Knowledge talk:WikiProject Mathematics/Archive/2007/Dec

5195:

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 Knowledge. So far for contributive definitions.] 16:43, 30 December 2007 (UTC)

3079:

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.

1699:

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

4178:. 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 π 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. — 4369:, 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. 1278:(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 Knowledge, I don't think that would be allowed by Knowledge policies. It would have to be under a free license which allows everyone, not just Knowledge, to use, modify, and distribute the images. -- 2432:

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. --

47: 4402:. 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 4147:

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.

2187:, I am exploring the possibility of creating a Knowledge Visualization Project to allow Knowledge to take advantage of the Wolfram Demonstrations Project resources and similar Internet resources for scientific and mathematical visualization. Knowledge already makes extensive use of MathWorld which is hosted on the Wolfram Research website. 2529: 3837:, 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 Knowledge pages. I have raised this issue with Wolfram and am told a better navigation system will be in place by the end of January. 2020: 3652: 4324:

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 Knowledge, that they are not encyclopedic, they do not mean that a proof is inherently unencyclopedic. What they mean,

3848:

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

3829:

What I am trying to work out is the details of how Knowledge 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 Knowledge with

3015:

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

2724:

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

1333:

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

4119:

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

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5. Finding good matches between specific demonstrations and specific Knowledge articles. It seems to me that the thing Wolfram could do that would be most helpful to Knowledge would be to make it easy to match up demonstrations and articles. Better navigational tools on the Demonstrations site would

3204:

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.

3057:

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

2369:

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

2353:

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

1903:

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

1862:

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

1789:

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

1515:

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

2720:

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

2431:

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

1698:

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

1379:

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"

4146:

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

4097:

I am somewhat torn about these. Obviously proofs are crucial for mathematics. But to what extent are they implied by the mission of Knowledge? 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

3844:

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

3704:

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

3439:

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,

3078:

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.

2296:

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

1999:

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

1291:

I think the best thing we can do right now is wait for the results of the discussion on the German Knowledge. 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

5194:

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

4372:

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

3922:

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

4376:

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

5237:

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

4944:

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,

3025:

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

2610:

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

3683:

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

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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?

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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. --

2193:, 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 2611:

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. --

1922:

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.

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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. --

1325:

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

5168:

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. — Carl

3306:

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

1770:. 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? 1292:

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 Knowledge does not accept fair use pictures (probably for legal reasons), but of course that doesn't restrict us. --

2547:. 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 3483:) 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 4397:

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:

5072:, 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. -- 5097:

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?) — Carl

4429:

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.

1348:

It isn't German law. German Knowledge doesn't use nonfree images because they don't want to. We use them because there is no consensus on English Knowledge to get rid of them. The Wikimedia foundation allows each project to decide individually. — Carl

2200:

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.

1885:

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

2108:

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.

4868:

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.

3879: 5087:

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.

4308:

If proofs are not allowed, I'm going to start nominating every single article on Knowledge for deletion. Proofs are nothing more than lists of facts that form a logical sequence. Which basically describes any worthwhile article on Knowledge.

3578:. 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 :-) 1913:

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

2253:

Some of those may inspire good mathematics pictures for Knowledge (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.

3857:

by pasting in all the names of published demonstrations formatted so that the names would link to Knowledge 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.

2354:

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.

2799:

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"

2628:

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

2276:

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.

3814:

the MathWorld license that is at issue. That has not changed. It is the Wolfram Demonstration Project license that has been altered to accommodate Knowledge. I left controls in because they show what parameters are at issue.

1423:

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.)

2074:?), 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 4413:

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.

4445:

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

3923:

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. --

3575: 3249: 2565:

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

3902:(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. -- 2758:

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

2409:

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

4885:

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?

3205:

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.

1844:"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" 3840:

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 Knowledge page, often the type is hard to read. I'm not sure what the solution is.

2040:

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.

2204:

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?

2023: 3735:, 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.-- 3830:

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.)

3955:, 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. 2455:

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.

3861:

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.

1500:

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

70: 2777:

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

3845:

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.

1309:

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.

2944:

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." --

2687:, 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. 3791:

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. --

3339:. 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 2785:

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? --

1964:"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 2099:(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? -- 4055: 1338:

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? --

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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 (

3487:'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 2994:, 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. -- 4076: 3026:

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. --

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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

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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. --

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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. — Carl

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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

1164: 1109: 1050: 995: 940: 885: 830: 775: 720: 665: 610: 555: 500: 445: 390: 335: 280: 225: 170: 115: 25: 4707: 4692: 3053:), 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 63: 3174: 3292: 3202: 109: 105: 101: 97: 4524:

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

2826:

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"

1443:", 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). 5287: 1688:

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.

21: 56: 4601: 1268:. 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. 5019: 3985:, who tagged the article talk page with the WikiProject Philosophy banner. The question is, are there reliable secondary sources that support notability? 3891: 2221: 2166:

I agree. I guess it was created (recently) for consistency with other WikiProjects. Instead they should be encouraged to adopt the "rating" approach :-)

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software world; it would be highly inappropriate to mount a project that is essentially a commercial promotion for the increased use of thier software.

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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

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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 Knowledge.

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selected subcategories. The question is which, if any, subcategories (and if the parent itself) should be adopted under the umbrella of our project.

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Mathematicians, PLEASE weigh in on this one. Deletion is being urged on the grounds that an encyclopedia should not contain mathematical proofs.

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to mean -- it seems to create a category that privileges things with spatiotemporal extent and mass-energy without having to debate whether they

2144:. 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 4038: 3245: 1440: 17: 5037:

Salix alba's RFA ended successfully with 80 supporting opinions and no opposing opinions, which is a strong expression of confidence. — Carl

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mathematics). The fact that mathematics are so useful in the sciences does not necessarily mean that they themselves constitute a science. --

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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.

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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

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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. —

1649: 1983:? The appearance of mathematical constants in physical formulas simply reflects the use of mathematical models such as Euclidean space. 5269: 4456: 3656: 4824:

Taking out the definitions, which belong in other articles, this would say: "The Fourier transform of a function is an element in an

2888:

Well isn't it a good thing, science just relates to one particular universe, whereas mathematics relate to all possible universes. --

1957:"When specified, they represent mathematical or physical invariants": anyone care to reveal what the invariant is represented by the 5239: 4662:

May I request your attention for the following burning question: should the verifier-based definition of NP-complete in the section

4346:

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

4329:, the proof of an encyclopedic fact need not be encyclopedic, for reasons of being (these reasons are my own; add any if you like): 4029: 2232: 4175: 1877:

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

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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

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Mathematical objects are figments of the imagination. Perhaps this means that mathematics is a subdicipline of psychology? --

1846:. 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. 1645: 1404: 1376: 1368: 3952: 3458:

What a persistent edit warrior! Surely there is a pretty solid case for an extended or indefinite block at this point, no? —

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of economics, sociology etc. The frequent assumption that the natural sciences are the only sciences causes confusion here.

4335:

Neither trivial nor routine, but far too long to justify the inclusion of the whole proof just to get at the notable point;

3303:. This is obviously an extremely important article for a general encyclopedia. Give it a read to see how far it has come. 1629: 4810:

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. --

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is worthless for the first and fourth reasons above. Likewise, I would not advocate including the entire proof that the

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The Wolfram Demonstrations Project ("this Site") is an informational resource made freely available by Wolfram Research.

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I think including proofs in articles can be a powerful way of helping to ensure verifiability. Please, let's keep them.

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Ick. Is WAREL really annoying enough to go through the trouble of filing such a report? Or is the policy of revert-: -->

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Having more math images is great. However, I would disagree with images (and captions) as on the right (taken from the

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of the aforementioned items in educational resources around the web, for example on Knowledge and university websites.

