are there Wikipedians interested in the subject of visualization who would be willing to help? --Pleasantville (talk) 22:31, 26 November 2007 (UTC)


 * We do have a sub-project WikiProject Mathematics/Graphics which may fit the bill.
 * A quick look at the Wolfram terms of use it seems like the demonstrations are not full GFDL, so it may be worth raising this at Wikipedia talk:Copyright problems to find out if this is. I could not find any reference to GFDL on the site. --Salix alba (talk) 00:00, 27 November 2007 (UTC)


 * Some of those may inspire good mathematics pictures for Wikipedia (not necessarily done with mathematica). If anybody can think of any figure there for which we'd need something similar, I (and I think other people) can try to make them. Oleg Alexandrov (talk) 07:43, 27 November 2007 (UTC)


 * In response to Salix alba, it appears that after all the discussion of selecting the right type of Creative Commons license, the Terms of Use have not yet been modified on the site. I've asked why that hasn't been changed yet. --Pleasantville (talk) 13:12, 27 November 2007 (UTC)

Personally, I deplore the fact that much of mathematics software is proprietary, and not open to public examination, use, development and maintenance. Now, I am not a Free-software purist; I can live in a middle ground. However, Wolfram has no track record at all in aiding and assisting the Free software world; it would be highly inappropriate to mount a project that is essentially a commercial promotion for the increased use of thier software. linas (talk) 15:00, 27 November 2007 (UTC)
 * Nothing wrong per se with promoting one's software. :) And their gallery gave me ideas for at least of couple of pictures we could use on Wikipedia. Oleg Alexandrov (talk) 16:20, 27 November 2007 (UTC)

The new improved Terms of Use on the Wolfram Demonstrations site ( a combination of one of the Creative Commons licenses & and the MIT license) should be up by tomorrow. --Pleasantville 18:26, 3 December 2007 (UTC)

Revised Terms of Use for demonstrations.wolfram.com. Here we go. I believe these are GFDL-compatible: Terms of Use The Wolfram Demonstrations Project ("this Site") is an informational resource made freely available by Wolfram Research.

All content on this site is licensed under the Creative Commons Attribution - Noncommercial - Share Alike 3.0 Unported License. By accessing the site or using it in any way, you accept and agree to be bound by the terms of this license. If you do not agree to these Terms of Use, you may not use this Site or content obtained from this Site. Wolfram Research reserves the right to change, modify, add to, or remove portions of these Terms of Use at any time without notice. Please refer back to this page for the latest Terms of Use.

A summary of the licensing terms can be found at: http://creativecommons.org/licenses/by-nc-sa/3.0

The full legal code can be found at: http://creativecommons.org/licenses/by-nc-sa/3.0/legalcode

In addition, the preview animations of each Demonstration, the pop-up snapshots, and the images available after clicking "Link to this Demonstration" are also licensed under the MIT License. The MIT License allows unrestricted use provided that the copyright notice is preserved. We encourage the use of the aforementioned items in educational resources around the web, for example on Wikipedia and university websites.

The full text of the MIT License can be found at: http://www.opensource.org/licenses/mit-license.php Please have a look and tell me what you think. --Pleasantville (talk) 21:26, 4 December 2007 (UTC)


 * Any image or media licensed with the MIT license is fine here; use MIT on the image page. The CC-BY-NC-SA is not fine, because of the 'NC' which means 'no commercial reuse'. For better or worse we don't permit the NC restriction. But we can link to it as an external link, and use the MIT licensed preview image here. &mdash; Carl (CBM · talk) 13:15, 5 December 2007 (UTC)


 * Which is actually an OK situation as the preview animations/single screenshots would be the the only sort of media we might be interested in. Other media types such as the mathematic-notebook applications would create a lot of technical and legal problems (lack of free reading software). One slight problem is the the notebook source code is cc-by-nc-sa, so its not possible to create derived works (say slightly different animations) from these and place them on wikipedia. I believe the reason why the nc part is not acceptable is that wikipedia is mirrored by commercial organisations so nc media would limit others ability to mirror the full wikipedia content. Anyway nice one for doing the work it getting these mathematica to go with these more open licences. --Salix alba (talk) 14:13, 5 December 2007 (UTC)


 * I would be happier if the description text for each visualization were also under an MIT license. Other than that, this looks good to me.  Let's hear it for scale-free living through clean licensing. +sj + 09:31, 13 December 2007 (UTC)

Isn't the subject of Math a science?
Math is one of the many Sciences (others being, chemistry, physics, biology, geology, etc....) just curious -- Storkian aka iSoroush Talk  23:43, 3 December 2007 (UTC)
 * This is controversial. See talk:mathematics/Archive 5 for what some Wikipedians think, and why. --Trovatore 23:52, 3 December 2007 (UTC)
 * Some say that mathematics is a science. Others say that it is an art. I say that it is a religion. --Ramsey2006 00:00, 4 December 2007 (UTC)
 * It is a science, an artform, and a religion. Aint that cool? Geometry guy 00:11, 4 December 2007 (UTC)
 * Yes, all of these are descriptions of the same elephant by different blind men [[image:smiley.svg || 15 px]] Arcfrk 00:33, 4 December 2007 (UTC)

