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Proving induction

Please take a look to the article proof of mathematical induction. As a consequence of a remark of mine [1] an editor made some addition to the hypothesis of the proof to make it work. I would like to understand if this proof is "standard" (it should be other wise would be original research) and what is his original form (in particular which hypothesis should we require). What do you think?--Pokipsy76 15:41, 23 July 2006 (UTC)

The concept of "proving" induction is strange. Typically we use an axiom scheme that explicitly states that induction works. A quick glance at this leaves me feeling that it's a bad article. --KSmrq^T 19:02, 23 July 2006 (UTC)

The concept of proving the principle of mathematical induction is certainly not strange - it is a well-known part of mathematical logic and the development of the number system logically. The article might need a bit of work, but the idea is good. Madmath789 19:15, 23 July 2006 (UTC)

I'm not quite sure what you mean by "proving". For example, here's a quote from Peano axioms:

---

Informally, the Peano axioms may be stated as follows:

• 0 is a natural number.
• Every natural number a has a successor, denoted by Sa or $a'$.
• No natural number has 0 as its successor.
• Distinct natural numbers have distinct successors: a = b if and only if Sa = Sb.
• If a property holds for 0, and holds for the successor of every natural number for which it holds, then the property holds for all natural numbers. This axiom of induction legitimizes the proof method known as mathematical induction (induction over the naturals).

---

I draw your attention to the last item. Essentially it says we "build in" induction; we don't deduce it. Although there are many ways to approach foundations, I don't think we can avoid something along these lines; natural numbers and induction are inseparable. If natural numbers are defined per Peano this whole proof article is silly. If not, the article is confusing; it's not clear where we're beginning, nor exactly what is being accomplished.

If we are going to discuss the article further, we should do so on its talk page. --KSmrq^T 23:19, 23 July 2006 (UTC)

Proving just means deduction from axioms. Clearly, in PA, mathematical induction is an axiom, but in developing maths from ZFC, it is not an axiom, so it needs to be proved from the axioms. Madmath789 06:51, 24 July 2006 (UTC)

I have to agree with both KSmrq and Madmath: The idea of proving the induction principle is not "strange" in itself, and yet the article in question is a bad article (and I have my doubts that any article with that title would be good). Induction is not assumed explicitly in, say, the usual formulations of ZFC, and can be proved once you've defined the naturals. But there's less here than meets the eye; it's a boring technical detail rather than something particularly significant, and having an article about it might give the misimpression that there's something fundamental being done. The existing article is worse than that; it starts with the assumption that the naturals are wellordered. From there the induction principle really is a triviality. --Trovatore 19:56, 23 July 2006 (UTC)

It's not clear to me in which sense can we be supposed to prove induction principle from the well ordering assumption: the well ordering itself is useless unless we have some extra assumption to work with (for example the assumption that x#0→x=y+1)--Pokipsy76 20:04, 23 July 2006 (UTC)

I gave that article a prod. -lethe ^{talk +} 20:37, 23 July 2006 (UTC)

Maybe you could have waited a little bit to let us discuss about it before going to vote.--Pokipsy76 20:55, 23 July 2006 (UTC)

Prodding does not involve a voting process. We have ample time to discuss this. --Lambiam^Talk 00:39, 24 July 2006 (UTC)

Are you sure? Look here.--Pokipsy76 20:59, 24 July 2006 (UTC)

The PROD, which involves no voting and can be halted in an instant, was forced into AfD, which requires voting and admin participation. The official decision was no consensus. My unofficial summary of the comments: the article needs improving, and probably the proof should be merged into the parent article. It would be nice for one of the "keep" voters (Pokipsy76?, Ryan Reich?) to volunteer. --KSmrq^T 00:18, 1 August 2006 (UTC)

Done. I "morally" merged the article; the actual material in it was sort of long-winded. I also put in the stuff on transfinite induction and included a reference to Kolmogorov and Fomin. The original proof article remains, with a {{merging}} tempate added. Ryan Reich 02:23, 1 August 2006 (UTC)

Thanks, that's much better. --KSmrq^T 09:56, 6 August 2006 (UTC)

Good. I've changed the old article to a redirect now. Ryan Reich 15:25, 6 August 2006 (UTC)

Articles listed at Articles for deletion

The following articles have been listed at Articles for deletion but not caught by the 'bot:

• Wilkinson's polynomial (AfD discussion)

Uncle G 11:54, 25 July 2006 (UTC)

it is now. Septentrionalis 21:25, 26 July 2006 (UTC)

The decision on Wilkinson's polynomial was keep, after a number of editors worked on cleaning it up and clarifying its significance. --KSmrq^T 00:15, 31 July 2006 (UTC)

The following articles have been listed at Articles for deletion but not caught by the 'bot:

• Imaginary logarithm (AfD discussion)

Uncle G 17:24, 28 July 2006 (UTC)

The bot runs once a day; it may be preferable either to wait a day and see if it is picked up, or add this to the list by hand. Septentrionalis 22:49, 28 July 2006 (UTC)

The decision on imaginary logarithm was redirect to complex logarithm, agreed unanimously. --KSmrq^T 09:54, 6 August 2006 (UTC)

article variational number theory is back

User_talk:Karl-H has recreated the page. He's also made edits to calculus of variations and number theory among others. Somebody familiar with the subjects and the original RfD might want to take a look. Lunch 19:09, 26 July 2006 (UTC)

Integral equations has been edited too. Lunch 19:14, 26 July 2006 (UTC)

Reverted all of those. — Arthur Rubin | (talk) 21:18, 26 July 2006 (UTC)

Removing the redlinks in the list of mathematicians

Currently the list of mathematicians has a certain number of redlinks. I would argue that that was a good thing when Wikipedia was new and plenty of famous people did not have articles and when there was no bot to maintain that list.

I would think that now we would be better off having the list of mathematicians list articles which actually exist, with redlinks (requests for new articles) going to Wikipedia:Requested articles/Mathematics instead. Removing the redlinks from the list of mathematicians would also make it easier to see what mathematician articles got created/deleted by inspecting the Current activity.