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definitions of mathematics and mathematical concepts. "Make everything as simple as possible, but not simpler." —

4490: 3288: 2494: 1798:, which I put under "Geometry" and also under "Linear Algebra" (although I guess it's not true unless you're in a 1780:

I'm working on that, in alphabetical chunks. If someone could review my work when I'm done, that would be great. -

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criteria that can be used to judged whether a certain proof is reasonable for a reference encyclopedia? — Carl

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can become an article about the general concept, or a disambiguation page? I don't like the idea much. I think

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anymore. I will continue to do what is right and productive with my students. Thank you for your attention.

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There was some discussion of proofs here a few weeks ago so I thought people might be interested in this one.

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Math is one of the many Sciences (others being, chemistry, physics, biology, geology, etc....) just curious --

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on my talk page, I wonder, should we consider this category as part of mathematics? If yes, mathbot will add

4862:

article currently does not so much as even mention Hilbert spaces; I think the connection ought to be made.

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article I'm working on. I've basically rewritten most of the article, do you think I'm on the right track?

2019:), for numerical values for parameters in a class of models giving a good fit. See for example these uses: 5229: 5212: 4432: 4280: 4149: 4072: 3987: 3796: 3509: 3496: 3430: 3255: 2517: 2168: 2005: 1653: 1555: 1518: 1311: 4373:

still protected by the normal Knowledge standards, and the fact that they are proofs doesn't change that.

4358:; an outline is more than sufficient both to document the technique and its application, and is probably 3948: 3940: 5243: 4987: 4919: 3583: 3574:

Some users are talking about starting a Wiki Project for mathematical biology, e.g. in user space this

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vector space, which is getting towards analysis). Corrections and improvements are more than welcome. -

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Otherwise worthy, except not as worthy as another proof that either is, or could be, included already;

4120:

Boy's surface this proof may be only be found in one paper and the are no reference to verify this. --

4062: 1954:"Numerical constants are fixed numbers or values": are there any numbers or values that are not fixed? 5128: 5120: 5089: 5023: 4874: 4837: 4797: 4782: 4738: 4627: 4586: 4533: 4525: 4510: 4502: 4472: 4382: 4261: 4217: 4125: 4084: 3907: 3899: 3774: 3740: 3710: 3669: 3629: 3441: 3332: 3210: 3111: 3099: 2893: 2506:

Some say that mathematics is a science. Others say that it is an art. I say that it is a religion. --

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The term "numerical constant" is used in diverse contexts, without being tied to what we think of as

1924: 1868: 1864: 1828: 1767: 1615: 1582: 1472: 1425: 1293: 1269: 5132: 4645: 4605: 4415: 4179: 2839: 2817: 2790: 2768: 2478: 1795: 1752: 3759:, there not released under that licences its cc-at-nc-sa (non free). I've changed a couple to use 4815: 4399: 4294: 4235: 4202: 3924: 3862: 3816: 3693: 3606: 3336: 3325: 3063: 2804:; "Natural science - the sciences involved in the study of the physical world and its phenomena" 2485: 2381: 2328: 2278: 2206: 2063: 1948:, and I'd be in favour of having simple sections here, referring to these as the "Main articles". 1915: 1851: 1824: 1791: 1771: 1689: 1490: 1444: 1416: 1230: 1979:"Emphasis will be given to those that appear both in mathematics and science": Like which ones? 5018:

position. If you know Salix alba and would like to comment in the discussion, you can do so at

4773:

Season greetings! I have an article spotted on new(ish) pages patrol for you to consider. It's

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G forms a group, since aa = bb = e, ba = ab, and baba = e. So (G,M) forms a permutation group.

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My brain says I added it around 20 December, but the edit history says I didn't. Freaky. --

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existence). This is the key distinction between the natural sciences and the formal sciences.

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in the widest sense of the word, since it is a systematic body of knowledge. However, it is a

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Yeah, but a consistent pattern of offending opponents is probably even worse than ignorance.

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I think it very much depends on the individual proof. To a certain extent wikipedia follow a

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I think, there is an invalid statement in the middle of the section Examples in the article

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exceptional form of empiricism though - if I were to do a mathematical experiment (à la

4911: 4641: 3978: 3423:(In either case, we need to revert that idiotic superscript 2 character to <sup: --> 3368: 3126: 3051: 2835: 2813: 2786: 2764: 2726: 2688: 2659: 2634: 2612: 2598: 2594: 2586: 2498: 2231:

it seems like the demonstrations are not full GFDL, so it may be worth raising this at

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natural) to have an article on "universal constants", those that crop up all the time.

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video compression and you will see math. The Tree of Knowledge is not Totally Ordered.

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I'm surprised. Information theory is a part of probability theory. Shannon's paper "

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Fourier analysis and Fourier series. Are they both legit? Are they well coordinated?

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is where they should (in theory) appear, however there are none. There are a few in

3724: 3689: 3346: 3314: 3300: 3059: 2571: 2556: 2417: 2374: 2155: 1893: 1738: 1596: 1356: 1330:, so the arguments that something is fair use under American law may not carry over. 3597:

After being in unsatisfactory form as a subpage of a user page for a long time, the

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and go down, you can get to lots of articles that are clearly not mathematics, like

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also mentions the more general fact that composition of functions is associative. —

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Isn't it better to phrase this as that the Fourier transform itself is a (unitary)

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As is not unusual on Knowledge, the most elementary maths articles are the worst.

4481:- Fairly standard algebra, not particularly interesting as a proof. Unreferenced. 3947:

If you weren't having enough AfD fun already, I happened to notice that the page

3875:

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

3295:

today; it isn't A-class yet but the comments show it is getting close. Meanwhile

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a natural science. I don't see how that can be at all unclear or controversial.

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Yes, all of these are descriptions of the same elephant by different blind men

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However nowhere is mentioned associativity of permutations, although there is

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to find out if this is. I could not find any reference to GFDL on the site. --

1980: 2812:

a natural science. End of story. I have no interest in debating metaphysics.

2658:

sciences. Natural science is not necessarily the same as physical science. --

1260:

There is an interesting collection of photos of lots(!) of mathematicians at

5203:

your contribution? As your IP address hasn't made prior contributions, and

4354:

is independent of ZF, although it introduced the prize-winning technique of

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help, but wouldn't completely address the issue. I made a first crack at it

1664:

probably aren't (at least not with all subcats), and I'm not too sure about

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physical constants, such as the speed of light or the Planck constant, are

1554:. At least the latter seems mathematical to me - and it's a subcategory of 4710:

since then, but my request doesn't appear on that page. Why is that? --

4234:

Yes, I mentioned that on that page to those who were offending opponents.

1467:

says its within the scope of WikiProject Mathematics, so I guess it is! --

1266:

http://de.wikipedia.org/Portal_Diskussion:Mathematik#Biographien_und_Fotos

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Talk:P = NP problem#Request for comments: "the" verifier or "a" verifier?

4553: 4528:, for example. Attempting to argue with such a person on the grounds of 4116: 4101: 3488: 3484: 3342: 3310: 3103: 3027: 2413: 2151: 2096: 2067: 2055: 2051: 1919: 1889: 1882: 1859: 1855: 1847: 1820: 1592: 1352: 2087:

Thanks for taking the initiative. By the way, does this make any sense:

2054:

were not at all about numerical constants, and so I've moved it back to

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Knowledge:Featured list removal candidates/Lists of mathematics topics

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is incorrect, but the formula itself is right. It is valid to insert

3144:

The portion of the proof which "derives" the Euler-Wallis formula for

4733:

and the Bot only adds requested articles from the last week or so. --

1881:

article about advanced math. On the other hand, in the current setup

4377:

attractively present all of human knowledge. There's a difference.

2395:

Any image or media licensed with the MIT license is fine here; use

5207:

doesn't seem to exist, I don't know what you're talking about. —

3877: 3650: 3628:. The page history is not that important, but it is nice to have. 2528: 3951:

seems a little, well, confused. As elaborated at further length

3246:

talk:Lists of mathematics topics#This article doesn't pass WP:VER

1489:

Hang on a minute, everyone: we are not talking about the article

4979:

is the study of Fourier series and integrals." J. Duoandikoetxea

4023:

Requested move Boolean logic in computer science → Boolean logic

3491:

whether it's static or dynamic by filing an abuse report.... —

1380:

so that a few people can check it out and fix it up. Thanks! --

4828:

space." Quite true; possibly worth saying in so many words in

3425:. Is it possible for an AWB substitution to select those?) — 2941: 1231: 40: 2515:

It is a science, an artform, and a religion. Aint that cool?