I consider mathematics to be one of the humanities. Like philosophy, which I would consider its closest relative. Clearly, mathematical physics or applied PDEs or economics are social sciences or sciences, but they aren't properly mathematics (in the sense that analytical number theory is number theory that happens to use analysis, these are subjects that happen to use mathematics). The fact that mathematics are so useful in the sciences does not necessarily mean that they themselves constitute a science. --Cheeser1 01:40, 4 December 2007 (UTC)


 * Every definition of science is either subjective (in which case everything is a science) or it refers to the study of empirical evidence. In mathematics this is done very infrequently. Now ask if the ironically named computer science is a science. Skippydo 01:44, 4 December 2007 (UTC)


 * Mathematics is a science in the widest sense of the word, since it is a systematic body of knowledge. However, it is a formal science, which is a category distinct from the natural sciences of chemistry, physics, biology etc. and the social sciences of economics, sociology etc. The frequent assumption that the natural sciences are the only sciences causes confusion here. Gandalf61 09:58, 4 December 2007 (UTC)


 * The last sentence is correct. However the question can be rephrased "is mathematics a natural science?" or "is mathematics an empirical science?", and these versions also are controversial. If you see mathematics from a realist perspective, as discussing non-physical objects that truly exist independently of our reasoning about them, then it's not absurd to see mathematics as a natural, empirical science that attempts to discover the properties of these objects, in a similar way that physics tries to determine the properties of physical objects we can't see or taste. --Trovatore 16:48, 4 December 2007 (UTC)


 * Nevertheless, the objects that are studied in physics and the other natural sciences are physical objects, whereas the objects that are studied in mathematics are not physical objects (even though we may grant them an abstract Platonic existence). This is the key distinction between the natural sciences and the formal sciences. Gandalf61 17:05, 4 December 2007 (UTC)


 * No, I don't agree. That's the distinction with the physical sciences. Natural science is not necessarily the same as physical science. --Trovatore 17:26, 4 December 2007 (UTC)


 * No, physical science, by convention, means a non-biological natural science. It would be more logical if physical science were synonymous with natural science, but that's not how the terminology has evolved. Gandalf61 17:33, 4 December 2007 (UTC)


 * No, it would not be more logical if physical science were synonymous with natural science, because that would imply that what is not physical is thereby not natural. How are mathematical objects, granted that they exist, not part of nature? I suppose you could claim that they're supernatural, but that's not really what I personally think of when I use that word.
 * Just where the edge of the "natural" lies I'm not sure; I can't really accept the definition of naturalism that Maddy uses, which is effectively a methodological one, but I don't have a good definition of my own either. But I will say that it's not about whether the object has a spatiotemporal extent or mass-energy. --Trovatore 18:28, 4 December 2007 (UTC)


 * Well, if you want to use your own definitions then that is your prerogative. However, with the standard definitions the natural sciences deal only with physical objects and physical phenomena and so mathematics is not a natural science. I don't see how that can be at all unclear or controversial. Gandalf61 (talk) 21:49, 4 December 2007 (UTC)
 * I don't actually recall ever seeing (except maybe in the WP article) any requirement that natural sciences deal only with physical objects and physical phenomena. As far as I know they deal with natural objects and natural phenomena. I sense that maybe you're coming at this with a preconception that physical objects have some preferred status; that they're somehow more "real" than non-physical objects? --Trovatore (talk) 22:13, 4 December 2007 (UTC)
 * No, it's not just a WP definition. "Natural science - any of the sciences (as physics, chemistry, or biology) that deal with matter, energy, and their interrelations and transformations or with objectively measurable phenomena" Merriam_Webster Online; "Natural science - the sciences involved in the study of the physical world and its phenomena" WordWeb Online. Standard definition. Mathematics is not a natural science. End of story. I have no interest in debating metaphysics. Gandalf61 (talk) 12:01, 5 December 2007 (UTC)
 * Hmm, well the metaphysics is the interesting part. Looks like you're right about the dictionary definitions; it's too bad though, as it's not what "natural science" ought to mean -- it seems to create a category that privileges things with spatiotemporal extent and mass-energy without having to debate whether they should be privileged. --Trovatore (talk) 18:31, 5 December 2007 (UTC)


 * Well isn't it a good thing, science just relates to one particular universe, whereas mathematics relate to all possible universes. --Salix alba (talk) 18:41, 5 December 2007 (UTC)


 * The OED contains a similar definition: "The branch of knowledge that deals with the natural or physical world; a life science or physical science, such as biology, chemistry, physics, or geology." -- Dominus (talk) 15:34, 5 December 2007 (UTC)


 * Mathematical objects are figments of the imagination. Perhaps this means that mathematics is a subdicipline of psychology? --Ramsey2006 19:40, 4 December 2007 (UTC)
 * L. E. J. Brouwer, who was fond of taking his ideas to their extreme consequences, was a proponent of that classification, but as far as I know none of his followers has defended this position. --Lambiam 01:18, 5 December 2007 (UTC)


 * There are real issues that people discuss when asking "Is mathematics a science?" Regardless of their definition of science, unless they are asking a contentless question, they are asking if mathematics has property X. Often they may be asking something such as X = scientific method or empiricism or whatever.