In short, how about removing all the redlinks from the list of mathematicians? Oleg Alexandrov (talk) 20:32, 29 July 2006 (UTC)

I think that's a good idea. Can I also encourage people to add to the requested mathematician list? As a grad student, I'm hesitant to create articles for mathematicians that work at my school. I'd feel more comfortable if they were on the requested list. Thanks. Originalbigj 19:45, 30 July 2006 (UTC)

The bot now removes redlinks from the list of mathematicians (log). Oleg Alexandrov (talk) 23:53, 31 July 2006 (UTC)

It appears that you removed the redlink to Thomas Jech from the list of mathematicians, but did not add it to the list of requested articles on mathematicians. If a redlink is removed from one, I think that it should be added to the other (if not already there). And what if someone destroys the article or moves it to another name? JRSpriggs 03:10, 1 August 2006 (UTC)

Update. I just created a stub for Thomas Jech. I did not see the redlink removal in the log. But I remember creating a redlink for him a month or two back. JRSpriggs 03:27, 1 August 2006 (UTC)

I did not add the redlinks to Wikipedia:Requested articles/Mathematics on purpose, it is not clear if those redlinks are indeed "Wanted" articles.

If an article gets deleted (which only administrators can do) my bot will remove it from the list of mathematicians. If an article gets renamed, the bot will reflect the rename in the list. Oleg Alexandrov (talk) 04:55, 1 August 2006 (UTC)

Oyam's Pyramid

The article Oyam's Pyramid is currently proposed for deletion. It seems to me that it would be likely to be covered by some area of mathematics rather than being a complete hoax, but I've been unable to track down any evidence for its existence with this title. Could somebody take a look and see if a) it's a valid but wrongly-titled article, b)it needs merging or redirecting to some other concept, or c) it's complete garbage. Thanks Yomangani 10:46, 31 July 2006 (UTC)

Since there are no Google hits for any of this (except to Wikipedia), it is definitely made up. In my opinion it doesn't make much practical sense if you actually mean to build a pyramid. (Disclaimer: I have no actual experience in pyramid construction.) Mathematically it seems to be a pointless triviality. --Lambiam^Talk 23:00, 31 July 2006 (UTC)

Piotr Blass

I was wondering what people thought of the article Piotr Blass and the anon User: 69.163.189.9 who has created it and spent some time inserting the name of Piotr Blass into the articles of several distinguished mathematicians, e.g. Hassler Whitney and Heisuke Hironaka. I spy several dubious claims to fame in the Blass article, e.g. inventing the World Wibe Web. There's also a very interesting assertion that he's the student of a number of famous mathematicians (such as the ones I mentioned prior). Blass is apparently enough of a famous mathematician that the statement that Whitney taught "mathematics education" to Blass is an important thing to include into Whitney's article.

Blass' publication list looks fairly average and is bolstered by a number of publications to a journal that he founded and that I've never heard of. To be fair, I noticed that Zariski surface exists and was created by User:r.e.b.; it appears that Blass named Zariski surfaces and has some papers on them in respectable journals. So I wouldn't advocate a deletion of the Blass article. But it seems there's a lot of what might be called "tooting one's own horn" (if the anon is indeed Blass). --Chan-Ho (Talk) 17:14, 31 July 2006 (UTC)

A quick google reveals Blass was given Grothendieck's prenotes for EGA 5. [2] So he certainly knew some influential people. There also seem to be proof of editorship of journal [3], standing in elections as a write in candidate (lots of links). Slashdot (that most relaible of sorces) mentions hims in conection with some dubious compression algorithm work with ZeoSync [4]. --Salix alba (talk) 19:35, 31 July 2006 (UTC)

And another quick look at Google Schoolar shows 24 publications mentioning his name, including some on Zariski surfaces. Google Print also gives few hits. On the other hand, the article needs copyedit and other claims ('one of the fathers of the Internet) seem more dubious.-- _{Piotr Konieczny aka Prokonsul Piotrus | talk}  02:53, 2 August 2006 (UTC)

I removed links to his name from several well known mathematicians. Math Genealogy lists two advisors: James Milne and Melvin Hochster. Others may have taught him some undergrad classes but anyway this is not notable. Using ip trace I found a clear evidence that he is trying to promote himself and is using WP for political purposes. I actually don't mind (and don't care) whatever is on the page on him but find inappropriate the insertion of his name averywhere. Inventor of WWW is simply laughable (he does give half the credit to Sir. Tim Berners-Lee). Mhym 14:36, 2 August 2006 (UTC)

15 of his 33 publications are in the Ulam Quarterly, which he founded. This journal was founded in 1987; before going defunct in 1997, it published a whopping 10 issues, each of which contains at least one (sometimes two) articles co-authored by Piotr Blass. This journal is, according the journal website, also the first electronic mathematics journal and is apparently the basis for Blass' claim of being inventor of the WWW.

It's not just the WWW claim that is dubious. A number of his achievements listed are suspect. Simply knowing and interacting with famous people is not an achievement. In fact, a number of people do this...that goes hand-in-hand with being famous (a lot of people know and talk to you). Organizing seminars at IAS is not an achievement. Being a member (even visiting), would be.

Blass' claim to fame is doing some of the early work on Zariski surface and naming it. I'm not sure if he's even as notable as Norman Johnson. But like I said, his bio should probably stay, but it needs to be heavily edited by people other than Blass. --Chan-Ho (Talk) 16:51, 2 August 2006 (UTC)

I got the founding date of 1987 for the journal from the anon/Blass edit, but apparently the first issue came out in 1992 according to the journal website (see contents of first issue) and MathSciNet. I don't suppose this really matters or adds anything except to give a more accurate context for Blass' WWW claim. --Chan-Ho (Talk) 17:29, 2 August 2006 (UTC)

There is some wonderful dirt on Blass [5]

[6] I don't quite understand it all but it seems to involve a company called CyberNet, 5 Star Trust Bank, kids in abusive treatment center, Diebold. Seems like Blass had evidence of defects in Diabold voting machines, being hacked by kind from Bay Point School correction facility (where he taught), but he withheld information due to ties with an atoney with connections to the republican party (the attony helped Blass get his son out of another correction facility).