5220:

It should also be pointed out that there are always simple,

3605:. Of course it could still use improvement, so work on it! 2008:, and these numerical values are not the physical constants. 4850:

on some such a space? It is a bit curious that our article

4604:, which I think may be a more appropriate place for this. — 3757:

Category:Creative Commons Attribution-ShareAlike 3.0 images

3755:

I also note the images are currently incorrectly tagged as

3367:

Can anyone confirm what Silverman actually proved from the

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

2365:

http://creativecommons.org/licenses/by-nc-sa/3.0/legalcode

4975:"Fourier Analysis is a large branch of mathematics whose 4465:- Hand wavy proof, by reference to a graph, no references 1842:

The justification that Randomblue gave for the move was:

4600:

I've started a discussion (in very unspecific terms) at

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suggests that Hilbert spaces are somehow important to

4256:. We might want to check the AfD for outside votes. -- 4254:

Slashdot - Should Knowledge Allow Mathematical Proofs?

1827:. I'd argue that the former name is better. Comments? 4658:

Request for comments: "the" verifier or "a" verifier?

3733:, merge, publish, distribute, sublicense, and/or sell 3182: 3150: 3102:

suggested I came here for insightful comments on the

5190:

A simpler, more beautiful definition of mathematics?

2337:

Revised Terms of Use for demonstrations.wolfram.com.

