User talk:R.e.b./Archive 5

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Multiplicity-one theorem

Multiplicity-one theorem is a new article written by someone clearly unfamiliar with Wikipedia usage conventions. It seems to be about group representation theory. Can you help clean it up? Michael Hardy (talk) 04:51, 1 February 2010 (UTC)

The present form of the article seems harmless. r.e.b. (talk) 05:19, 1 February 2010 (UTC)

It seems to have changed a lot since I posted the comment above.... Michael Hardy (talk) 07:21, 1 February 2010 (UTC)

...just to be clear, this is the version that I first saw, where the opening line was "Let k be a field". Michael Hardy (talk) 19:38, 2 February 2010 (UTC)

You should not worry so much. Anyone looking up "multiplicity-one theorem" probably knows what a field is. r.e.b. (talk) 20:19, 2 February 2010 (UTC)

But most of the articles on Wikipedia that I see are not on things that I looked up. Michael Hardy (talk) 22:05, 2 February 2010 (UTC)

Yau article

It's a potential embarrassment, since great chunks of non-encyclopedic material are now being added. I can handle the adminstrator's angle. Over-claiming on the mathematical front is not going to be good for Yau, though, either. You'll probably see why I'm concerned. Charles Matthews (talk) 16:56, 4 February 2010 (UTC)

I would wait a couple of weeks for everyone to lose interest, then quietly clean it up. As long as no-one is adding anything libelous it is not worth worrying about. r.e.b. (talk) 17:21, 4 February 2010 (UTC)

Talk:Hecke operator

Another familiar name. Charles Matthews (talk) 10:21, 6 February 2010 (UTC)

He's been around for several years under various IP addresses. r.e.b. (talk) 14:56, 6 February 2010 (UTC)

Crooked egg curve

Hello. If you know some algebraic geometry, maybe you could comment on this: Wikipedia:Articles for deletion/Crooked egg curve. Michael Hardy (talk) 15:59, 15 March 2010 (UTC)

Seems to be a made up name for an uninteresting curve. r.e.b. (talk) 16:36, 15 March 2010 (UTC)


Thanks for correcting my embarrassing oversight [1], and even calling it a "typo". Sometimes I love Wikipedia. Hans Adler 19:18, 20 March 2010 (UTC)


I added a link from Herglotz–Zagier function to Don Zagier and vice-versa. So far there's only one link to the new article besides the bot-added link from the list of mathematics articles. I seems probable that some other articles should link to it. Michael Hardy (talk) 16:44, 24 March 2010 (UTC)

...and now I've linked to two eponyms: Gustav Herglotz and Don Zagier, and it seems not altogether impossible that the first one is the wrong one, so you may want to look at that. Michael Hardy (talk) 16:53, 24 March 2010 (UTC)

Whittaker model

In the above-mentioned article, you only define a Kirillov model, not a Whittaker model. Is this a typo? --Roentgenium111 (talk) 11:26, 25 March 2010 (UTC)

Yes. Fixed. r.e.b. (talk) 14:28, 25 March 2010 (UTC)
Thank you. --Roentgenium111 (talk) 18:22, 25 March 2010 (UTC)


Osgood curve and William Fogg Osgood now link to each other. Several other articles now link to Osgood curve but only as a "see also", except two articles that are lists. So if there are others that should link there or if it can be included within the body of the text rather than as a "see also", you might think about adding those links. Michael Hardy (talk) 04:50, 28 March 2010 (UTC)

......I suppose the lack of a concrete example of an Osgood curve is a "typo". But maybe that kind of typo would take considerable work to fix. Michael Hardy (talk) 04:52, 28 March 2010 (UTC)

Laziness rather than a "typo". It's easy enough to describe explicit examples as variations of the Peano curve, but the topic is so obscure it didnt seem worth the bother. r.e.b. (talk) 05:06, 28 March 2010 (UTC)

Hypergeometric series / Hypergeometric function

You've probably got them on your watchlist, but anyway you'll probably be interested in this edit summary. If you can convince me here as well that's fine- it looks like you know what you're doing, I just don't want a situation where one editor thinks it should be one way, then the next one to come along thinks the other etc. Peter 16:16, 13 April 2010 (UTC)