So to add to inventing the WWW, we might add Blass was responsible for Bush getting into the whitehouse in 2000. --Salix alba (talk) 18:19, 2 August 2006 (UTC)

AfD it is Wikipedia:Articles for deletion/Piotr Blass. --Salix alba (talk) 19:11, 2 August 2006 (UTC)

Prerequisites

I was reading an amusing interchange on the talk page for Lie groups just now. (Sorry, I don't know how to link to the specific section in the talk page. Maybe someone can help me with that.) Anyway, a user who clearly didn't understand the complexity of Lie group theory was trying to suggest that the page was worthless. This user suggested that the complexity of the article meant that the uninitiated could not follow it and the initiated didn't need it since they knew it already.

While I vehemently disagree with these sentiments, the discussion did lead me to think that maybe we need some system by which we can communicate prerequisites to those seeking information on a topic for the first time. No textbook would ever discuss Lie groups without either mentioning in the preface the need for a solid background in smooth manifolds, or else providing a reasonably comprehensive introduction to the subject in the book itself. I fully realize that Wikipedia is an encyclopedia and not a textbook. Nevertheless, a newcomer to Lie groups should know first thing that they ought to be comfortable with smooth manifolds (and probably some group theory too) before attempting to read (let alone criticize) an article on Lie groups. (I am thinking about this for all math topics, not just Lie groups, of course.)

What do y'all think? VectorPosse 05:58, 6 August 2006 (UTC)

The link you want is to Talk:Lie group#is this useful?. I am not familiar with templates, but perhaps we need a template for pointing to another article containing the prerequisites for reading the current article. JRSpriggs 06:44, 6 August 2006 (UTC)

I strongly disagree with putting any list of prerequisites on top of articles.

First, if a user never heard of differential geometry before, and complains that Lie group is hard to read, he/she has only himself/herself to blame. Reminds me of somebody who complained that logarithm is a useless article, because that person could not find a motivation for that article to exist.

Second, a well-written article should have a good introduction, and relevant links to other subjects should be embedded in context. That's encyclopedic.

All in all, while I strongly agree that articles should be accessible, boxes of prerequisites are not the solution. Oleg Alexandrov (talk) 07:07, 6 August 2006 (UTC)

An encyclopedia article is not a textbook, nor even a chapter of a textbook. Also, the web of knowledge admits no simple linear ordering. We get complaints about mathematics articles being opaque on a regular basis. The appropriate response depends on the state of the article, and on the topic.

People can arrive at an article in many ways. Perhaps they were searching the web for a word or phrase. Perhaps they were reading another article that thought this would be a useful link, either for background or enrichment. Maybe someone overheard the topic in a conversation and wanted to get a feel for what it's about. Or maybe someone has a text that is less than clear to them and thought Wikipedia could help. (We wish!)

Sound like a challenge? It is. A good mathematics article on a popular topic is especially hard. If that topic includes a modicum of technical difficulty, look out. If lots of people think they know something about it, the editing can get controversial.

Unfortunately, "Lie group" should be a major service article. It needs an introduction that a high school student can handle, but also needs to touch on material that can occupy months of graduate study.

We never want to say "if you haven't studied group theory and differentiable manifolds, go away". And what about matrices, since many of our examples occur as subgroups of GL(n,R)? No, prerequisites are unacceptable.

What might be more helpful is a "related topics" box. We would want to indicate something about the nature of the relationship, and we would need to avoid the temptation to link everything to everything. But I think it could be a major project to begin augmenting our articles in this way, and I'm not sure who would do it. Meanwhile, we do have a "Categories" area at the bottom of the page, which means it is often overlooked. --KSmrq^T 09:48, 6 August 2006 (UTC)

I initiated the discussion without any preconceived notion of what might be a "good" or "bad" way to approach the idea, but now that I've seen some of the discussion, I would tend to agree with Oleg Alexandrov. A well-written introduction can and should refer to the subjects that are required without causing any great disruption to the thousands of pages that already exist. (Having said that, many such pages probably do need better introductions. The more abstruse pages seem very far removed from their basic categories.)

I do not think that prerequisites suggest "go away". If presented correctly, they should come across as helpful. Those who are curious about an advanced topic will try to read the article anyway (and this is a good thing), but at least they are informed as to why the article is confusing to them and where they can go for more basic information. I think there are unintimidating ways of writing an introduction that communicate the essence of a topic, but at the same time point the reader toward articles which may be more appropriate for their level. I would guess that this is an ideal that we can all get behind. VectorPosse 21:30, 6 August 2006 (UTC)

This might be a good time to mention that we do have a Manual of Style specifically for mathematics, and that the first piece of advice offered is:

"Probably the hardest part of writing a mathematical article (actually, any article) is the difficulty of addressing the level of mathematical knowledge on the part of the reader. For example, when writing about a field, do we assume that the reader already knows group theory? A general approach is to start simple, then move toward more abstract and technical statements as the article proceeds."

In my experience, the advice is accurate, but no substitute for experience! Anyway, perhaps that article will help. --KSmrq^T 23:27, 6 August 2006 (UTC)

Proposed merge: "Bicomplex number" into "Tessarine"

Hello. I recently came across the article bicomplex number, which appear isomorphic to tessarines. The latter appear the first use of this arithmetic, and all properties listed in "bicomplex number" are already contained in "tessarine". Another complication is that when Hamilton's quaternions were still new, some also referred to them as "bicomplex number" (but I have not seen this term used for quaternions in articles in the past 100 years). See also talk:bicomplex number.

As a suggestion, we could have bicomplex number redirect to tessarine, and add the isomorphism (with the one reference) there. The tessarine article itself needs some minor work, e.g. to list its algebraic properties first and then refer to isomorphic numbers (I acknowledge having contributed to this disorder while working on rewriting hypercomplex number; sorry for that, I simply haven't gotten to clean up "tessarine" yet).