 * There is something odd about how many people assert that the empirical investigation of prime numbers is somehow not "empirical" the way the study of photons is. Or how dark energy, and the like, is somehow considered more physical than sphere packings.  On the other hand, there's something undeniably natural about making this kind of distinction.  Mathematics is able to accomodate people with both kinds of feelings so some people don't have to decide either way.  --C S 17:53, 4 December 2007 (UTC)


 * I think it's a very bizarre exceptional form of empiricism though - if I were to do a mathematical experiment (à la Doron Zeilberger ), it would certainly be investigative and experimental. I do this relatively frequently (I am a combinatorialist), but the interesting thing is that my empirical data is generated by things that are imagined and that do not exist. Empirical investigation is, when I think of it, usually something you measure physically or observe about a real-world object. However, empirical mathematics are not so. In a sense, it's applying a scientific method to mathematics (which may or may not make mathematics a part of the sciences). --Cheeser1 (talk) 21:37, 4 December 2007 (UTC)


 * Math participates in the natures of Science, Engineering, Philosophy, and Art. Science: consider a measurement made of the ratio of the circumference of a circle to its diameter, made with telescopes and atomic clocks. Compute one more digit of pi than is given by the accuracy of the measurement. Predict. Wait for one more digit in a future measurement. Hypothesis confirmed. So the Scientific Method can apply to math, and in a sense, the number pi is "real", even if Transcendental :-) Engineering: Science is figuring stuff out, engineering is making machines that reliably fulfill your design intent. Kepler was a scientist, an aerospace engineer building a moon rocket is an engineer. Lot's of math has been engineering, in that sense, for centuries. I don't have to squeeze my brain or have an insight to apply the Quadratic Formula to a quadratic; plug and chug. Art: that's the part where we don't know what we're doing, and generally in math don't write about it. We only publish when we have facts, and the art is lost, but we've all experienced the artistic struggle from before we got the facts. And finally math is something unto itself; that notion of applying to all universes, and not just the natural one, mentioned by Salix alba. "Is math science?" is not a good yes/no question, but it's a good question. Pete St.John (talk) 21:41, 5 December 2007 (UTC)

Constant article
User:Oleg Alexandrov suggested I came here for insightful comments on the constant article I'm working on. I've basically rewritten most of the article, do you think I'm on the right track? Randomblue (talk) 21:00, 6 December 2007 (UTC)

Wallis product
Would someone be so kind and have a look at the "wrong proof". Thanks --Meisterkoch (talk) 16:21, 8 December 2007 (UTC)
 * The portion of the proof which "derives" the Euler-Wallis formula for $$\sin(x)$$ is incorrect, but the formula itself is right. It is valid to insert $$\pi/2$$ into that formula and equate both sides, and since the infinite product converges it is also valid to take the inverse of both sides and equate them.  So the proof is "right", but presented in a rather uninformed, naive way.  Also, Wallis' formula has an elementary proof using integration by parts.  I will correct what is there but I do not advocate adding the second proof; it is not of encyclopedic value and I'm not sure about the one that's there either.  It at least has the virtue of being entertaining. Ryan Reich (talk) 16:45, 8 December 2007 (UTC)
 * ;-). Thanks --Meisterkoch (talk) 16:48, 8 December 2007 (UTC)

Lists of mathematics topics issues
See talk:Lists of mathematics topics and Featured list removal candidates/Lists of mathematics topics.  Th e Tr ans hu man ist   22:28, 10 December 2007 (UTC)

A-class rating
I removed Homotopy groups of spheres from WikiProject_Mathematics/A-class_rating today; it isn't A-class yet but the comments show it is getting close. Meanwhile Pi is a new candidate, nominated by Disavian. This is obviously an extremely important article for a general encyclopedia. Give it a read to see how far it has come.

Although it's a relatively low-volume process, the A-class rating system gives detailed peer review about mathematics articles by editors who are familiar with the topic, without the hassle of the featured article process. I hope more editors will take advantage of it. &mdash; Carl (CBM · talk) 16:46, 11 December 2007 (UTC)

Mathematical logic
With help from Hans Adler, I have been working on a major expansion of Mathematical logic. If you have interest or expertise in the area, and the time to read through it, I would appreciate any suggestions you have to fill out the coverage or improve the exposition. &mdash; Carl (CBM · talk) 20:32, 11 December 2007 (UTC)

Wieferich prime and WAREL
Can anyone confirm what Silverman actually proved from the abc Conjecture? The consensus seems to be:


 * for any positive integer a &gt; 1, there exist infinitely many primes p such that p² does not divide ap &minus; 1 &minus; 1.

but WAREL quotes


 * there exist infinitely many primes p such that p² does not divide 2p &minus; 1 &minus; 1.