Schwartz's list

Since you are working over the hypergeometric function, I thought I'd go back to the reference I know about the finite monodromy case (an old book by Poole on differential equations). What in fact is there is a "Schwartz list" of 15 spherical triangles, classified by the resulting finite group. This must be the same thing, and all very "well-knowable", but not the best sort of citation given that the connection may be somewhat folkloric, or reliant on the old papers of Schwartz and Klein. I first came across this business in papers of Nick Katz. So I wonder if there is a sensible modern reference. Charles Matthews (talk) 18:10, 14 April 2010 (UTC)

It's in Erdelyi, vol 1, page 98 or

Schwarz, H. A. (1873), "Ueber diejenigen Fälle in welchen die Gaussichen hypergeometrische Reihe eine algebraische Function ihres vierten Elementes darstellt", Journal für die reine und angewandte Mathematik: 292–335, ISSN 0075-4102  r.e.b. (talk) 19:03, 14 April 2010 (UTC)

Thanks - I found a whole book by Matsuda that is online[2]. Charles Matthews (talk) 09:33, 15 April 2010 (UTC)

Hypergeometric moves

I'm sorry if I caused confusion in your hypergeometric rearrangements two days ago: I thought your db-g6 tag on Generalized hypergeometric function meant that you wanted to move Hypergeometric series to that title, so I did that and then conscientiously fixed all the resulting double redirects, thinking I was being helpful, and was worried to see that you had to change them all back. Did I misunderstand, or were you engaged in a more complex reshuffle? I have tended to be rather shy of db-g6 (and am even more so now) because of the double redirect problems that arise. Maybe the best thing would be to ignore the seductive "click here to perform the move" link on the template, just do the deletion, and then say to the tagger "Right, I've deleted it, now you sort out the rest of what you want to do". Regards, JohnCD (talk) 22:04, 13 April 2010 (UTC)

No problem, and thanks for the deletion. It was part of a complicated multiple reshuffle to sort out a complete mess: the article titled "hypergeometric function" was largely about the generalized hypergeometric function, and meanwhile the information on the hypergeometric function itself was scattered over several other articles, with the result that almost every redirect in the area was wrong anyway (so a few more or less made little difference). I didnt explain at the time because I hadnt decided exactly what to, but I think everything is now more or less in the right place. There is usually no need to fix double redirects as there are bots that do it automatically if you wait a day or two. r.e.b. (talk) 22:44, 13 April 2010 (UTC)

How many valid formulae did you delete this time? —Preceding unsigned comment added by A. Pichler (talkcontribs) 07:49, 16 April 2010 (UTC)

Not sure. I moved a lot to different articles, and deleted some unsourced ones that were either trivial or not notable. r.e.b. (talk) 15:02, 16 April 2010 (UTC)

Pochhammer curve

It can be used to represent the beta function and the hypergeometric function as contour integrals.

So the obvious question is how that is done.

Once upon a time I heard this question: How can one hang a picture from two nails in such a way that if either nail is removed, the picture falls? The answer is this curve (the nails are the deleted points and the picture is located somewhere along the curve). I thought at first I couldn't figure this out without some effort and then a few seconds later this curve came to mind. I'd seen it in a complex variables course, but until I saw your new article here tonight I didn't know that name for it. A philosophy professor to whom I posed this question suggested this: a closed loop of string enters a hole drilled in the picture, goes through to the other side and returns back out through the hole. So there's an end of the loop on each side that you can hang on a nail. It works. But that's not what was intended by the question.

Picture a new curve running at a right angle to the plane through one of the deleted points, then turning so that it gets farther from the other deleted point, winding around the Pochhammer curve and returning to where it started. Then put another closed loop like that where it passes through the other deleted point. You get Borromean links. Do you think that's worth mentioning in the article? Michael Hardy (talk) 05:25, 15 April 2010 (UTC)

I guess that explains why people do not hire philosophy professors as interior decorators. I dont see why you shouldnt add your observations to the article. It really needs a picture but I'm too lazy to draw one. r.e.b. (talk) 05:52, 15 April 2010 (UTC)

I've added a picture that at least conveys the idea. Michael Hardy (talk) 06:06, 15 April 2010 (UTC)

OK, I'm wondering about this:

The beta function is given by Euler's integral
provided that the real parts of α and β are positive, which may be converted into an integral over the Pochhammer contour C as
The contour integral converges for all values of α and β and so gives the analytic continuation of the beta function.