Any comment, concern, or help is appreciated. Thanks, Jens Koeplinger 13:17, 8 August 2006 (UTC)

After finding at least four different uses of the term "bicomplex number" within just a few hours, we may be looking at (yet another) term that appears to have been used freely in mathematics, where each use was apparently clear within the context of the particular program where it was used. Similar to the use of "hypercomplex number". Well that's just great. I hope for the future that the internet, and in particular establishments like Wikipedia and full-text search, will give authors better tools to research existing terminology when scoping out naming for something they deem "new". Therefore, maybe we should rather make the "bicomplex number" article in a way that disambiguates all these uses. A simple disambiguation may not be enough, because one may want to write a few sentences for each section. Oh well. Thanks for any comment or additional information (see also talk:bicomplex number. Jens Koeplinger 17:18, 8 August 2006 (UTC)

Looks like the current version of the bicomplex number article stub refers to a special type of the multicomplex number program, and appears to be widely used. Therefore, I've added a new multicomplex number stub, with some barebone description, and updated some references and isomorphisms. So the bicomplex number article is really for keepers, but we must also provide reference to the other uses. One use (synonym to quaternions) is outdated and can be referenced as such, another use is actually from a compound term "variational bicomplex" and we can provide a link to this different area (which doesn't exist yet in Wikipedia). I'll follow-up on the one remaining use (appears to be initiated by Aristophanes Dimakis and Folkert Müller-Hoissen about 6 years ago), as name for an algebra program. - - - Thanks for your patience in reading my monologues here; though I'd always be glad for *any* kind of feedback. Thanks, Jens Koeplinger 01:42, 9 August 2006 (UTC)

I noticed that the article Hypernumber (redirected from Conic quaternion) states the following: "Conic quaternions are isomorphic to tessarines". I have to confess ignorance as to the proper terminology in this area, but this should be taken into account if true, or corrected if wrong. --Lambiam^Talk 01:53, 9 August 2006 (UTC)

Agreed, just updated, thanks for letting me know. For reference on the term "conic quaternion" see e.g. the preprint http://www.kevincarmody.com/math/sedenions1.pdf . Thanks, Jens Koeplinger

Hypernumbers crackpottery

From the immediately preceding discussion I stumbled upon the article on hypernumbers which is, at best, incomprehensible (to me being a mathematician) and probably plain crackpottery. Nowhere does the article state what hypernumbers actually are (presumably certain finite-dimensional algebras over the real numbers, but what properties are sought of them is left entirely unstated), nor is the linked site http://www.kevincarmody.com/math/hypernumbers.html any clearer. (On the other hand, it does contain such ridiculous statements as "New kinds of number [sic] will likewise give rise to new areas of science." or "This enables great advances in consciousness and matter." (page 15 of http://www.kevincarmody.com/math/hypernumberreference.pdf — which claims to be a reference but still does not explain what hypernumbers are).)

The only reference we are given are the papers of a certain Charles A. Musès, all published in Appl. Math. Comput., so I looked them up in MathSciNet and the reviews are eloquent enough (indeed, most reviewers flatly decline to comment, or seem to have found them hilariously funny); in fact, such sentences from the articles are quoted as: "How can any mathematician doubt where the source of new creativity in mathematics lies? […] We suggest that hypernumbers in our unrestricted sense are the key to a coming and deeper nuclear mathematics; that their explanation and delineation will mark as great a step as did the implications of nuclear structure in modern physics." (this is from "Hypernumbers II. Further concepts and computational applications", Appl. Math. Comput. 4 (1978), 45–66). Obviously C. Musès found the editors or referees of Appl. Math. Comput. sympathetic to his kind of crackpottery.

It would be nice to have the Wikipedia article deleted, but as it is nearly impossible to suppress an article, I guess we should just put up a banner of some kind. Ideally, the article would be reduced to a sentence such as: "Hypernumbers are a 16-dimensional non-associative algebra over the real numbers (or certain subalgebras thereof) which was studied by Charles A. Musès who believed in their application to physics, biology and engineering." Perhaps with a description of the generators and relations of the algebra, if anybody can make sense out of them.

(I don't have time to fight this battle or to argue with crackpots, so I'm just writing to make sure other participants are aware of this.) --Gro-Tsen 11:25, 9 August 2006 (UTC)

Your last sentence is remarkable. I thought I had filtered the properties of certain hypernumber types from all of the rest Musès wrote. The filter I applied was that at least two people had published about it (C. Musès and K. Carmody), and that I could understand and confirm it from defining relations. I find Mr. Carmody's works on hypernumber arithmetic clear, sound, and well written. I find the focus on multiplicative modulus of a number interesting, do believe they qualify as their own number system, and do not believe that deletion of the article is an improvement. How do we deal with a situation where the person who discovered something gives ridiculous and even derogatory statements, throws out statements and "proofs" that don't work? I do not find Musès' articles funny, I am actually frequently offended by them. To my knowledge, though, it was him who found the real powers and logarithm of $\varepsilon$ (the non-real root of +1 that is also part of split-complex algebra), and it was K. Carmody who found sedenions with a multiplicative modulus. As far as I can see, what's currently on the Wikipedia page "works" ... What do we do? Thanks, Jens Koeplinger 15:25, 9 August 2006 (UTC)

I think for a start, we should define hypernumbers. I don't understand after reading the article what they are, and I followed the link to Carmody's page, and I can't tell from what he has there what they are either. Everything that is written seems to assume that the reader is familiar with the definition. Take the subsection Hypernumber#Epsilon numbers, from which no one could deduce what an epsilon number is, what epsilon itself is, and what it means for them to be the third level in the program. Not to mention that the seemingly fundamedntal idea of "power orbit" is referenced everywhere but never described (I suppose it means "all powers of a number", but the terminology is new to me, and confusing). I have to say that everything in the article strikes me as typical of what crackpot ideas I've seen: a confusing and grandiose compilation of claimed results without clear definitions, consistent notation, or verifiable statements. Of course, that's the way the articles on Carmody's page are written too, so it's not necessarily your fault...but if there doesn't exist a coherent account of this stuff I would say it's the work of a crackpot. However, if it's been published it may be "notable", so at the very least it would then be our duty to figure out what "it" is in the first place. Ryan Reich 20:46, 9 August 2006 (UTC)