(In either case, we need to revert that idiotic superscript 2 character to 2 . Is it possible for an AWB substitution to select those?) &mdash; Arthur Rubin |  (talk) 18:02, 12 December 2007 (UTC)


 * Well, block him first, and we can discuss if he is right later. :) Seriously, it is highly unlikely he is right, and he has shown to be a very poor expert in mathematics (one of his recent claim was that any integral domain was a division ring). I suggest that when in doubt his edits be reverted, just to keep on the safe side. Oleg Alexandrov (talk) 05:43, 13 December 2007 (UTC)


 * What a persistent edit warrior! Surely there is a pretty solid case for an extended or indefinite block at this point, no? —Cronholm144 06:02, 13 December 2007 (UTC)


 * His actual accounts (except WAREL) have been indefblocked as sockpuppets. (I think the explanation for some of the sockpuppets is that he forgot the password to WAREL.  After all, it may be an English word, and it's clear he doesn't understand English.)   At least one admin believes this IP to be in SoftBank's dynamic pool, even though all edits from the IP have been in WAREL's style, so it can't be indefblocked.  WHOIS says "status:       ALLOCATED PORTABLE".  I suppose we could ask SoftBank whether it's static or dynamic by filing an abuse report....  &mdash; Arthur Rubin |  (talk) 18:00, 13 December 2007 (UTC)
 * Oleg was the last to block WAREL, back in '06. &mdash; Arthur Rubin |  (talk) 18:03, 13 December 2007 (UTC)


 * Ick. Is WAREL really annoying enough to go through the trouble of filing such a report? Or is the policy of revert->block->ignore enough? —Cronholm144 18:12, 13 December 2007 (UTC)

Mathematical & Computational Biology
Some users are talking about starting a Wiki Project for mathematical biology, e.g. in user space this tentative project page. I added math to the list of related projects. On account of my interest in convergence phenomena in self-adapting genetic algorithms, I'm a big believer that we can suck up their wisdom the way we have leeched physicists for centuries :-) Pete St.John (talk) 17:35, 13 December 2007 (UTC)

List of triangle topics
After being in unsatisfactory form as a subpage of a user page for a long time, the list of triangle topics is now an article, no longer a red link within the lists of mathematics topics. Of course it could still use improvement, so work on it! Michael Hardy (talk) 01:30, 14 December 2007 (UTC)
 * I merged the page history from User:DavidCBryant/List of triangle topics into List of triangle topics. The page history is not that important, but it is nice to have. Oleg Alexandrov (talk) 06:25, 14 December 2007 (UTC)

Mathworld Wolfram Demonstrations Project images
Having more math images is great. However, I would disagree with images (and captions) as on the right (taken from the chain rule article). It is basically an advertisement for the Wolfram Demonstrations Project. If the mathematica people are sincere in their desire to help with math images they could as well remove the ugly software controls and limit themselvs to acknowledgements in the image page itself. Comments? Oleg Alexandrov (talk) 04:45, 14 December 2007 (UTC)


 * Wow. Yeah. This should not be a place for Mathematica/Wolfram to show off. I use Mathematica constantly, and appreciate the availability of alot of cool images, but this is really not the place to showcase all the fancy new features of Mathematica like that. Cropping the image would make it much more reasonable. --Cheeser1 (talk) 04:59, 14 December 2007 (UTC)


 * I agree. Actually, in this particular case, I can't see what this image is doing in the chain rule article in the first place. Does the static image really illustrate the chain rule in a way that helps with understanding for the reader? What is the point being made here? What understanding of the chain rule is the reader supposed to be absorbing by gazing upon this particular image? I think that a useful image for this article would have to be more carefully thought out, and be presented with surrounding text to explain the point about the chain rule that is being illustrated. --Ramsey2006 (talk) 05:05, 14 December 2007 (UTC)


 * The mathworld images are released under the mit license, which allows use, copy, modify, merge, publish, distribute, sublicense, and/or sell, as long a copyright information is retained. So there is nothing to stop us cropping the image to remove the wolframe ad at the bottom and the sliders at the top which serve no purpose as a static image.--Salix alba (talk) 08:13, 14 December 2007 (UTC)


 * I also note the images are currently incorrectly tagged as Category:Creative Commons Attribution-ShareAlike 3.0 images, there not released under that licences its cc-at-nc-sa (non free). I've changed a couple to use, other still need to have correct licence tag. --Salix alba (talk) 08:37, 14 December 2007 (UTC)


 * I agree with Ramsey that in this case, the image does not seem helpful in explaining the chain rule, and thus I removed it from the article. Generally, such images should be cropped. -- Jitse Niesen (talk) 12:55, 14 December 2007 (UTC)

For clarification, it is not the MathWorld license that is at issue. That has not changed. It is the Wolfram Demonstration Project license that has been altered to accommodate Wikipedia. I left controls in because they show what parameters are at issue. --Pleasantville (talk) 13:19, 14 December 2007 (UTC) What I am trying to work out is the details of how Wikipedia can take advantage of the license change, and I have made a number of suggestions to Wolfram based on my experience yesterday and the day before about how Wolfram could do things differently to make it easier for someone from Wikipedia with 1/2 and hour to spare to find something useful on the Demonstrations site and find the right spot for it. Here are the issues that have come up so far. (Feel free to add to this list; changes can be made.)

1. Navigation within the site: It is not instantly obvious that the gray words on the background of the Demonstrations splash page are clickable links to subject areas. There is an index to the complete list of demonstrations, but it is in tiny gray letters at the bottom of the page. There is also a search feature, but it seems to me that blind searches are less-than-optimal way of finding illustrations for specific Wikipedia pages. I have raised this issue with Wolfram and am told a better navigation system will be in place by the end of January.