1794:, because there are two covered in the article; and 4452:I've had a look though some of the proof articles: 3601:is now an article, no longer a red link within the 2654:No, I don't agree. That's the distinction with the 4708:Knowledge:WikiProject Mathematics/Current activity 4693:Knowledge:WikiProject Mathematics/Current activity 3769:, other still need to have correct licence tag. -- 3504:Oleg was the last to block WAREL, back in '06. — 3196: 3168: 2375:http://www.opensource.org/licenses/mit-license.php 2373:The full text of the MIT License can be found at: 2357:A summary of the licensing terms can be found at: 2380:Please have a look and tell me what you think. -- 1972:?", what is the class of functions indicated by 32:Knowledge talk:WikiProject Mathematics/Archive 32 4459:- Proof using sucessor operations, no references 3981:it with notification to the original author and 3888:Knowledge:Requested pictures/Science#Mathematics 3563:", Journal of Number Theory, 30:2 (1988) 226-237 3293:Knowledge:WikiProject_Mathematics/A-class_rating 3125:Would someone be so kind and have a look at the 2721:what I personally think of when I use that word. 2359:http://creativecommons.org/licenses/by-nc-sa/3.0 3835:an index to the complete list of demonstrations 1652:are probably within the scope of this project; 4393:Related issue: Are original proofs acceptable? 3335:, I have been working on a major expansion of 2472: 2070:, if it is kept at all (why not a redirect to 2062:(please review, revise and expand), and made 1239:This page has archives. Sections older than 64: 8: 4706:a few days ago, and Jitse's bot has updated 4602:Knowledge talk:Biographies of living persons 3723:The mathworld images are released under the 3561:Wieferich's criterion and the abc-conjecture 3058:make mathematics a part of the sciences). -- 2593:of chemistry, physics, biology etc. and the 2551:analysis, these are subjects that happen to 2497:for what some Wikipedians think, and why. -- 2148:already lists all the math articles. — Carl 5020:Knowledge:Requests for adminship/Salix alba 4678:verifier)? The discussion has stalled. See 4636:) has unprotected it, with conditions. See 3892:Knowledge:WikiProject Mathematics/Graphics 3622:User:DavidCBryant/List of triangle topics 2222:Knowledge:WikiProject Mathematics/Graphics 1395:Is information theory part of mathematics? 71: 57: 4487:- A little bit of calculus. Unreferenced. 3186: 3181: 3149: 1454:sounds like mathbot needs an update. :-) 5056:Example in the article Permutation group 4704:Knowledge:Requested_articles/mathematics 4365:I just spent some time neatening up the 3570:Mathematical & Computational Biology 2589:, which is a category distinct from the 2543:I consider mathematics to be one of the 2089:"A mathematical constant is a quantity " 1762:Help organize the "list of inequalities" 1713:Michael, an example of a subcategory of 5254: 4362:writing than including the whole proof. 3552: 2405:on the image page. The CC-BY-NC-SA is 1628:Of 10 top level subcategories, I'd say 1552:Category:Error detection and correction 95: 3383:1, there exist infinitely many primes 2808:. Standard definition. Mathematics is 2066:for now redirect to that. The article 1539: 1441:A Mathematical Theory of Communication 18:Knowledge talk:WikiProject Mathematics 5288:WikiProject Mathematics archives/2007 4674:verifier) or the indefinite article ( 3647:Wolfram Demonstrations Project images 2363:The full legal code can be found at: 1731:Category:Lossy compression algorithms 7: 4725:It must have been a while back, the 2473:Isn't the subject of Math a science? 1544:Error-correcting codes with feedback 5153:Product and inverse of permutations 4832:; but not an article. Do redirect. 4775:Hilbert Spaces and Fourier analysis 4769:Hilbert Spaces and Fourier analysis 3896:Category:Knowledge requested images 3407:there exist infinitely many primes 1918:, but because of the redirect from 5270:The Wolfram Demonstrations Project 4505:) 20:54, 16 December 2007 (UTC) -- 4457:Addition of natural numbers/Proofs 3657:The Wolfram Demonstrations Project 3655:Computer Model of the Chain Rule ( 2197:, I consult for Wolfram Research. 52:WikiProject Mathematics archives ( 39: 4475:so high on the notability states. 4030:Boolean logic in computer science 3849:and post those on a large scale. 3299:is a new candidate, nominated by 2233:Knowledge talk:Copyright problems 1411:does not add its articles to the 1243:may be automatically archived by 2527: 2134:This is currently a redirect to 2129:Template:WikiProject Mathematics 1854:. Perhaps the idea was that now 45: 4664:Formal definitions for P and NP 4581:has been protected, to supress 4274:Beetle B. commented at the AfD 4174:A good example, to my mind, is 3620:I merged the page history from 3440:just to keep on the safe side. 2495:talk:mathematics/Archive 5#Poll 1727:Category:Compression algorithms 1558:which also seems mathematical. 1493:here, we are talking about the 4176:Proof that 22 over 7 exceeds π 3882:Cropped version of above image 3371:? The consensus seems to be: 3163: 3157: 1666:Error detection and correction 1634:Algorithmic information theory 1606:Right, so we can include only 1405:list of mathematics categories 1369:Independent Component Analysis 1: 5248:01:18, 31 December 2007 (UTC) 5233:00:59, 31 December 2007 (UTC) 5216:00:55, 31 December 2007 (UTC) 5182:20:21, 28 December 2007 (UTC) 5164:12:13, 28 December 2007 (UTC) 5141:02:13, 28 December 2007 (UTC) 5124:02:08, 28 December 2007 (UTC) 5111:01:28, 28 December 2007 (UTC) 5093:01:18, 28 December 2007 (UTC) 5082:00:03, 28 December 2007 (UTC) 5050:13:08, 25 December 2007 (UTC) 5032:16:35, 17 December 2007 (UTC) 4992:18:37, 25 December 2007 (UTC) 4955:16:28, 25 December 2007 (UTC) 4924:14:06, 25 December 2007 (UTC) 4891:13:42, 25 December 2007 (UTC) 4879:21:35, 25 December 2007 (UTC) 4842:06:50, 25 December 2007 (UTC) 4820:06:32, 25 December 2007 (UTC) 4806:06:29, 25 December 2007 (UTC) 4787:06:22, 25 December 2007 (UTC) 4761:20:59, 24 December 2007 (UTC) 4743:10:26, 24 December 2007 (UTC) 4720:03:02, 24 December 2007 (UTC) 4687:08:39, 22 December 2007 (UTC) 4650:01:38, 19 December 2007 (UTC) 4614:05:35, 18 December 2007 (UTC) 4595:05:08, 18 December 2007 (UTC) 4563:03:11, 19 December 2007 (UTC) 4542:03:07, 19 December 2007 (UTC) 4515:20:54, 16 December 2007 (UTC) 4469:Proof of Bertrand's postulate 4437:20:08, 16 December 2007 (UTC) 4424:19:55, 16 December 2007 (UTC) 4387:02:07, 17 December 2007 (UTC) 4367:proof of Bertrand's postulate 4319:01:31, 17 December 2007 (UTC) 4299:15:51, 16 December 2007 (UTC) 4285:15:25, 