Sounds great to me. I recognize that the article is not well structured and lacks clarity, and it would be wonderful if it could be improved. What about adding an "algebra stub" notice on the article, to highlight that the article cannot remain in its current form? Thank you very much for pointing out several weaknesses. While we may have trouble finding a definition of hypernumbers in general (Musès did not provide one ...), we can put the numbers that are currently stated on the page on defining relations. We could say "Musès conceived hypernumbers as [...thisandthat...] Select examples are [...]" and so on. As for the definitions that are missing, epsilon is a non-real base number with $\varepsilon {}^{2}=1$ and is identical to j from split-complex algebra. The "power orbit" of a number b is $b^{\alpha }$ with $\alpha$ real. Maybe it would make sense to have two sections in the article, the first section focusing on the hypernumber types containing reals, imaginaries, and $\varepsilon$ bases, and then a section that gives a briefer overview over the three other types currently listed. Well, let me put the stub notice out there for now, hopefully we'll get more responses (possibly on talk:hypernumber?). Thanks a lot, Jens Koeplinger 01:18, 10 August 2006 (UTC)

Already the article on split-complex numbers seems of dubious interest to me: most unfortunately it does not mention the (obvious) fact that, by the Chinese remainder theorem, "split-complex numbers" / "epsilon numbers" can be identified with pairs of real numbers with termwise addition and multiplication (I mean, not only are they a two-dimensional algebra over the reals, but actually they are the direct product of two copies of the real numbers), which makes them sort of boring (why bother about the product of two copies of the reals, not arbitrary tuples?); the identification takes the pair $(a,b)$ to ${\frac {a+b}{2}}+{\frac {a-b}{2}}\varepsilon$ (the number $\varepsilon$ is called $j$ in the article on split-complex numbers; and it's a trivial exercise to see that this is indeed an isomorphism). (Also, incidentally, the article is wrong in stating that split-complex numbers have nilpotents: they don't, they have divisors of zero but no nilpotents.) I'm stating all this to refute the idea that the number $\varepsilon$ is an interesting object. As to it's "power orbit", i.e., a one-parameter subgroup, once we have identified split-complex numbers with pairs of real numbers as I explained, and the number $\varepsilon$ with the pair $(1,-1)$, it is clear that one-parameter subgroups all lie in one connected component (both coordinates positive) of the multiplicative group of invertible split-complex numbers, and $\varepsilon$ is not there, so it does not have a "power orbit" (no more than -1 has in the real numbers). Similarly, trying to add both $i$ with $i^{2}=-1$ and $\varepsilon$ with $\varepsilon ^{2}=1$ just gives you pairs of complex numbers, again not very interesting. This is all basic algebra and applications of the Chinese remainder theorem. --Gro-Tsen 10:15, 10 August 2006 (UTC)

I can only agree that many articles need improvement (but I am glad that you did respond). If you repost your last message in talk:split-complex number I'd be glad to respond (it's getting very specific now). Or, to save you time, I'd also be glad to cite your last post there ... This will be funny, I'm looking forward for the reactions.

As for the hypernumbers page, I do thank anyone for the attention, and I'm glad to "let go" and answer question on the talk page, from what I can answer. I'm a physicist, with interest on physics on numbers that are not typically used, and I noticed gaps, missing information, and missing links (isomorphisms) in Wikipedia. So I've added some as good as I can, though I'm not native to the field (mathematics). Any review or improvement is, as always, welcome. Thanks again, Jens Koeplinger 12:08, 10 August 2006 (UTC)

Feel free to repost my comment elsewhere if you think it wise. Personally I won't follow the "split-complex numbers" page because I don't think it's interesting in any way (but it's not really crackpot stuff either: it's just entirely boring) and I don't have time to improve it. I just find it laughable if it turns out that nobody noticed that these "split-complex numbers" are just isomorphic to pairs of real numbers (something which should be obvious from the start to anyone with a minimal background in algebra, e.g., having read Lang's book). Btw, "tessarines" / "bicomplex numbers" are similarly isomorphic to pairs of complex numbers. Any (commutative and associative) étale algebra over the real numbers is a product of copies of the real numbers and the complex numbers, anyway. --Gro-Tsen 12:38, 10 August 2006 (UTC)

I looked at this Kevin Carmody's website, the main reference of the hypernumbers page, and I'd like to point out that he's an unmitigated crackpot. Even if this topic were at all standard, we probably shouldn't be using his website as a reference. I will say that it can be very difficult to tell crackpot math from real math, especially if the crackpot in question studied mathematics in earnest before losing their grip, and especially they attract followers. I think this is the situation we have going here. It just has that certain feel - think of John Nash in "A Beautiful Mind" with the newspaper and magazine clippings. Originalbigj 16:55, 10 August 2006 (UTC)

Please see talk:hypernumber for the list of sources from which I directly drew from, and the reasoning behind it. Thanks, Jens Koeplinger 18:03, 10 August 2006 (UTC)

I would like to point out that "epsilon number" already has an established meaning. An epsilon number is an ordinal $\epsilon _{\alpha }\!$ such that $\epsilon _{\alpha }=\omega ^{\epsilon _{\alpha }}\!$. JRSpriggs 02:58, 11 August 2006 (UTC)

This is one of several meanings of ε, ranging from conic sections to calculus. If Carmody and Musès have come up with another one, so be it. Nor are they entirely original; the use of ε for a non-trivial unit is fairly common in the study of rings - outshone, I think, only by ω. Septentrionalis 13:57, 11 August 2006 (UTC)

Adminship requested

I have requested adminship, largely to deal with the backlogs of move and discussion pages. Since Oleg endorses, I think I can mention it here. See Wikipedia:Requests_for_adminship/Pmanderson. Septentrionalis 20:50, 12 August 2006 (UTC)

Am I the main math admin lobby or what? :) Good luck! Oleg Alexandrov (talk) 20:55, 12 August 2006 (UTC)

Ovoids in polar spaces

Hello,

as you can see I am on the list of participants of the Math Project. I'm still not experienced in creating my own articles.