2. Size: The images on the WDP site tend to be bigger than 400 pixels wide. When shrunk so that they would reasonably fit on a Wikipedia page, often the type is hard to read. I'm not sure what the solution is.

3. Labeling: Because these are computer models, often important tags are embedded in the gray Manipulate interface Oleg was complaining about. In principle, the Manipulate interface can be cropped out, but then somehow the tags need to be reintroduced, either via the caption (which may not always work) or via work in something like Photoshop. Also, as noted in 2, if the graphic is smaller than a certain size, the text on the graphic may not be legible. I'm not sure what the solution is.

4. Still images vs. animation: in some cases, the information conveyed by the demonstrations is conveyed by motion, and still images do not capture it. This might be solved by miniaturized animated gifs, but creating those may be up to Wikipedians. I'm not sure that Wolfram would be willing to create and post those on a large scale.

5. Finding good matches between specific demonstrations and specific Wikipedia articles. It seems to me that the thing Wolfram could do that would be most helpful to Wikipedia would be to make it easy to match up demonstrations and articles. Better navigational tools on the Demonstrations site would help, but wouldn't completely address the issue. I made a first crack at it here by pasting in all the names of published demonstrations formatted so that the names would link to Wikipedia pages of the same name if such pages existed. There are maybe a hundred overlaps. But I think this could be done a lot better.

Is there a centralized list of articles needing illustrations? Or could a wishlist be created? That would probably also be helpful in creating a system that would make it easy to find good matches. Pleasantville (talk) 14:29, 14 December 2007 (UTC)

I've had a go at cropping the above image for demonstration/discussion purposes.

As for requested picture Requested pictures/Science/WikiProject Mathematics/Graphics is where they should (in theory) appear, however there are none. There are a few in Category:Wikipedia requested images for example Talk:Lissajous orbit (more physics than mathematics). This lack of formal requests should not be taken as an indication that there is no need for pictures, as there are many many mathematics articles lacking any sort of illustration. --Salix alba (talk) 15:16, 14 December 2007 (UTC)


 * I have begun to raise the issue of type size with Wolfram.


 * Also, it occurs to me that it would be possible to have images created by Wikipedians in Mathematica where a full animated/notebook version would be hosted on the Demonstrations site as a Demonstration. I know that there is a submission and editorial process for the Demonstrations site, though I don't know the details since I've had no involvement in that. But in principle, it seems to that this could potentially add additional functionality to images created by Wikipedians who have the use of Mathematica. --Pleasantville (talk) 15:23, 14 December 2007 (UTC)

"Natural mathematics"
If you weren't having enough AfD fun already, I happened to notice that the page Natural mathematics seems a little, well, confused. As elaborated at further length here, there's reason to suspect it's a work of, er, fractured ceramics. Somebody more familiar than I with the philosophy of mathematics might be better able to tell if there's content there worth salvaging.

Cheers, Anville (talk) 19:33, 16 December 2007 (UTC)


 * Salix Alba has taken it to AfD. I was about to prod it with notification to the original author and Gregbard, who tagged the article talk page with the WikiProject Philosophy banner. The question is, are there reliable secondary sources that support notability? Geometry guy 19:57, 16 December 2007 (UTC)


 * Notability issues may be confused by other topics being discussed under the same name; I believe there's a concept in children's mathematics education which goes by the same name . Anville (talk) 21:19, 16 December 2007 (UTC)

Requested move Boolean logic in computer science → Boolean logic
A requested move Boolean logic in computer science → Boolean logic  is being discussed here. --Lambiam 22:50, 17 December 2007 (UTC)

Totient function/Proofs is at AfD here
There was some discussion of proofs here a few weeks ago so I thought people might be interested in this one. Ben 04:52, 15 December 2007 (UTC)


 * I've also nominated Boy's surface/Proofs, AfD. --Salix alba (talk) 09:23, 15 December 2007 (UTC)


 * I am somewhat torn about these. Obviously proofs are crucial for mathematics. But to what extent are they implied by the mission of Wikipedia? It seems to me that proofs are covered by the mission when they are "encyclopedic" - but what should that mean? Can we arrive at some agreement here about criteria that can be used to judged whether a certain proof is reasonable for a reference encyclopedia? &mdash; Carl (CBM · talk) 14:30, 15 December 2007 (UTC)
 * I think it very much depends on the individual proof. To a certain extent wikipedia follow a case law system and these AfD will help us decide the criteria for proof articles. Standard AfD procedures can be applied, are there exteral references to the particular proof. For the totient function, I think was was probably taught it in college and similar proof could be found in numerous text books. For Boy's surface this proof may be only be found in one paper and the are no reference to verify this. --Salix alba (talk) 16:07, 15 December 2007 (UTC)