I'd have thought there might be something that says

and to the right of "=" an expression including an integral along the Pochhammer curve, but what's there includes B(αβ) within the whole expression.

A typo? Michael Hardy (talk) 17:11, 16 April 2010 (UTC)

Yes. Fixed. r.e.b. (talk) 17:37, 16 April 2010 (UTC)

I should have guessed that's what you meant, but instead I wondered if only the B(αβ) should be on the other side. I really haven't looked at that thing closely yet. Michael Hardy (talk) 22:11, 16 April 2010 (UTC)

The contour integral converges for all values of α and β

Does that include "converging" to ∞ if α or β is 0? And if either parameter is an integer multiple of 2πi, does one just use continuity to define the function there? Michael Hardy (talk) 22:20, 16 April 2010 (UTC)

No. The contour integral converges to a FINITE value for ALL complex alpha, beta. r.e.b. (talk) 23:11, 16 April 2010 (UTC)

Oh.... It's not the integral that blows up; it's the quotient of the integral by one of those differences. So when α or β is an integer, then the denominator (1 −e2πiα) (1 −e2πiβ) is 0, and if α or β is 0 then the numerator is not 0. Michael Hardy (talk) 01:34, 17 April 2010 (UTC)

FLT and set theory

In case this is of interest.[3] The subject came up on your talk page a while back. I don't understand the article myself. I look at the FOM mailing list archives sometimes and I found the reference there. (talk) 08:17, 8 May 2010 (UTC)

Thanks. It seems little more than superficial speculation by someone who does not appear to know what etale cohomology is. It is fairly clear to anyone who works with etale cohomology that the vast set theoretic structures are not really necessary, but that eliminating them would be more trouble than it is worth. (One might be able do this painlessly by using the fact that ZFC can prove the existence of universes for any finitely axiomatizable fragment of ZFC.) r.e.b. (talk) 14:34, 8 May 2010 (UTC)

Lakes of Wada


we (some french speaking wikinautes) try to include the file

First five stages of the Lakes of Wada

in the french version of the article Lakes of Wada. It seems that it doesn't work. Maybe you should put the picture in wikicommon ?

Best regards. -- (talk) 08:54, 13 June 2010 (UTC) (Biajojo in french wp) —Preceding unsigned comment added by (talk) 08:55, 13 June 2010 (UTC)

I don't know how to transfer files to wiki commons, but if you can figure this out you are welcome to do it yourself. r.e.b. (talk) 14:33, 13 June 2010 (UTC)
I figured it out: it should work now. r.e.b. (talk) 14:56, 13 June 2010 (UTC)
Thanks a lot !!!!!-- (talk) 14:32, 18 June 2010 (UTC)

Pochhammer contour

I've finally added the Borromean link comment and the popular puzzle to the Pochhammer contour page. Michael Hardy (talk) 23:25, 10 June 2010 (UTC)


The new article titled mandelbox has a big fat red flag: it's a brand-new thing (introduced during 2010) that cites no refereed source. I won't be surprised if it arouses suspicions about "OR". Michael Hardy (talk) 03:21, 28 June 2010 (UTC)

You are correct. I made an exception per WP:IAR on the grounds that it is the most impressive fractal I have seen. r.e.b. (talk) 04:34, 28 June 2010 (UTC)

...but it still might be prudent to find something to cite that will impress suspiciously inclined people. Michael Hardy (talk) 20:53, 28 June 2010 (UTC)

named after Riemann

I've added Zariski–Riemann space to the list of topics named after Bernhard Riemann. If you know of any others that should be there but are not, could you add those too? Michael Hardy (talk) 02:54, 1 July 2010 (UTC)


Thanks for your note. I'm glad somebody is actually using zeteo! I fixed the two issues you mentioned. Jakob.scholbach (talk) 21:39, 3 August 2010 (UTC)

Brouwer fixed point theorem

You added an proof of Brouwer fixed point theorem via Stokes theorem. Could you please explain me, why is the exterior ederivative of volume form is zero? Kishmakov (talk) 13:10, 2 September 2010 (UTC)