16 December 2007 (UTC) 4266:15:17, 16 December 2007 (UTC) 4244:03:21, 16 December 2007 (UTC) 4226:00:54, 16 December 2007 (UTC) 4211:21:12, 15 December 2007 (UTC) 4188:00:11, 16 December 2007 (UTC) 4154:23:28, 15 December 2007 (UTC) 4130:16:07, 15 December 2007 (UTC) 4111:14:30, 15 December 2007 (UTC) 4089:09:23, 15 December 2007 (UTC) 4066:04:52, 15 December 2007 (UTC) 4046:22:50, 17 December 2007 (UTC) 4015:21:19, 16 December 2007 (UTC) 3992:19:57, 16 December 2007 (UTC) 3968:19:33, 16 December 2007 (UTC) 3933:15:23, 14 December 2007 (UTC) 3912:15:16, 14 December 2007 (UTC) 3871:14:29, 14 December 2007 (UTC) 3825:13:19, 14 December 2007 (UTC) 3801:12:55, 14 December 2007 (UTC) 3779:08:37, 14 December 2007 (UTC) 3745:08:13, 14 December 2007 (UTC) 3715:05:05, 14 December 2007 (UTC) 3698:04:59, 14 December 2007 (UTC) 3678:04:45, 14 December 2007 (UTC) 3638:06:25, 14 December 2007 (UTC) 3615:01:30, 14 December 2007 (UTC) 3588:17:35, 13 December 2007 (UTC) 3536:18:12, 13 December 2007 (UTC) 3513:18:03, 13 December 2007 (UTC) 3500:18:00, 13 December 2007 (UTC) 3463:06:02, 13 December 2007 (UTC) 3450:05:43, 13 December 2007 (UTC) 3434:18:02, 12 December 2007 (UTC) 3352:20:32, 11 December 2007 (UTC) 3320:16:46, 11 December 2007 (UTC) 3278:22:28, 10 December 2007 (UTC) 2463:09:31, 13 December 2007 (UTC) 2322:16:20, 27 November 2007 (UTC) 2307:15:00, 27 November 2007 (UTC) 2287:13:12, 27 November 2007 (UTC) 2264:07:43, 27 November 2007 (UTC) 2245:00:00, 27 November 2007 (UTC) 2215:22:31, 26 November 2007 (UTC) 2050:I noticed that many links to 2046:23:51, 30 November 2007 (UTC) 2036:22:59, 30 November 2007 (UTC) 1993:21:39, 30 November 2007 (UTC) 1928:16:52, 30 November 2007 (UTC) 1909:16:35, 30 November 2007 (UTC) 1899:13:04, 30 November 2007 (UTC) 1873:10:08, 30 November 2007 (UTC) 1837:04:59, 30 November 2007 (UTC) 5010:I have nominated one of us, 4485:Chebyshev polynomials/Proofs 4341:Too technical for Knowledge. 4252:Oh looks like we are famous 3229:16:48, 8 December 2007 (UTC) 3215:16:45, 8 December 2007 (UTC) 3139:16:21, 8 December 2007 (UTC) 3116:21:00, 6 December 2007 (UTC) 3089:21:41, 5 December 2007 (UTC) 3068:21:37, 4 December 2007 (UTC) 3031:17:53, 4 December 2007 (UTC) 2999:01:18, 5 December 2007 (UTC) 2987:19:40, 4 December 2007 (UTC) 2954:15:34, 5 December 2007 (UTC) 2898:18:41, 5 December 2007 (UTC) 2844:18:31, 5 December 2007 (UTC) 2822:12:01, 5 December 2007 (UTC) 2795:22:13, 4 December 2007 (UTC) 2773:21:49, 4 December 2007 (UTC) 2730:18:28, 4 December 2007 (UTC) 2692:17:33, 4 December 2007 (UTC) 2663:17:26, 4 December 2007 (UTC) 2638:17:05, 4 December 2007 (UTC) 2616:16:48, 4 December 2007 (UTC) 2602:09:58, 4 December 2007 (UTC) 2575:01:44, 4 December 2007 (UTC) 2560:01:40, 4 December 2007 (UTC) 2536:00:33, 4 December 2007 (UTC) 2522:00:11, 4 December 2007 (UTC) 2511:00:00, 4 December 2007 (UTC) 2502:23:52, 3 December 2007 (UTC) 2488:23:43, 3 December 2007 (UTC) 2442:14:13, 5 December 2007 (UTC) 2423:13:15, 5 December 2007 (UTC) 2390:21:26, 4 December 2007 (UTC) 2332:18:26, 3 December 2007 (UTC) 2173:21:16, 4 December 2007 (UTC) 2161:15:59, 4 December 2007 (UTC) 2146:List of mathematics articles 2114:16:30, 4 December 2007 (UTC) 2104:14:25, 1 December 2007 (UTC) 2083:13:42, 1 December 2007 (UTC) 1807:18:49, 3 December 2007 (UTC) 1785:18:14, 3 December 2007 (UTC) 1775:16:22, 3 December 2007 (UTC) 1756:17:46, 3 December 2007 (UTC) 1746:17:30, 3 December 2007 (UTC) 1708:17:16, 3 December 2007 (UTC) 1693:16:05, 3 December 2007 (UTC) 1673:17:46, 3 December 2007 (UTC) 1630:Algebraic information theory 1624:15:49, 3 December 2007 (UTC) 1602:14:09, 3 December 2007 (UTC) 1563:13:44, 3 December 2007 (UTC) 1523:10:31, 3 December 2007 (UTC) 1506:K Video Compression Dynamics 1477:09:25, 3 December 2007 (UTC) 1459:06:51, 3 December 2007 (UTC) 1448:06:38, 3 December 2007 (UTC) 1434:06:22, 3 December 2007 (UTC) 1415:. Prompted by a question by 1413:list of mathematics articles 1390:01:53, 3 December 2007 (UTC) 1362:02:28, 4 December 2007 (UTC) 1343:02:23, 4 December 2007 (UTC) 1316:17:17, 1 December 2007 (UTC) 1297:17:03, 1 December 2007 (UTC) 1283:14:58, 1 December 2007 (UTC) 1273:14:47, 1 December 2007 (UTC) 4638:Talk:Carl Hewitt#Suggestion 4532:will only lead to trouble. 4463:Approximation theory/Proofs 3973:Salix Alba has taken it to 3603:lists of mathematics topics 3238:Lists of mathematics topics 2493:This is controversial. See 1719:Category:Information theory 1715:Category:Information theory 1608:Category:Information theory 1548:Category:Information theory 1498:Category:Information theory 1401:Category:Information theory 5304: 4670:use the definite article ( 4491:Christoffel symbols/Proofs 3289:Homotopy groups of spheres 1717:that is not mathematical: 1650:Quantum information theory 3886:As for requested picture 3810:For clarification, it is 2341:these are GFDL-compatible 2220:We do have a sub-project 2072:Constant (disambiguation) 2060:Constant (disambiguation) 1959:Euler-Mascheroni constant 1723:Category:Data compression 1668:. What do others think? - 4731:canonical representative 4700:canonical representative 4406:and disallowed as such. 2006:dimensionless quantities 1256:photos of mathematicians 4411:Totient function/Proofs 4348:Totient function/Proofs 4052:Totient function/Proofs 3626:List of triangle topics 3599:list of triangle topics 3593:List of triangle topics 3169:{\displaystyle \sin(x)} 2224:which may fit the bill. 1968:whose base has an area 1790:of inequalities twice: 1642:Entropy and information 1465:Talk:Information theory 5151:I've added a section " 5117:associativity#examples 4471:- A proof appeared in 3883: 3660: 3576:tentative project page 3198: 3197:{\displaystyle \pi /2} 3170: 2802:Merriam_Webster Online 2378: 2339:Here we go. I believe 2013:mathematical constants 1940:We also have articles 1556:Category:Coding theory 1246:Lowercase sigmabot III 3881: 3654: 3199: 3171: 2481:Storkian aka iSoroush 2345: 2183:At the suggestion of 2179:Visualization project 2093:Mathematical constant 2076:Mathematical constant 2058:. I've also expanded 1942:Mathematical constant 1646:Information theorists 1502:Journal of Multimedia 5159:. Please review. -- 5155:" to the article on 5129:Function composition 5006:Salix alba for admin 4526:continuum hypothesis 4473:Proofs from THE BOOK 4073:Boy's surface/Proofs 4071:I've also nominated 3900:Talk:Lissajous orbit 3180: 3148: 3100:User:Oleg Alexandrov 3043:I think it's a very 2229:Wolfram terms of use 2227:A quick look at the 1768:List of inequalities 1583:Category:Mathematics 1262:http://owpdb.mfo.de/ 5064:. There is stated: 