 * Proofs in an article are encyclopedic when they add value to an article with distorting the balance. They often are good content in my opinion. Separate proof articles are encyclopedic when they are self-contained and notable. The whole proof "subpages" story was a worthwhile experiment (now more than two years old), which was successful in separating detailed proof from article content, but (in my view) unsuccessful at producing good articles on proofs. The "subpage" idea just encourages bad writing, in which statement and notation from the main page is assumed. Lets be bold, and convert these so-called subpages into proper articles, where this has merit, and merge or delete them where it does not. Geometry guy 23:28, 15 December 2007 (UTC)


 * A good example, to my mind, is Proof that 22 over 7 exceeds π. It provides sources for why this proof (and not just the fact that it is a proof of) is important, starts with a quick summary of the proof, goes through the proof carefully and clearly, describes an extension of the proof idea that provides a quick and more accurate approximation, and gives some history of the use of this proof idea as part of a contest problem. In contrast, the two ".../Proofs" articles consist solely of the "going through the proof" part and do not make any attempt to set these proofs in context. Also note that the &pi; article has a proper name that leads one to expect an article that stands on its own. Viewed as standalone articles, the two ".../Proofs" articles fail to assert notability of the proofs per se, and therefore could plausibly be considered candidates for A7 speedy deletion. —David Eppstein (talk) 00:11, 16 December 2007 (UTC)

Mathematicians, PLEASE weigh in on this one. Deletion is being urged on the grounds that an encyclopedia should not contain mathematical proofs. Michael Hardy (talk) 21:12, 15 December 2007 (UTC)
 * Yeah, but a consistent pattern of offending opponents is probably even worse than ignorance. Oleg Alexandrov (talk) 00:54, 16 December 2007 (UTC)


 * Yes, I mentioned that on that page to those who were offending opponents. Michael Hardy (talk) 03:21, 16 December 2007 (UTC)


 * Oh looks like we are famous Slashdot - Should Wikipedia Allow Mathematical Proofs?. We might want to check the AfD for outside votes. --Salix alba (talk) 15:17, 16 December 2007 (UTC)


 * Beetle B. commented at the AfD here. Geometry guy 15:25, 16 December 2007 (UTC)
 * I think including proofs in articles can be a powerful way of helping to ensure verifiability. Please, let's keep them. Shinobu (talk) 15:51, 16 December 2007 (UTC)

If proofs are not allowed, I'm going to start nominating every single article on Wikipedia for deletion. Proofs are nothing more than lists of facts that form a logical sequence. Which basically describes any worthwhile article on Wikipedia. Loisel (talk) 01:31, 17 December 2007 (UTC)


 * I share your frustration, but reading your comment brought into focus, for me, why the widespread panic and/or outrage here is excessive. When it is said, by opponents of proofs in Wikipedia, that they are not encyclopedic, they do not mean that a proof is inherently unencyclopedic.  What they mean, instead, is that in general, the proof of an encyclopedic fact need not be encyclopedic, for reasons of being (these reasons are my own; add any if you like):
 * Trivial or routine;
 * Neither trivial nor routine, but far too long to justify the inclusion of the whole proof just to get at the notable point;
 * Otherwise worthy, except not as worthy as another proof that either is, or could be, included already;
 * Too technical for Wikipedia.
 * I make it a personal practice not to get involved in any deletion debates (they make me too angry), but my personal opinion is that Totient function/Proofs is worthless for the first and fourth reasons above. Likewise, I would not advocate including the entire proof that the axiom of choice is independent of ZF, although it introduced the prize-winning technique of forcing; an outline is more than sufficient both to document the technique and its application, and is probably better writing than including the whole proof.
 * I just spent some time neatening up the proof of Bertrand's postulate, and I'm still not sure about it. But at least it's notable as a proof, having come from a book which exists to single out particularly slick proofs.  In general, I would say that unless a proof is notable specifically for being slick, there is no need to include all of it, because we are not a record of mathematics.  In an encyclopedia I expect to find information about a theorem, its context, its value, etc.  But the proof I can look up in the literature if I want it, and it will be better typeset.
 * The only reason that this (and related other) deletion debates are so galling is that they smack of arrogant interference by ignorant outsiders. However, cutting these deadwood proofs is hardly the first step down a slippery slope with no proofs at the bottom; good proofs with good articles are still protected by the normal Wikipedia standards, and the fact that they are proofs doesn't change that.
 * Conversely, however, we shouldn't try to argue that being irrefutable logic makes a proof automatically verifiable and exempts it from the requirements that other articles must satisfy to be good. We are not here to collect all true statements into a single Web site; we are here to collect and attractively present all of human knowledge.  There's a difference. Ryan Reich (talk) 02:07, 17 December 2007 (UTC)

Related issue: Are original proofs acceptable?
A related issue that comes up regularly concerns proofs, often elementary inductions, added to articles without crediting a source for that proof. I'm no longer convinced that this is a good idea, but here's an example of one I added myself, over a year ago: Fáry's theorem. If an article contains a proof, is it necessary that the proof adhere closely to one of the published proofs of the same result and be credited to a reliable source, or do we view proofs of this type as self-verifying? Obviously if a particularly clever proof can be attributed to someone, it should be, as a matter of good scholarship, but I am thinking here more about whether an uncredited proof should be viewed as original research and disallowed as such.