Any quick look at Ovoid (polar space) would be appreciated, also because of the fact that English is not my native language (I do my best though).

And one fundamental question : what to do with these ovoids, they are often only treated in the case of finite polar spaces, while in fact there isn't exactly anything wrong with the definition for infinite polar spaces.

Thanks a lot,

Evilbu 22:32, 12 August 2006 (UTC)

What's lacking most are the references. --Lambiam^Talk 02:24, 13 August 2006 (UTC)

You could probably say the same about polar space though at least there's a wiki-link to Tits there. Lunch 02:45, 13 August 2006 (UTC)

Okay, I get the message. There should be references. I am willing to accept any suggestion. The problem is that incidence geometry is not well represented on the net, most of the sources would be (online) courses from my own university. It would help me a great deal if I could know which users are into geometry as well. Evilbu 12:24, 13 August 2006 (UTC)

Use Google scholar as a starting point, and the library resources of your university to find good references, usually either a textbook, or the original articles introducing the concepts. Another acceptable source is the Encyclopaedia of Mathematics. Make sure the article agrees with the reference. --Lambiam^Talk 18:25, 13 August 2006 (UTC)

Our university does have a library... But on a side note : the first professor's article on that Google scholar link, is my own professor, who taught me the definition of polar space... Evilbu 19:05, 13 August 2006 (UTC)

Verifying a reference

An anonymous contributor has edited A. Cohn's irreducibility criterion to claim that the criterion has been proved to hold for the case n=2, whereas the relevant PlanetMath page says that this is a conjecture. The contributor provided the following link to a dvi file as a reference. I cannot read the dvi file, but I think it contains an article by number theorist Ram Murty published in Amer. Math. Monthly, Vol. 109 (2002), no. 5, 452-458. Perhaps someone with a dvi reader, or with access to the journal itself, can verify that this paper does indeed provide a proof for the case n=2 ? Gandalf61 10:25, 14 August 2006 (UTC)

It gives a new proof for the n>2 case, then a long discussion and another lemma claimed to give the n=2 case as well. JPD (talk) 11:20, 14 August 2006 (UTC)

JPD - thank you for the prompt response. Gandalf61 15:54, 14 August 2006 (UTC)

Well, it seems the Planet Math page is very outdated, giving as the only reference Polya and Szego vol 2, which is actually a very old book: the 1998 version is just a reprint of the 1976 English edition which was translated and revised by someone other than the original authors. Furthermore the 1976 German edition (according to Math Reviews reviewer) differs very little from the original 1925 edition. In any case, the Murty paper mentioned above gives as the first reference a 1981 paper which proves Cohn's theorem for any base (Brillhart, John; Filaseta, Michael; Odlyzko, Andrew On an irreducibility theorem of A. Cohn. Canad. J. Math. 33 (1981), no. 5, 1055--1059.) The review for it on MathSciNet notes that the original Cohn theorem was mentioned in Polya and Szego. So it seems this conjecture has been known to be closed for quite a while. --Chan-Ho (Talk) 02:07, 15 August 2006 (UTC)

I updated the article A. Cohn's irreducibility criterion to reflect Brillhart et al's priority for the n=2 case. In a future edit I hope to change the letters used for certain subscripts to agree with the Ram Murty paper, because using 'n' it is easy to confuse the base used with the degree of the polynomial. The other improvement that might be suggested is to change the title to 'Cohn's Irreducibility Criterion', because Wikipedia's search function is too feeble to return this article in the first screen when you type in 'A. Cohn'. EdJohnston 22:04, 18 August 2006 (UTC)

Antiderivative

I wonder if there are any comments on this edit (please write them at talk:derivative). Thanks. Oleg Alexandrov (talk) 16:16, 14 August 2006 (UTC)

Did you mean to say write comments at Talk:Antiderivative? I don't see much need for discussion; the matter was already considered and decided long ago, at the top of the talk page. Are you suggesting it should be reconsidered? (Follow-ups to talk.) --KSmrq^T 03:37, 15 August 2006 (UTC)

Mathematics needed

Please help with adding the various mathematical analyses of the game Fetch (game) to the article. (See the references and further reading given in the article.) Uncle G 10:56, 15 August 2006 (UTC)

The process by which a dog tries to catch a ball may be similar to the way that a fielder in baseball tries to catch a ball which has been hit in his general direction. I know that that has been analyzed mathematically, but I do not remember the details. JRSpriggs 05:10, 16 August 2006 (UTC)

Abel Prize more prestigious than Wolf Prize in Mathematics?

That is what one anon has insisted, but I believe this is unsubstantiated and actually OR. See Talk:Wolf_Prize for my lengthy comment with diffs. Perhaps a personal remark here is in order. When the anon replaced the mention of the Wolf in the intro to Serre's article (saying Wolf is not more prestigious than Abel), I was willing to let it go as I thought at least that the Abel would be more familiar to the lay reader (due to the extensive media coverage); however, a later edit revealed that this person regards the Abel as more prestigious than the Wolf and that would be appear the basis for the first edit. I would appreciate if people could take a look, particularly mathematicians who have been been in the mathematical community for a longer time than me who can gauge this issue with their more extensive experience. I think this is kind of an interesting math cultural issue. --Chan-Ho (Talk) 11:33, 15 August 2006 (UTC)

I take the Wolf Prize to be, de facto, the top lifetime achievement award. That being said, we can't possibly talk about prestige in the abstract (would have to be via quotes). I suggest just removing all loose talk. Charles Matthews 12:19, 15 August 2006 (UTC)

Ditto. Prestige is in the eye of the beholder. Speaking of which, please report all rumors on the talk page of Grigori Perelman! ---CH 07:17, 16 August 2006 (UTC)

That's also how I would rank them, but looking at the winners they seem to be the best of the best for both, so now I wonder, what would actually make one more prestigious than the other? For the Fields Medal, could it play a role that it is only awarded once every four years? And of course you can't be an old geezer, so it does not honour a lifetime of servitude service to mathematics, but specific memorable achievements.