4571:Page protection of 4332:Trivial or routine; 4037:is being discussed 3949:Natural mathematics 3941:Natural mathematics 3688:more reasonable. -- 1796:Triangle inequality 1662:Network performance 5115:It's mentioned at 4977:point of departure 3884: 3661: 3646: 3559:J. H. Silverman, " 3337:Mathematical logic 3326:Mathematical logic 3194: 3166: 2725:or mass-energy. -- 2195:my Knowledge entry 2064:Numerical constant 2017:physical constants 1916:numerical constant 1852:Numerical constant 1825:Numerical constant 1823:page was moved to 1546:which was in both 1540:#proposed deletion 1491:Information theory 5180: 5109: 5062:permutation group 5048: 4877: 4840: 4830:Fourier transform 4561: 4522:original research 4404:original research 4325:instead, is that 4109: 4027:A requested move 3977:. I was about to 3644: 3403:but WAREL quotes 3375:for any positive 3350: 3318: 2834:be privileged. -- 2581:Mathematics is a 2421: 2159: 1946:Physical constant 1897: 1850:now redirects to 1792:Weyl's inequality 1600: 1360: 1253: 1252: 102:Nov 2002–Dec 2003 30:(Redirected from 5295: 5273: 5259: 5205:User:Felipe Razo 5170: 5099: 5038: 4873: 4860:Fourier analysis 4856:Fourier analysis 4836: 4794:Fourier analysis 4579:Talk:Carl Hewitt 4573:Talk:Carl Hewitt 4551: 4099: 3768: 3762: 3564: 3557: 3531:ignore enough? — 3340: 3308: 3273: 3270: 3267: 3264: 3261: 3258: 3203: 3201: 3200: 3195: 3190: 3175: 3173: 3172: 3167: 3095:Constant article 3049:Doron Zeilberger 2992:L. E. J. Brouwer 2685:physical science 2591:natural sciences 2568:computer science 2531: 2483: 2411: 2404: 2398: 2149: 2143: 2137: 1887: 1658:Data compression 1638:Detection theory 1590: 1388: 1350: 1248: 1232: 73: 66: 59: 49: 41: 35: 5303: 5302: 5298: 5297: 5296: 5294: 5293: 5292: 5278: 5277: 5276: 5260: 5256: 5192: 5058: 5024:Oleg Alexandrov 5008: 4871:Septentrionalis 4858:, but that the 4834:Septentrionalis 4798:Oleg Alexandrov 4771: 4727:4th Dec version 4696: 4660: 4587:Oleg Alexandrov 4583:this discussion 4576: 4534:Perturbationist 4479:Cardioid/Proofs 4395: 4352:axiom of choice 4218:Oleg Alexandrov 4059: 4025: 3945: 3766: 3760: 3727:, which allows 3670:Oleg Alexandrov 3649: 3630:Oleg Alexandrov 3595: 3572: 3567: 3558: 3554: 3550: 3442:Oleg Alexandrov 3365: 3358:Wieferich prime 3331:With help from 3329: 3285: 3271: 3268: 3265: 3262: 3259: 3256: 3242: 3178: 3177: 3146: 3145: 3123: 3097: 2595:social sciences 2479: 2475: 2402: 2396: 2314:Oleg Alexandrov 2256:Oleg Alexandrov 2181: 2141: 2135: 2132: 1829:Oleg Alexandrov 1817: 1764: 1616:Oleg Alexandrov 1495:entire category 1426:Oleg Alexandrov 1397: 1384: 1373: 1270:Jakob.scholbach 1258: 1244: 1233: 1227: 1218: 1104: 94: 93: 80: 77: 37: 36: 29: 28: 12: 11: 5: 5301: 5299: 5291: 5290: 5280: 5279: 5275: 5274: 5253: 5252: 5251: 5235: 5218: 5191: 5188: 5187: 5186: 5185: 5184: 5148: 5147: 5146: 5145: 5144: 5143: 5133:David Eppstein 5126: 5057: 5054: 5053: 5052: 5007: 5004: 5003: 5002: 5001: 5000: 4999: 4998: 4997: 4996: 4995: 4994: 4980: 4964: 4963: 4962: 4961: 4960: 4959: 4958: 4957: 4935: 4934: 4933: 4932: 4931: 4930: 4929: 4928: 4927: 4926: 4912:Fourier series 4900: 4899: 4898: 4897: 4896: 4895: 4894: 4893: 4883: 4882: 4881: 4770: 4767: 4766: 4765: 4764: 4763: 4746: 4745: 4695: 4690: 4668:P = NP problem 4659: 4656: 4655: 4654: 4653: 4652: 4617: 4616: 4606:David Eppstein 4575: 4569: 4568: 4567: 4566: 4565: 4545: 4544: 4495: 4494: 4488: 4482: 4476: 4466: 4460: 4450: 4449: 4448: 4447: 4440: 4439: 4416:David Eppstein 4400:Fáry's theorem 4394: 4391: 4390: 4389: 4374: 4370: 4363: 4344: 4343: 4342: 4339: 4336: 4333: 4306: 4305: 4304: 4303: 4302: 4301: 4269: 4268: 4249: 4248: 4247: 4246: 4229: 4228: 4199: 4198: 4197: 4196: 4195: 4194: 4193: 4192: 4191: 4190: 4180:David Eppstein 4163: 4162: 4161: 4160: 4159: 4158: 4157: 4156: 4137: 4136: 4135: 4134: 4133: 4132: 4092: 4091: 4058: 4049: 4034:Boolean logic 4024: 4021: 4020: 4019: 4018: 4017: 3995: 3994: 3944: 3937: 3936: 3935: 3919: 3918: 3808: 3807: 3806: 3805: 3804: 3803: 3784: 3783: 3782: 3781: 3750: 3749: 3748: 3747: 3718: 3717: 3701: 3700: 3648: 3642: 3641: 3640: 3594: 3591: 3571: 3568: 3566: 3565: 3551: 3549: 3546: 3545: 3544: 3543: 3542: 3541: 3540: 3539: 3538: 3520: 3519: 3518: 3517: 3516: 3515: 3502: 3468: 3467: 3466: 3465: 3453: 3452: 3424:2</sup: --> 3421: 3420: 3401: 3400: 3369:abc Conjecture 3364: 3355: 3328: 3323: 3284: 3283:A-class rating 3281: 3241: 3235: 3234: 3233: 3232: 3231: 3219:;-). Thanks -- 3193: 3189: 3185: 3165: 3162: 3159: 3156: 3153: 3122: 3121:Wallis product 3119: 3096: 3093: 3092: 3091: 3075: 3074: 3073: 3072: 3071: 3070: 3036: 3035: 3034: 3033: 3020: 3019: 3018: 3017: 3010: 3009: 3008: 3007: 3006: 3005: 3004: 3003: 3002: 3001: 2973: 2972: 2971: 2970: 2969: 2968: 2967: 2966: 2965: 2964: 2963: 2962: 2961: 2960: 2959: 2958: 2957: 2956: 2921: 2920: 2919: 2918: 2917: 2916: 2915: 2914: 2913: 2912: 2911: 2910: 2909: 2908: 2907: 2906: 2905: 2904: 2903: 2902: 2901: 2900: 2865: 2864: 2863: 2862: 2861: 2860: 2859: 2858: 2857: 2856: 2855: 2854: 2853: 2852: 2851: 2850: 2849: 2848: 2847: 2846: 2806:WordWeb Online 2743: 2742: 2741: 2740: 2739: 2738: 2737: 2736: 2735: 2734: 2733: 2732: 2722: 2703: 2702: 2701: 2700: 2699: 2698: 2697: 2696: 2695: 2694: 2672: 2671: 2670: 2669: 2668: 2667: 2666: 2665: 2645: 2644: 2643: 2642: 2641: 2640: 2621: 2620: 2619: 2618: 2605: 2604: 2587:formal science 2578: 2577: 2570:is a science. 2541: 2540: 2539: 2538: 2513: 2504: 2474: 2471: 2470: 2469: 2468: 2467: 2466: 2465: 2448: 2447: 2446: 2445: 2444: 2426: 2425: 2325: 2324: 2294: 2293: 2292: 2291: 2290: 2289: 2269: 2268: 2267: 2266: 2248: 2247: 2225: 2180: 2177: 2176: 2175: 2131: 2126: 2125: 2124: 2123: 2122: 2121: 2120: 2119: 2118: 2117: 2116: 2091:? That's what 2009: 1996: 1995: 1986: 1985: 1984: 1977: 1962: 1955: 1949: 1937: 1936: 1935: 1934: 1933: 1932: 1931: 1930: 1816: 1813: 1812: 1811: 1810: 1809: 1763: 1760: 1759: 1758: 1753:David Eppstein 1711: 1710: 1686: 1685: 1684: 1683: 1682: 1681: 1680: 1679: 1678: 1677: 1676: 1675: 1587:Google Answers 1572: 1571: 1570: 1569: 1568: 1567: 1566: 1565: 1530: 1529: 1528: 1527: 1526: 1525: 1513: 1482: 1481: 1480: 1479: 1451: 1450: 1403:is not in the 1396: 1393: 1372: 1366: 1365: 1364: 1323: 1322: 1321: 1320: 1319: 1318: 1302: 1301: 1300: 1299: 1286: 1285: 1257: 1254: 1251: 1250: 1238: 1235: 1234: 1229: 1225: 1223: 1220: 1219: 1217: 1216: 1161: 1105: 1103: 1102: 1047: 992: 937: 882: 827: 772: 717: 662: 607: 552: 497: 442: 387: 332: 277: 222: 167: 112: 91: 90: 89: 86: 85: 82: 81: 76: 75: 68: 61: 53: 50: 44: 38: 15: 14: 13: 10: 9: 6: 4: 3: 2: 5300: 5289: 5286: 5285: 5283: 5271: 5267: 5263: 5258: 5255: 5249: 5245: 5241: 5236: 5234: 5231: 5227: 5223: 5219: 5217: 5214: 5210: 5206: 5202: 5198: 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3608: 3607:Michael Hardy 3604: 3600: 3592: 3590: 3589: 3585: 3581: 3577: 3569: 3562: 3556: 3553: 3547: 3537: 3534: 3528: 3527: 3526: 3525: 3524: 3523: 3522: 3521: 3514: 3511: 3507: 3503: 3501: 3498: 3494: 3490: 3486: 3482: 3478: 3474: 3473: 3472: 3471: 3470: 3469: 3464: 3461: 3457: 3456: 3455: 3454: 3451: 3447: 3443: 3438: 3437: 3436: 3435: 3432: 3428: 3419:divide 2 − 1. 