I note that Totient function/Proofs survived AfD without this issue really being directly addressed; it has since been sprinkled with fact tags, but those are for the individual assertions within its proofs, not for the provenance of the proof as a whole. —David Eppstein (talk) 19:55, 16 December 2007 (UTC)


 * I think the details of a proof are self-verifying. However, the proof should have an overall provenance. What is needed in this article is not a string of citations, but a couple of references to good number theory textbooks which contain these results. Geometry guy 20:08, 16 December 2007 (UTC)


 * In theory a proof could be self-verifying, but in practice how many of the proof of these articles have been checked? Could there be typo errors or even invalid assumptions. A reference adds to the verifiability of the article.

I've had a look though some of the proof articles: --Salix alba (talk) 20:54, 16 December 2007 (UTC) --Salix alba (talk) 20:54, 16 December 2007 (UTC)
 * Addition of natural numbers/Proofs - Proof using sucessor operations, no references
 * Approximation theory/Proofs - Hand wavy proof, by reference to a graph, no references
 * Proof of Bertrand's postulate - A proof appeared in Proofs from THE BOOK so high on the notability states.
 * Cardioid/Proofs - Fairly standard algebra, not particularly interesting as a proof. Unreferenced.
 * Chebyshev polynomials/Proofs - A little bit of calculus. Unreferenced.
 * Christoffel symbols/Proofs - Poor on context, hard to tell whats being proved as no theorem statements. unreferenced.


 * I think the original research policy is very clear on this. Original proofs are not allowed. Otherwise we will have no protection against a crank who wants to post a "self-verifying proof" of the continuum hypothesis, for example. Attempting to argue with such a person on the grounds of correctness will only lead to trouble. Perturbationist (talk) 03:07, 19 December 2007 (UTC)


 * Proofs of new results are no good, for the reason you just gave. On the other hand, a new exposition of a well-know result using a standard technique is probably fine. &mdash; Carl (CBM · talk) 03:11, 19 December 2007 (UTC)

Page protection of Talk:Carl Hewitt
Talk:Carl Hewitt has been protected, to supress this discussion. Is that appropriate? Comments? (I guess we need to comment here, since again, that talk page is protected). Oleg Alexandrov (talk) 05:08, 18 December 2007 (UTC)


 * I've started a discussion (in very unspecific terms) at Wikipedia talk:Biographies of living persons, which I think may be a more appropriate place for this. —David Eppstein (talk) 05:35, 18 December 2007 (UTC)


 * Update: has unprotected it, with conditions. See Talk:Carl Hewitt. JRSpriggs (talk) 01:38, 19 December 2007 (UTC)

Request for comments: "the" verifier or "a" verifier?
May I request your attention for the following burning question: should the verifier-based definition of NP-complete in the section Formal definitions for P and NP of P = NP problem use the definite article (the verifier) or the indefinite article (a verifier)? The discussion has stalled. See Talk:P = NP problem. --Lambiam 08:39, 22 December 2007 (UTC)

WikiProject Mathematics/Current activity
I added canonical representative to Requested_articles/mathematics a few days ago, and Jitse's bot has updated WikiProject Mathematics/Current activity since then, but my request doesn't appear on that page. Why is that? -- Dominus (talk) 03:02, 24 December 2007 (UTC)
 * It must have been a while back, the 4th Dec version had canonical representative and the Bot only adds requested articles from the last week or so. --Salix alba (talk) 10:26, 24 December 2007 (UTC)


 * My brain says I added it around 20 December, but the edit history says I didn't. Freaky.  -- Dominus (talk) 20:59, 24 December 2007 (UTC)

Hilbert Spaces and Fourier analysis
Season greetings! I have an article spotted on new(ish) pages patrol for you to consider. It's Hilbert Spaces and Fourier analysis. Thanks! --Malcolmxl5 (talk) 06:22, 25 December 2007 (UTC)
 * Thanks for finding it. I doubt the article has any value. If there's agreement on this, rather than going through AfD we could quietly redirect it to Fourier analysis. Comments? Oleg Alexandrov (talk) 06:29, 25 December 2007 (UTC)
 * It looks kind of like an essay, rather than an article for an encyclopedia. I'm not an analyst though, so I'm not sure. --Cheeser1 (talk) 06:32, 25 December 2007 (UTC)
 * Taking out the definitions, which belong in other articles, this would say: "The Fourier transform of a function is an element in an L2 space." Quite true; possibly worth saying in so many words in Fourier transform; but not an article. Do redirect. Septentrionalis PMAnderson 06:50, 25 December 2007 (UTC)
 * Isn't it better to phrase this as that the Fourier transform itself is a (unitary) operator on some such a space? It is a bit curious that our article Hilbert space suggests that Hilbert spaces are somehow important to Fourier analysis, but that the Fourier analysis article currently does not so much as even mention Hilbert spaces; I think the connection ought to be made.
 * Into such a space; the transform maps (part of) the space of functions into a different space, of countable dimension. But Lambiam's suggestion and mine are both moves to greater abstraction, which may not be desirable; our function is to communicate. Septentrionalis PMAnderson 21:35, 25 December 2007 (UTC)
 * Is it certain that all of the material in the article is either covered elsewhere or else not worth preserving? Is anyone here sufficiently familiar with the subject matter to make a definite statement on this? --Lambiam 13:42, 25 December 2007 (UTC)