Because it is an n-form on an n-1 dimensional manifold. r.e.b. (talk) 14:18, 2 September 2010 (UTC)
It's written that “ω is a volume form on the boundary”, so it should be n-1–form, shouldn't it? Fot example in case of n = 2 ω = r dφ in standard polar coordinat system (r, φ). Kishmakov (talk) 14:03, 3 September 2010 (UTC)
Yes. r.e.b. (talk) 14:43, 3 September 2010 (UTC)

Roth's obituary of Francesco Severi

Hi R.e.b., I saw you added a obiuary notices of L. Roth about Francesco Severi to the related entry: do you worry if I move it to the "Bibliography" section? I think it would be a better place, since there you'll find other biographical notices about him. Thank you for your attention (and of course for your help in the making of the entry! :D ): Daniele.tampieri (talk) 18:40, 3 September 2010 (UTC)

I have no objection to moving it. In fact I'm not even sure what the difference between "references" and "bibliography" is; one possibility would be to amalgamate them to save having to think about the difference. Some biographies list the person's works under "publications" and put articles by others under "references". r.e.b. (talk) 20:50, 3 September 2010 (UTC)

Linear disjointness and MathOverflow

What is said about linear disjointness and composita of fields in tensor product of fields doesn't match up to the MathOverflow thread about it.[4] What we currently do is to reference the EoM. MO's thread (at answer #4) references Zariski-Samuel, which is accessible to me; otherwise I'm not quite sure how to make the discussion there (which I'm sure is pretty good) verifiable: probably everything is known but where is it written down? This issue is actually why I got interested in MO in the first place, but I don't seem to have made progress (in other words I have got distracted by the Recent Changes there). Charles Matthews (talk) 08:58, 20 September 2010 (UTC)

Both the MO thread and the wikipedia article are quite long, and there seem to be several different definitions of linear disjointness in the literature, so I'm not quite sure in what way they are incompatible. Z-S seems the best reference for this sort of stuff, though its a long time since I looked at it. r.e.b. (talk) 14:04, 20 September 2010 (UTC)

Lattès map

In Lattès map, is the affine map from the torus to itself thought of as a map from a 2-dimensional real space rather than as a 1-dimensional complex space (so the composition of the three things is not in general holomorphic)? Michael Hardy (talk) 20:00, 21 September 2010 (UTC)

All maps are holomorphic. r.e.b. (talk) 20:08, 21 September 2010 (UTC)

Nomination of Otomar Hájek for deletion

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A discussion has begun about whether the article Otomar Hájek, which you created or to which you contributed, should be deleted. While contributions are welcome, an article may be deleted if it is inconsistent with Wikipedia policies and guidelines for inclusion, explained in the deletion policy.

The article will be discussed at Wikipedia:Articles for deletion/Otomar Hájek until a consensus is reached, and you are welcome to contribute to the discussion.

You may edit the article during the discussion, including to address concerns raised in the discussion. However, do not remove the article-for-deletion template from the top of the article. -- PhantomSteve/talk|contribs\ 08:12, 5 October 2010 (UTC)


Hi R.e.b. I'm sorry if this is a violation of Wikipedia's guidelines, but I found this page on MathOverflow recently. I've done some editing on Wikipedia so I figured that the 'reb' there might be you. Could you please answer the question raised by Joel Hamkins there(if indeed it is you)? I thought that your answer was very interesting, so I would like to know more. Again, I'm sorry for the invasion of privacy as well as the possible violation of guidelines.

Chimpionspeak (talk) 22:02, 30 October 2010 (UTC)

Sorry, but I don't know any good references. The best I can suggest is looking at some of the papers on Harvey Friedman's home page. r.e.b. (talk) 04:28, 31 October 2010 (UTC)
Oh, okay. I'll give it a look. Thanks a lot. Chimpionspeak (talk) 17:42, 31 October 2010 (UTC)

Reynolds operator

Hi, thanks for your edits to the Reynolds operator page. I did have one point of contention, though, about your non-English sources. Since the article is on the English Wikipedia, English sources are preferred. Are there any English versions or translations of the citation you listed (reproduced below)?