3418: 3414: 3410: 3406: 3405: 3404: 3398: 3394: 3390: 3386: 3381: 3378: 3374: 3373: 3372: 3370: 3363: 3359: 3356: 3354: 3353: 3348: 3344: 3338: 3334: 3327: 3324: 3322: 3321: 3316: 3312: 3304: 3302: 3298: 3294: 3290: 3282: 3280: 3279: 3276: 3275: 3274: 3251: 3247: 3239: 3236: 3230: 3226: 3222: 3218: 3217: 3216: 3212: 3208: 3191: 3187: 3183: 3160: 3154: 3151: 3143: 3142: 3141: 3140: 3136: 3132: 3128: 3127:"wrong proof" 3120: 3118: 3117: 3113: 3109: 3105: 3101: 3094: 3090: 3086: 3082: 3077: 3076: 3069: 3065: 3061: 3056: 3052: 3050: 3046: 3042: 3041: 3040: 3039: 3038: 3037: 3032: 3029: 3024: 3023: 3022: 3021: 3014: 3013: 3012: 3011: 3000: 2997: 2993: 2990: 2989: 2988: 2985: 2981: 2980: 2979: 2978: 2977: 2976: 2975: 2974: 2955: 2951: 2947: 2943: 2939: 2938: 2937: 2936: 2935: 2934: 2933: 2932: 2931: 2930: 2929: 2928: 2927: 2926: 2925: 2924: 2923: 2922: 2899: 2895: 2891: 2887: 2886: 2885: 2884: 2883: 2882: 2881: 2880: 2879: 2878: 2877: 2876: 2875: 2874: 2873: 2872: 2871: 2870: 2869: 2868: 2867: 2866: 2845: 2841: 2837: 2833: 2829: 2825: 2824: 2823: 2819: 2815: 2811: 2807: 2803: 2798: 2797: 2796: 2792: 2788: 2784: 2780: 2776: 2775: 2774: 2770: 2766: 2762: 2757: 2756: 2755: 2754: 2753: 2752: 2751: 2750: 2749: 2748: 2747: 2746: 2745: 2744: 2731: 2728: 2723: 2719: 2716:No, it would 2715: 2714: 2713: 2712: 2711: 2710: 2709: 2708: 2707: 2706: 2705: 2704: 2693: 2690: 2686: 2682: 2681: 2680: 2679: 2678: 2677: 2676: 2675: 2674: 2673: 2664: 2661: 2657: 2653: 2652: 2651: 2650: 2649: 2648: 2647: 2646: 2639: 2636: 2632: 2627: 2626: 2625: 2624: 2623: 2622: 2617: 2614: 2609: 2608: 2607: 2606: 2603: 2600: 2596: 2592: 2588: 2584: 2580: 2579: 2576: 2573: 2569: 2564: 2563: 2562: 2561: 2558: 2554: 2550: 2546: 2537: 2534: 2530: 2525: 2524: 2523: 2520: 2519: 2514: 2512: 2509: 2505: 2503: 2500: 2496: 2492: 2491: 2490: 2489: 2486: 2484: 2482: 2464: 2461: 2458: 2454: 2453: 2452: 2451: 2450: 2449: 2443: 2439: 2435: 2430: 2429: 2428: 2427: 2424: 2419: 2415: 2408: 2401: 2394: 2393: 2392: 2391: 2387: 2383: 2382:Pleasantville 2377: 2376: 2371: 2367: 2366: 2361: 2360: 2355: 2351: 2349: 2344: 2342: 2338: 2334: 2333: 2330: 2329:Pleasantville 2323: 2319: 2315: 2311: 2310: 2309: 2308: 2304: 2300: 2288: 2284: 2280: 2279:Pleasantville 2275: 2274: 2273: 2272: 2271: 2270: 2265: 2261: 2257: 2252: 2251: 2250: 2249: 2246: 2242: 2238: 2234: 2230: 2226: 2223: 2219: 2218: 2217: 2216: 2212: 2208: 2207:Pleasantville 2202: 2198: 2196: 2192: 2188: 2186: 2178: 2174: 2171: 2170: 2165: 2164: 2163: 2162: 2157: 2153: 2147: 2140: 2130: 2127: 2115: 2112: 2107: 2106: 2105: 2102: 2098: 2094: 2090: 2086: 2085: 2084: 2081: 2077: 2073: 2069: 2065: 2061: 2057: 2053: 2049: 2048: 2047: 2044: 2039: 2038: 2037: 2034: 2030: 2027: 2024: 2021: 2018: 2014: 2010: 2007: 2003: 1998: 1997: 1994: 1991: 1987: 1982: 1978: 1975: 1971: 1967: 1963: 1960: 1956: 1953: 1952: 1950: 1947: 1943: 1939: 1938: 1929: 1926: 1921: 1917: 1912: 1911: 1910: 1907: 1902: 1901: 1900: 1895: 1891: 1884: 1880: 1876: 1875: 1874: 1870: 1866: 1861: 1857: 1853: 1849: 1845: 1841: 1840: 1839: 1838: 1834: 1830: 1826: 1822: 1815:Constant move 1814: 1808: 1805: 1801: 1797: 1793: 1788: 1787: 1786: 1783: 1779: 1778: 1777: 1776: 1773: 1772:Michael Hardy 1769: 1761: 1757: 1754: 1750: 1749: 1748: 1747: 1744: 1740: 1739:Category:iPod 1736: 1732: 1728: 1724: 1720: 1716: 1709: 1706: 1702: 1697: 1696: 1695: 1694: 1691: 1690:Michael Hardy 1674: 1671: 1667: 1663: 1659: 1655: 1654:Coding theory 1651: 1647: 1643: 1639: 1635: 1631: 1627: 1626: 1625: 1621: 1617: 1613: 1609: 1605: 1604: 1603: 1598: 1594: 1588: 1584: 1580: 1579: 1578: 1577: 1576: 1575: 1574: 1573: 1564: 1561: 1557: 1553: 1549: 1545: 1541: 1538: 1537: 1536: 1535: 1534: 1533: 1532: 1531: 1524: 1521: 1520: 1514: 1511: 1507: 1503: 1499: 1496: 1492: 1488: 1487: 1486: 1485: 1484: 1483: 1478: 1474: 1470: 1466: 1462: 1461: 1460: 1457: 1453: 1452: 1449: 1446: 1445:Michael Hardy 1442: 1438: 1437: 1436: 1435: 1431: 1427: 1422: 1418: 1417:Michael Hardy 1414: 1410: 1406: 1402: 1394: 1392: 1391: 1387: 1383: 1378: 1370: 1367: 1363: 1358: 1354: 1347: 1346: 1345: 1344: 1341: 1337: 1331: 1329: 1317: 1314: 1313: 1308: 1307: 1306: 1305: 1304: 1303: 1298: 1295: 1290: 1289: 1288: 1287: 1284: 1281: 1277: 1276: 1275: 1274: 1271: 1267: 1263: 1255: 1247: 1242: 1237: 1236: 1222: 1221: 1215: 1211: 1207: 1203: 1199: 1195: 1191: 1187: 1183: 1179: 1175: 1171: 1167: 1166: 1162: 1160: 1156: 1152: 1148: 1144: 1140: 1136: 1132: 1128: 1124: 1120: 1116: 1112: 1111: 1107: 1106: 1101: 1097: 1093: 1089: 1085: 1081: 1077: 1073: 1069: 1065: 1061: 1057: 1053: 1052: 1048: 1046: 1042: 1038: 1034: 1030: 1026: 1022: 1018: 1014: 1010: 1006: 1002: 998: 997: 993: 991: 987: 983: 979: 975: 971: 967: 963: 959: 955: 951: 947: 943: 942: 938: 936: 932: 928: 924: 920: 916: 912: 908: 904: 900: 896: 892: 888: 887: 883: 881: 877: 873: 869: 865: 861: 857: 853: 849: 845: 841: 837: 833: 832: 828: 826: 822: 818: 814: 810: 806: 802: 798: 794: 790: 786: 782: 778: 777: 773: 771: 767: 763: 759: 755: 751: 747: 743: 739: 735: 731: 727: 723: 722: 718: 716: 712: 708: 704: 700: 696: 692: 688: 684: 680: 676: 672: 668: 667: 663: 661: 657: 653: 649: 645: 641: 637: 633: 629: 625: 621: 617: 613: 612: 608: 606: 602: 598: 594: 590: 586: 582: 578: 574: 570: 566: 562: 558: 557: 553: 551: 547: 543: 539: 535: 531: 527: 523: 519: 515: 511: 507: 503: 502: 498: 496: 492: 488: 484: 480: 476: 472: 468: 464: 460: 456: 452: 448: 447: 443: 441: 437: 433: 429: 425: 421: 417: 413: 409: 405: 401: 397: 393: 392: 388: 386: 382: 378: 374: 370: 366: 362: 358: 354: 350: 346: 342: 338: 337: 333: 331: 327: 323: 319: 315: 311: 307: 303: 299: 295: 291: 287: 283: 282: 278: 276: 272: 268: 264: 260: 256: 252: 248: 244: 240: 236: 232: 228: 227: 223: 221: 217: 213: 209: 205: 201: 197: 193: 189: 185: 181: 177: 173: 172: 168: 166: 162: 158: 154: 150: 146: 142: 138: 134: 130: 126: 122: 118: 117: 113: 111: 107: 103: 99: 96: 92:Earlier years 88: 87: 84: 83: 79: 74: 69: 67: 62: 60: 55: 54: 48: 43: 42: 33: 27: 23: 19: 5266:Ed Pegg, Jr. 5262:"Chain Rule" 5257: 5226:Arthur Rubin 5221: 5209:Arthur Rubin 5200: 5193: 5157:permutations 5119:, at least. 5069: 5065: 5059: 5016:adminstrator 5009: 4976: 4865: 4847: 4825: 4796:. Comments? 