Problem editor

All mathematics editors should be alert to the ongoing behavior of Bo Jacoby (talk). In article after article Bo has tried to use invented (original research) notation. Then Bo lures others into endless discussions on the talk pages, where a host of editors again and again waste their time saying the same thing: "Don't do it." Examples include

• Talk:Function (mathematics)
• Talk:Root of unity
• Talk:Discrete Fourier transform
• Talk:Exponentiation
• Wikipedia:Articles for deletion/Ordinal fraction

A related wrong-headed persistence has been seen at Talk:Wilkinson's polynomial. I do not know the cause nor the intent of this behavior, but we need to find some effective way to deal with it. Patient responses on article talk pages have not been effective. Please be vigilant to catch more abuses, and please do not let Bo turn article talk pages into his own chat room. --KSmrq^T 14:23, 16 August 2006 (UTC)

I would add to that talk:polynomial and talk:formal power series. I believe we are dealing with a person without formal math education, and it takes a long time (and many editors sometimes) to convince him that he is wrong. Oleg Alexandrov (talk) 16:25, 16 August 2006 (UTC)

Aha, I would also add Talk:Lebesgue integration. That explains a lot.--CSTAR 16:53, 16 August 2006 (UTC)

And Talk:Binomial transform. Bo's behaviour, while annoying and disruptive, is minor in comparison to some of the mono-maniacal and outrageous behaviour I've seen recently seen (e.g. my talk page, ughhh). linas 03:49, 17 August 2006 (UTC)

Wikipedia:Lamest where it applies. Charles Matthews 21:12, 17 August 2006 (UTC)

Could someone check out inferential statistics? This is an article that seems to have been largely written by Bo. Statistics is not my field, but some of the technical terms defined in the article, like "deduction distribution function" and "induction distribution function", don't seem to appear anywhere else on the web (at least, not with the same meaning). A closer look by a statistician might be warranted. Another article largely written by him, in which he cites his own publications, is Durand-Kerner method. Again, I have not checked this and make no claim as to whether it is good or bad, but it might be worth a closer look given Bo's past behavior. —Steven G. Johnson 15:45, 21 August 2006 (UTC)

Durand-Kerner is ok, he earlier claimed to be the inventor of the method, since he did not find related information, but changed or allowed to change to the more usual name. The method is, as it seems, not widely known, but (personal communication by prof. Yakoubsohn at Toulose) common knowledge in the root finding community.--LutzL 17:04, 21 August 2006 (UTC)

See also Talk:Fourier transform. —Steven G. Johnson 16:29, 21 August 2006 (UTC)

Meaning of QED

Should QED be:

1. a page about the phrase quod erat demonstrandum, with a dablink to QED (disambiguation),
2. a page about quantum electrodynamics, with a dablink to QED (disambiguation), or
3. a disambiguation page, with links to both the above and to lesser uses.

My opinion is clearly (3), but come share yours at talk:QED (disambiguation). --Trovatore 20:40, 17 August 2006 (UTC)

You have shown via your question that the term is ambiguous; therefore, it should be a disambiguation page. QED Ryan Reich 20:50, 17 August 2006 (UTC)

The discussion is taking place at talk:QED (disambiguation), not here; this is just a notice. --Trovatore 20:52, 17 August 2006 (UTC)

At least admit that it was good for a chuckle. Ryan Reich 20:57, 17 August 2006 (UTC)

You could have that on your tombstone. Charles Matthews 21:14, 17 August 2006 (UTC)

I'll take mushroom, black olive, and anchovies. --Trovatore 22:53, 17 August 2006 (UTC)

I've had pizza that chewed like marble myself...Septentrionalis 01:53, 19 August 2006 (UTC)

Oppose anchovies. --Chan-Ho (Talk) 04:56, 19 August 2006 (UTC)

• Per the ethics of terminology, QED as quod erat demonstrandum has priority by several thousand years over all the New QEDs On The Block. Jon Awbrey 05:26, 19 August 2006 (UTC)
  • Well, my feeling is that, if we were to take the intrinsic importance of the subject into account, it would have to swing massively the other direction: quantum electrodynamics is one of the most fundamental attempts to describe nature yet devised by the mind of man, whereas quod erat demonstrandum is just a phrase, a piece of historio-linguistic trivia. (Obviously this is quite distinct from any consideration of the importance of the idea of proof, or even of individual proofs at the end of which Q.E.D. has appeared; those are separate discussions altogether, and the Q.E.D. article isn't about them.) Perhaps more to the point, just from a practical point of view, it's an observed fact that lots of people link to QED from physics articles, which has bad consequences if it's a redirect to the Latin phrase.
  • Still, if you want to "vote", this isn't the place to do it; I've given a pointer above to the actual debate. --Trovatore 05:46, 19 August 2006 (UTC)

JA: The just notable difference tends to be relative and shifty from year to year. That's why we have rules like prior use. Of course, this is WP, and the rule is to find the "most illiterate use" and go with that, so why am I not already sleeping, he asks himself. Jon Awbrey 05:52, 19 August 2006 (UTC)

ICM Madrid

Starts 22 August, I believe. It would be good if we geared up for the Fields Medal awards. By which I mean: get ready with a story to offer the Main Page here; have articles ready on Terence Tao and Grigori Perelman who are the hot tips; be prepared to do something quick and dirty for anyone else on the list. Compared to 2002, the world's press are likely to turn to enWP for enlightenment, as soon as the news hits the wires. Charles Matthews 21:18, 17 August 2006 (UTC)

Uh, so who else is on the list? --Chan-Ho (Talk) 05:51, 19 August 2006 (UTC)