  1. Kampé de Fériet, J. (1934), La Science Aérienne 3: 9--34
  2. Kampé de Fériet, J. (1935), La Science Aérienne 4: 12--52
  3. Kampé de Fériet, J. (1949), "Sur un problème d'algèbre abstraite posé par la définition de la moyenne dans la théorie de la turbulence", Annales de la Societé Scientifique de Bruxelles. Série I. Sciences Mathématiques, Astronomiques et Physiques 63: 165–180, MR0032718, ISSN 0037-959X

If not, could you give some indication as to the purpose the references serve? I'm guessing from the location in the text that they're the references where J. Kampé de Fériet first named these operators "Reynolds operators", but it would be a little more clear if they were a footnote, esp. given that there are several.

Thanks again. --Charlesreid1 (talk) 23:20, 7 November 2010 (UTC)

As it states in the text, the purpose of the references is to give the earliest use of the phrase "Reynolds operator" (or rather its French version) and the original precise definition. There are several references because I have not yet made up my mind which is the best one. I agree that English sources are preferred, but in the case of original documents are sometimes not yet available. r.e.b. (talk) 00:04, 8 November 2010 (UTC)

Virasoro algebra

Greetings to all. There's an article on arXiv that you might want to add to the Virasoro algebra references. Best wishes for the New Year (even if you're asleep when it happens), (talk) 09:55, 30 December 2010 (UTC)

Harvard citations otherpage

You constructed {{Harvard citations}} and I'm hoping you might tell me where I can find the parameter otherpage explained (it looks to me like a never-implemented feature, but I'm just stumbling around in the code without fully understanding it).

Our initial problem (how to show two ISBNs) is described at WT:Citation templates#Citation problem. There is a good reason why we are trying to include two sets of page numbers in some refs (one for UK edition, one for US edition), and I was hoping otherpage might offer something more clever than just putting "pp=238 (209–10)". Johnuniq (talk) 03:29, 12 January 2011 (UTC)

"Otherpage" is a deprecated parameter that will not help for your problem. It allows you to link to a harvard citation on a different wikipedia page, if I remember correctly. r.e.b. (talk) 03:36, 12 January 2011 (UTC)
OK, thanks. Johnuniq (talk) 03:46, 12 January 2011 (UTC)

Desarguesian plane

Hi R.e.b. -- in this edit to Desarguesian plane, you replaced "finite geometries" more generally by non-Desarguesian planes, with the Moulton plane as an example, which, if I understand the term correctly, is not a finite geometry. Am I right in concluding that the article should start with "In projective geometry" rather than "In finite geometry"? Joriki (talk) 11:32, 24 January 2011 (UTC)

Page move back to Dehn Plane


Can you tell me why you moved the page back ? (on the articles talk page please)

Thanks Chaosdruid (talk) 06:08, 11 February 2011 (UTC)

Possible error in hypergeometric function article

Dear Prof. R.e.b,

The hypergeometric function article at (section Hypergeometric series) says the function has branch points at 0 and 1? Shouldn't that be 1 and infinity?

Thanks Commutator (talk) 12:05, 14 February 2011 (UTC)

No. 0 is a branch point in general. This is not obvious from the series, but a contour that starts at 0, circles around 1, and comes back to 0 will in general hit a branch point at 0. (Infinity is also a branch point, but a contour of integration in the complex plane by definition avoids infinity.) r.e.b. (talk) 15:18, 14 February 2011 (UTC)

Torsten Carleman

I restored the referenced material you removed, which was not "trivia", but referenced material, one from the Mathematical biographies page (ultimately from Wiener's famous autobiography, which was cited by page) and the other from a recent historian's book, which cites archival sources.

Please expand on Carleman's mathematics, but do not remove referenced sentences. Please consider discussing at the Wikiproject mathematics. Mvh,  Kiefer.Wolfowitz  (talk) 20:34, 12 February 2011 (UTC)

I agree with the removal since the added stuff creates drastically undue weight in the article for a narrow sensationalistic aspect of the subject's overall life and work. Also, discussion of the article content should normally go on the article talk page. (talk) 02:46, 17 February 2011 (UTC)
Please see the talk page for a longer response. I shortened this section, which is now no longer than the on-line biography at St. Andrews. The longer version has been on the Swedish WP without challenge, btw.  Kiefer.Wolfowitz  (Discussion) 17:21, 22 March 2011 (UTC)