4777:. Thanks! -- 4772: 4697: 4675: 4671: 4661: 4630: 4577: 4529: 4520:I think the 4496: 4451: 4433:Geometry guy 4431: 4409:I note that 4408: 4396: 4359: 4326: 4307: 4281:Geometry guy 4279: 4200: 4150:Geometry guy 4148: 4060: 4028: 4026: 3988:Geometry guy 3986: 3957: 3946: 3898:for example 3885: 3874: 3860: 3851: 3847: 3843: 3839: 3832: 3828: 3811: 3809: 3793:Jitse Niesen 3730: 3728: 3685: 3662: 3596: 3580:Pete St.John 3573: 3560: 3555: 3506:Arthur Rubin 3493:Arthur Rubin 3476: 3427:Arthur Rubin 3422: 3416: 3412: 3408: 3402: 3396: 3392: 3388: 3384: 3379: 3366: 3330: 3305: 3286: 3254: 3253: 3243: 3124: 3098: 3081:Pete St.John 3055:generated by 3054: 3044: 2831: 2827: 2809: 2782: 2781:objects and 2778: 2760: 2717: 2655: 2567: 2552: 2548: 2542: 2518:Geometry guy 2516: 2480: 2476: 2406: 2379: 2372: 2368: 2362: 2356: 2352: 2348:Terms of Use 2347: 2346: 2336: 2335: 2326: 2295: 2203: 2199: 2189: 2182: 2169:Geometry guy 2167: 2139:maths rating 2133: 2088: 2001: 1973: 1969: 1965: 1878: 1843: 1818: 1799: 1765: 1735:Category:MP3 1712: 1705:Pete St.John 1700: 1687: 1611: 1519:Geometry guy 1517: 1510:Proxy server 1494: 1420: 1398: 1374: 1335: 1332: 1327: 1324: 1312:Geometry guy 1310: 1259: 1240: 1163: 1108: 1049: 994: 939: 884: 829: 774: 719: 664: 609: 554: 499: 444: 389: 334: 279: 274: 224: 169: 114: 110:Sep–Dec 2004 106:Jan–Aug 2004 51: 5250:Felipe Razo 5240:68.7.11.138 4984:Tom Tresser 4916:Tom Tresser 4530:correctness 3729:use, copy, 3725:mit license 3530:block-: --> 3475:His actual 3221:Meisterkoch 3131:Meisterkoch 3129:. Thanks -- 1560:PrimeHunter 5121:Algebraist 5090:Algebraist 5012:Salix alba 4875:PMAnderson 4838:PMAnderson 4779:Malcolmxl5 4735:Salix alba 4624:SlimVirgin 4507:Salix alba 4499:Salix alba 4379:Ryan Reich 4327:in general 4258:Salix alba 4122:Salix alba 4081:Salix alba 4054:is at AfD 3904:Salix alba 3771:Salix alba 3737:Salix alba 3707:Ramsey2006 3665:chain rule 3548:References 3411:such that 3387:such that 3333:Hans Adler 3287:I removed 3207:Ryan Reich 3108:Randomblue 2984:Ramsey2006 2890:Salix alba 2545:humanities 2508:Ramsey2006 2434:Salix alba 2237:Salix alba 2111:Randomblue 2101:Hans Adler 2043:Hans Adler 1981:0 (number) 1925:Hans Adler 1906:Randomblue 1865:Hans Adler 1469:Salix alba 1399:Currently 1336:proportion 1294:Hans Adler 98:Motivation 4642:JRSpriggs 3645:Mathworld 3016:whatever. 2836:Trovatore 2814:Gandalf61 2787:Trovatore 2765:Gandalf61 2727:Trovatore 2689:Gandalf61 2660:Trovatore 2635:Gandalf61 2613:Trovatore 2599:Gandalf61 2499:Trovatore 2002:numerical 1804:GTBacchus 1782:GTBacchus 1743:GTBacchus 1670:GTBacchus 1610:and just 1589:. — Carl 1542:is about 1340:Trovatore 5282:Category 4848:operator 4812:Cheeser1 4698:I added 4634:contribs 4622:Update: 4446:article. 4117:case law 3983:Gregbard 3958:Cheers, 3690:Cheeser1 3533:Cronholm 3489:SoftBank 3485:SoftBank 3479:(except 3477:accounts 3460:Cronholm 3301:Disavian 3104:constant 3060:Cheeser1 2656:physical 2631:Platonic 2572:Skippydo 2557:Cheeser1 2097:Quantity 2068:Constant 2056:Constant 2052:Constant 1920:constant 1883:constant 1879:constant 1860:constant 1856:constant 1848:Constant 1821:Constant 1766:Look at 1328:the same 24:‎ | 20:‎ | 5272:, 2007. 5161:Lambiam 5074:Tomaxer 5070:ab = ba 4888:Lambiam 4753:Dominus 4712:Dominus 4684:Lambiam 4356:forcing 4291:Shinobu 4043:Lambiam 4007:Anville 3960:Anville 3415:² does 3395:divide 3391:² does 3377:integer 3045:bizarre 2996:Lambiam 2946:Dominus 2783:natural 2779:natural 2583:science 2080:Lambiam 2033:Lambiam 1990:Lambiam 1456:Mct mht 1409:mathbot 1382:eykanal 1334:higher 1241:15 days 22:Archive 5230:(talk) 5213:(talk) 5014:, for 4947:Arcfrk 4360:better 4311:Loisel 3731:modify 3510:(talk) 3497:(talk) 3431:(talk) 3240:issues 2832:should 2533:Arcfrk 2028:, and 1800:normed 1508:, and 1407:, and 5222:wrong 5199:What 4682:. -- 4041:. -- 3624:into 3481:WAREL 3382:: --> 3362:WAREL 3291:from 2828:ought 2299:linas 2078:. -- 2031:. -- 1737:: --> 1733:: --> 1729:: --> 1725:: --> 1721:: --> 1463:Well 16:< 5244:talk 5177:talk 5137:talk 5106:talk 5078:talk 5045:talk 5028:talk 4988:talk 4951:talk 4920:talk 4866:Into 4816:talk 4802:talk 4783:talk 4757:talk 4739:talk 4729:had 4716:talk 4646:talk 4628:talk 4610:talk 4591:talk 4558:talk 4538:talk 4511:talk 4503:talk 4420:talk 4383:talk 4315:talk 4295:talk 4276:here 4262:talk 4240:talk 4222:talk 4207:talk 4184:talk 4126:talk 4106:talk 4085:talk 4079:. -- 4056:here 4039:here 4011:talk 4005:). 3979:prod 3964:talk 3953:here 3929:talk 3908:talk 3867:talk 3855:here 3821:talk 3797:talk 3775:talk 3741:talk 3711:talk 3694:talk 3686:much 3674:talk 3634:talk 3611:talk 3584:talk 3446:talk 3399:− 1. 3360:and 3347:talk 3315:talk 3260:e Tr 3248:and 3244:See 3225:talk 3211:talk 3135:talk 3112:talk 3085:talk 3064:talk 2950:talk 2940:The 2894:talk 2840:talk 2818:talk 2791:talk 2769:talk 2683:No, 2457:+sj 2438:talk 2418:talk 2386:talk 2318:talk 2303:talk 2283:talk 2260:talk 2241:talk 2211:talk 2156:talk 2015:(or 1944:and 1894:talk 1869:talk 1833:talk 1819:The 1660:and 1648:and 1620:talk 1612:some 1597:talk 1550:and 1473:talk 1430:talk 1386:talk 1375:The 1371:page 1357:talk 1280:Itub 1165:2024 1110:2023 1051:2022 996:2021 941:2020 886:2019 831:2018 776:2017 721:2016 666:2015 611:2014 556:2013 501:2012 446:2011 391:2010 336:2009 281:2008 226:2007 171:2006 116:2005 26:2007 5264:by 5228:| 5211:| 5201:was 5173:CBM 5102:CBM 5041:CBM 4886:-- 4702:to 4672:the 4666:of 4554:CBM 4102:CBM 4077:AfD 4063:Ben 3975:AfD 3812:not 3764:MIT 3508:| 3495:| 3429:| 3417:not 3393:not 3343:CBM 3311:CBM 3272:ist 3269:man 3263:ans 3252:. 3152:sin 3028:C S 2942:OED 2810:not 2761:not 2718:not 2553:use 2549:use 2414:CBM 2407:not 2400:MIT 2152:CBM 2025:, 1890:CBM 1593:CBM 1421:all 1377:ICA 1353:CBM 1214:Dec 1210:Nov 1206:Oct 1202:Sep 1198:Aug 1194:Jul 1190:Jun 1186:May 1182:Apr 1178:Mar 1174:Feb 1170:Jan 1159:Dec 1155:Nov 1151:Oct 1147:Sep 1143:Aug 1139:Jul 1135:Jun 1131:May 1127:Apr 1123:Mar 1119:Feb 1115:Jan 1100:Dec 1096:Nov 1092:Oct 1088:Sep 1084:Aug 1080:Jul 1076:Jun 1072:May 1068:Apr 1064:Mar 1060:Feb 1056:Jan 1045:Dec 1041:Nov 1037:Oct 1033:Sep 1029:Aug 1025:Jul 1021:Jun 1017:May 1013:Apr 1009:Mar 1005:Feb 1001:Jan 990:Dec 986:Nov 982:Oct 978:Sep 974:Aug 970:Jul 966:Jun 962:May 958:Apr 954:Mar 950:Feb 946:Jan 935:Dec 931:Nov 927:Oct 923:Sep 919:Aug 915:Jul 911:Jun 907:May 903:Apr 899:Mar 895:Feb 891:Jan 880:Dec 876:Nov 872:Oct 868:Sep 864:Aug 860:Jul 856:Jun 852:May 848:Apr 844:Mar 840:Feb 836:Jan 825:Dec 821:Nov 817:Oct 813:Sep 809:Aug 805:Jul 801:Jun 797:May 793:Apr 789:Mar 785:Feb 781:Jan 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