So, as part of that, anyone ready with good pictures for Kakeya problem page? Charles Matthews 21:21, 17 August 2006 (UTC)

Update: plenty of excitement as Perelman was a no-show; need work on Andrei Okounkov (I've just mailed Princeton to see if they have a photo), Wendelin Werner. Matter arising from the latter: self-avoiding random walk is surely worth an article. Charles Matthews 12:15, 22 August 2006 (UTC)

A Google Image search turns up photos for everyone, rights status unknown. --KSmrq^T 12:34, 22 August 2006 (UTC)

Perhaps self-avoiding random walk could start as a section of Random walk before being spun off on its own. Michael Kinyon 15:48, 22 August 2006 (UTC)

There is a raw definition somewhere there, true. Quick-and-dirty is to redirect and forget ... given a Fields has been awarded, there might be rather more to it. Also, an article on Charles Loewner would be good (there is a MacTutor article); I just had time to start some of Werner's lecture notes which do hark back to Loewner's work of the 1920s. Charles Matthews 16:10, 22 August 2006 (UTC)

Wikiversity Mathematics School open

I cordially invite the partisipants of this project to the newly founded wikiversity school of Mathematics. We are still working out the policies, but any help is appreciated. --Rayc 23:55, 17 August 2006 (UTC)

Eigenvalue, eigenvector and eigenspace

Eigenvalue, eigenvector and eigenspace is up for a featured article review. Detailed concerns may be found here. Please leave your comments and help us address and maintain this article's featured quality. Sandy 22:04, 18 August 2006 (UTC)

A novice editor has created an article for the Jacobi eigenvalue algorithm; a few fixes there could be a big help as well. --KSmrq^T 12:14, 19 August 2006 (UTC)

Talk:Pi#Move Pi to π, the official discussion!

This move idea has come up again. Please discuss. (I made the point that software limitations mean that the actual move, if this passes, will be to Π.) Septentrionalis 01:59, 19 August 2006 (UTC)

Kerala school?

I copied this message from Portal talk:Mathematics. -- Jitse Niesen (talk) 14:34, 19 August 2006 (UTC)

What do you guys think about the Kerala School article and the possible transmission of mathematics from Kerala to Europe? Should the theory get a mention on our articles about calculus, newton, wallis etc? Frankly, I'm a bit alarmed about the points brought up here. Borisblue 07:51, 19 August 2006 (UTC)

Unicode article names

User:CyberSkull moved T1 space to T₁ space, that's on the heels of a move of Mu operator to Μ operator. I believe that these are cheap Unicode tricks and not a solution to the fact that Wikipedia can't represent faithfully some mathematical notation.

T1 space should ideally be "T₁ space". Since that's impossible, I think T1 space is a better name than the T₁ space gimmick. Comments? Oleg Alexandrov (talk) 21:18, 19 August 2006 (UTC)

Unless Unicode tricks can solve all our problems along these lines, I would agree that we would be better sticking with things like T1 space. I think it would be better to be consistent and avoid gimmicks - and hope that some future version of the software will give a more sensible solution. Madmath789 21:32, 19 August 2006 (UTC)

My thanks to Oleg for fixing Mu operator and Mu-recursive function which had been moved inappropriately by User:CyberSkull. I agree that titles of articles and categories should not contain characters other than printable ascii characters. It is hard enough dealing with unusual characters in the text of an article. Having such characters in a title is much worse. One might look in the wrong place in the category listing (as I did for the two I mentioned above). Or one might fail to find them with a search or even be able to enter the correct title into the search box. Or the title might not display correctly depending on one's fonts. JRSpriggs 08:48, 20 August 2006 (UTC)

Fields template

If Grigori Perelman has declined his Fields Medal, how should Template:Fields medalists read? Charles Matthews 15:42, 22 August 2006 (UTC)

How about "Perelman (declined)"? Yes, I realize that if he has declined, then technically he is not a medalist, but there should be some indication that the award was offered to him. Michael Kinyon 15:46, 22 August 2006 (UTC)

According to the New York Times, Sir John M. Ball, president of the International Mathematical Union, said, "He has a say whether he accepts it, but we have awarded it." So maybe Perelman is technically a medalist. Having said that, I believe that Michael's suggestion is adequate. VectorPosse 20:50, 22 August 2006 (UTC)

Now of some urgency, since Template:In the news has the Fields as leading item. Charles Matthews 16:16, 22 August 2006 (UTC)

Since the fact the Perelman declined will be discovered at his article, perhaps it's enough to do nothing special. Or at least postpone a more clever solution. The exact details still seem mysterious, so letting the article explain seems wise. If "(declined)" is included, be sure to use   between it and his name to prevent an awkward break in the future. (Actually, the current breaks are none too appealing.) --KSmrq^T 18:38, 22 August 2006 (UTC)

It seems that he has indeed specifically declined to accept the Fields Medal. I agree with "Perelman (declined)" in the template. ---CH 23:39, 22 August 2006 (UTC)

Grigori Perelman

I've extensively rewritten this twice in the past week to incorporate latest news and clean up "edit creep" (well intentioned edits by inexperience writers--- or thoughtless ones--- which disrupt the flow of ideas, exhibit poor diction, and generally tend to eventually render an article unreadable.) There has been some apparent trolling by editors who want to discuss the Israeli-Palestine conflict, so watch out. Sheesh! ---CH 23:38, 22 August 2006 (UTC)

Madhava of Sangamagrama

Hello! This article is about Madhava, a mathematician who lived during the middle ages. Despite being one of the greatest mathematicians (he is, in fact considered as the founder of mathematical analysis), most of his work has been discredited. The talk page of the article has a large number of unanswered questions. It would be nice if someone well versed in mathematics take a look at them. I am not submitting the article for collaboration, because it fails the nomination criteria. However, it would be wonderful if people would come forward to cleanup all the confusion and chaos on this article. Thanks! -- thunderboltz^{a.k.a.Deepu Joseph |TALK}14:34, 23 August 2006 (UTC)