Legendrian geometry

Hi, Can you move Non-Legendrian geometry, which is eminently Legendrian, back to Dehn's plane? Tkuvho (talk) 05:35, 24 February 2011 (UTC)

Sorry, I can't, since this now requires admin tools. Since there has been a recent edit war, I would suggest waiting a few weeks before doing anything, to give everyone time to lose interest. "Semi-Euclidean geometry" might be a better title since there seem to be two different Dehn planes. r.e.b. (talk) 06:03, 24 February 2011 (UTC)
Where did you find two different Dehn planes? Are you referring to the two geometries discussed by Dehn, as I elaborated on the talkpage? The other one may not be a plane at all; I suspect it is a sphere of an infinite radius, but I have not gotten around to applying Google translate to his German text in the Annalen. The problem with "semi-Euclidean" is that it is too similar to "semi-Riemannian", which has an altogether different meaning today. Tkuvho (talk) 13:32, 24 February 2011 (UTC)
Actually, it might be a plane, since Dehn is trying to build counterexamples to show independence of plane axioms. The appropriate title is then "Dehn planes". Tkuvho (talk) 13:51, 24 February 2011 (UTC)
"Plane" can mean "2-dimensional geometry", as in "projective plane" or "hyperbolic plane". "Semi-Euclidean" does not sound like "Semi-Riemannian" to me, and is the name that Dehn and Hilbert use for it. I suggest moving the present article to "Semi-Euclidean geometry", writing a new article on Dehn's "Non-Legendrian geometry", and making "Dehn plane" a disambiguation page pointing to both. r.e.b. (talk) 14:13, 24 February 2011 (UTC)
There really isn't enough material here for two separate articles. Whenever someone gets around to reading Dehn's German, it would be helpful to add something on his non-Legendian example here, as well. I have no evidence that anyone after Hilbert called this "semi-Euclidean", so that term is a bit moot. Tkuvho (talk) 14:17, 24 February 2011 (UTC)
Regarding the infinitesimal navbox: what do you mean when you say that Dehn did not use infinitesimals "in this sense"? There are several theories of infinitesimals, old and new, represented in the navbox. Contrary to popular belief, Cantor, Dedekind, and Weierstrass did not eliminate infinitesimals from mathematics. Thus, in Dehn's time, there was active research going on in non-Archimedean fields, for instance Stolz, du Bois-Reymond, Borel, Levi-Civita, and others. I am not sure which theory exactly Dehn used, but it must have been somewhat powerful to be able to handle square roots. There is definite continuity among all these theories of infinitesimals. There is no reason to limit the navbox to surreals and hyperreals. In short, I am puzzled by your comment. Tkuvho (talk) 17:53, 26 February 2011 (UTC)
What about putting it back to the title I moved it to after the first move "Dehn non-parallel planar geometry", or perhaps "Dehn planar geometry" ? Chaosdruid (talk) 19:34, 26 February 2011 (UTC)
Please, let's not invent names for things. Sławomir Biały (talk) 20:04, 26 February 2011 (UTC)
Dehn's paper does not use infinitesimals in the sense of calculus or non-standard analysis. There is no real connection, except that Dehn and non-standard analysis both happen to use non-archimedean fields. r.e.b. (talk) 21:44, 26 February 2011 (UTC)
It is not a name, it is a descriptive title. Chaosdruid (talk) 21:58, 26 February 2011 (UTC)
What you are calling "non-parallel geometry" is usually called Non-Euclidean geometry. In this case, there are already well-established terms for what is under discussion (see R.e.b.'s post above). There is no need to invent our own very idiosyncratic terms to denote them, hence my comment above. Sławomir Biały (talk) 22:13, 26 February 2011 (UTC)


Since the previous thread seems to be focusing on the page dealing with Dehn's counterexamples, I am starting a separate thread on infinitesimals. Does Dehn's paper use the term "infinitesimal"? Whether he used Stolz's, du Bois-Reymond's, or Veronese's infinitesimals, he was using work that Cantor attacked as incoherent, without making a distinction between different types of non-Archimedean fields. An infinitesimal is by definition an element of a non-archimedean field that violates the archimedean axiom. To what extent these can be exploited in the calculus is a separate issue, and depends on the power of the field to handle various arithmetic operations, to what extent one has a transfer principle, etcetera. The infinitesimal navbox is intended to cover all notions of infinitesimals. I am not sure what you mean when you say that it is a coincidence that non-standard analysis and Dehn both used non-Archimedean fields. There is certainly no reason to limit the navbox to non-standard analysis. leibniz was not a non-standard analyst. Levi-Civita fields naturally belong here, as well, and for all I know Dehn might have used a Levi-Civita field in his construction. Tkuvho (talk) 05:44, 27 February 2011 (UTC)