 * Fourier series --Tom Tresser (talk) 14:06, 25 December 2007 (UTC)


 * Yes, all material of this article (minus errors) is covered elsewhere. But Lambiam made a valid point about the unsatisfactory state of both Hilbert space and Fourier analysis articles, which both lack an explanation of the connection. Also, I am a bit puzzled by the existence of two articles, Fourier analysis and Fourier series. Are they both legit? Are they well coordinated? Arcfrk (talk) 16:28, 25 December 2007 (UTC)


 * "Fourier Analysis is a large branch of mathematics whose point of departure is the study of Fourier series and integrals." J. Duoandikoetxea
 * --Tom Tresser (talk) 18:37, 25 December 2007 (UTC)

Salix alba for admin
I have nominated one of us, Salix alba, for adminstrator position. If you know Salix alba and would like to comment in the discussion, you can do so at Requests for adminship/Salix alba. Oleg Alexandrov (talk) 16:35, 17 December 2007 (UTC)


 * Salix alba's RFA ended successfully with 80 supporting opinions and no opposing opinions, which is a strong expression of confidence. &mdash; Carl (CBM · talk) 13:08, 25 December 2007 (UTC)

Example in the article Permutation group
I think, there is an invalid statement in the middle of the section Examples in the article permutation group. There is stated: G forms a group, since aa = bb = e, ba = ab, and baba = e. So (G,M) forms a permutation group. However nowhere is mentioned associativity of permutations, although there is ab = ba, which refers to commutative group. I'm only starting with group theory, so it might be correct, only I can't see how these properties imply associativity. Even if it is true, I think, it is a bit misleading. Please, somebody have a look at it. Thanks. --Tomaxer (talk) 00:03, 28 December 2007 (UTC)
 * Associativity is automatic, since G is contained in the permutation group on 4 letters, and composition of functions is always associative. Thus we just need to check that G contains the identity and is closed under composition and inverses. Algebraist 01:18, 28 December 2007 (UTC)
 * There is an issue - neither the permutation group article nor the symmetric group article seems to state explicitly that composition of bijections is associative. Does anyone want to take a stab at explaining it? Which page should it go on (both?) &mdash; Carl (CBM · talk) 01:28, 28 December 2007 (UTC)
 * It's mentioned at associativity, at least. Algebraist 02:08, 28 December 2007 (UTC)
 * Function composition also mentions the more general fact that composition of functions is associative. —David Eppstein (talk) 02:13, 28 December 2007 (UTC)


 * I've added a section "Product and inverse of permutations" to the article on permutations. Please review. --Lambiam 12:13, 28 December 2007 (UTC)
 * That's a natural place for it. I also added very brief paragraphs to the group articles. This is the sort of fact that writers are likely to take for granted but readers (especially if their prof has impressed the need to verify all the group axioms) may wonder about. &mdash; Carl (CBM · talk) 20:21, 28 December 2007 (UTC)

A simpler, more beautiful definition of mathematics?
As we have tried, and tried to improve mathematics education for elementary and secondary students, it is obvious that a simpler, humbler, more beautiful definition of mathematics is urgently needed. I am personally tired of trying to fit some of the narrow focused, often distracting, and often arrogant definitions I find at hand. Yes, we deal with forms. patterns, a language, and can discuss about structures being "pure" or "applied", but I am sure there are simpler ways of explaining the nature and high value of mathematics to our frustrated children and math-phobic adults. There is a great disservice being done today by much of the K-12 curriculum being defined by people who do not seem to understand the yearnings of common people to see the simpler meaning of things, precision, accuracy, reliable predictability, cost-benefit, and safety, among others. Mathematics, I believe is not "the language of god", as we sometimes want to define it, perhaps to give ourselves some self-improtance (talking like god?), but a useful tool that, pure or applied, is intended to be part of all our activities, sciences, arts, and religions, and make our lives easier, happier. I KNOW there are simpler definitions, but sometimes it feels like it will take another 100 years, before we can get off our high math horse - Last year I tried to suggest a new, more pragmatic addition to try to help on this, but that was removed (!!!) by Wikipedia. So far for contributive definitions.68.7.11.138 (talk) 00:51, 31 December 2007 (UTC)Felipe Razo]] 16:43, 30 December 2007 (UTC)
 * What was your contribution? As your IP address hasn't made prior contributions, and User:Felipe Razo doesn't seem to exist, I don't know what you're talking about.  &mdash; Arthur Rubin |  (talk) 00:55, 31 December 2007 (UTC)
 * It should also be pointed out that there are always simple, wrong definitions of mathematics and mathematical concepts. "Make everything as simple as possible, but not simpler."  &mdash; Arthur Rubin |  (talk) 00:59, 31 December 2007 (UTC)
 * OK, hard to chase this page editing tail format. I guess you are right, there are wrong, and oversimplified definitions, and that is NOT beautiful, you should know.  For some reason I feel that it is still hard to move out of the box on this issue, and I should not be wasting your, or my time anymore.  I will continue to do what is right and productive with my students.  Thank you for your attention. 68.7.11.138 (talk) 01:18, 31 December 2007 (UTC)Felipe Razo