Wikipedia talk:WikiProject Mathematics/Archive/2007/Dec

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. — Carl (CBM · talk) 02:28, 4 December 2007 (UTC)

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)

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)

#proposed deletion 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. — 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)

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)

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. — 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)

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. — 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)

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 Wikipedia: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. — 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)

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#Poll 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 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)

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)

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 ${\displaystyle \sin(x)}$ is incorrect, but the formula itself is right. It is valid to insert ${\displaystyle \pi /2}$ 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)

See talk:Lists of mathematics topics#This article doesn't pass WP:VER and Wikipedia:Featured list removal candidates/Lists of mathematics topics. The Transhumanist 22:28, 10 December 2007 (UTC)

I removed Homotopy groups of spheres from Wikipedia: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. — Carl (CBM · talk) 16:46, 11 December 2007 (UTC)

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. — Carl (CBM · talk) 20:32, 11 December 2007 (UTC)