Penrose transform + twistors

Despite what Penrose intended, twistors actually do generalize to higher dimensions in a natural way (see Berkovits on "pure spinors"). Further, your articles on this are full of mathematical jargon that is extremely obfuscatory considering that twistors are concrete accessible computational tools. Could you follow Berkovits more here? (talk) 06:08, 21 March 2011 (UTC)

Could you please be more specific? On first glance, references to Berkovits would seem to more befit an article on twistor-string theory rather than an article on (classical) twistor theory, which is an established area of mathematical research that predates string theory. It's actually a little alarming that we don't yet seem to have an article on twistor-string theory. Sławomir Biały (talk) 13:42, 21 March 2011 (UTC)
Yes, Berkovits was motivated by his pure-spinor string theory, but the idea is actually a natural generalization of twistors to any even dimension (possibly odd ones too, but that is not obvious). The relevant reference is a paper titled "Higher-dimensional twistor transforms using pure spinors" by Berkovits. The explicit relationship between complex structures and pure spinors is extremely illuminating, and it is phrased concretely there. (talk) 04:16, 22 March 2011 (UTC)
I am not currently editing articles on this topic. If you have a suggestion about some article I suggest putting it on the corresponding talk page. r.e.b. (talk) 04:50, 22 March 2011 (UTC)
I am starting a new discussion at Talk:Penrose transform. Sławomir Biały (talk) 12:10, 22 March 2011 (UTC)

Indefinite logarithm

Back in August, you PRODded this, and it was deleted. Undeletion has now been requested at WP:REFUND, so per WP:DEL#Proposed deletion I have restored it, and now notify you in case you wish to consider taking it to AfD. Regards, JohnCD (talk) 18:21, 22 March 2011 (UTC)

Speedy deletion nomination of Zenon Ivanovich Borevich.

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Quillen–Lichtenbaum conjecture

The article has a line that currently says this:

Was this supposed to be a piecewise equality? Michael Hardy (talk) 01:55, 30 April 2011 (UTC)

I'm not sure. It's taken from Quillen's paper, which does not seem to make sense: I've either misunderstood something or there is a misprint in it. r.e.b. (talk) 05:50, 30 April 2011 (UTC)
Check out Grayson's article in Motives I, p. 232 [5]: The coefficients of the étale cohomology on the left are 0 if q is odd and Z(i) if q = −2i is even. Clearly, they had some typesetting mishap. RobHar (talk) 05:59, 30 April 2011 (UTC)
I think it is sorted out now. Quillen's paper seems to confuse the cohomology group with its coefficients. r.e.b. (talk) 17:05, 30 April 2011 (UTC)

Refs for p-adic distributions

A nice reference for measures and p-adic distributions is the article of Mazur–Swinnerton-Dyer: Arithmetic of Weil curves. Also, note that the terminology is kind of a mess with different people calling different things by the same name. For a nice discussion of the modern take on these ideas see chapter 1 of Colmez's book Fontaine's rings and p-adic L-functions. I'd help out, but I'm pretty swamped right now. Cheers. RobHar (talk) 17:50, 12 May 2011 (UTC)

Apropos the reversions in the Bernoulli number article.

Hi R.e.b.!

Recently you made a change in the article 'Bernoulli number' which I reversed. You again reversed. So let me explain to you why I did so and why I think it should be reversed again.

It is about the convention B_1 = 1/2 or B_1 = -1/2. You are right that B_1 = 1/2 is the more common one. But we have to acknowledge that there are major writers which use B_1 = -1/2. See for example Neukirch, Jürgen, Algebraic Number Theory, Grundlehren der mathematischen Wissenschaften.

You write: "Let's use the most common standard convention." Such a convention is fine and everyone giving a lecture or writing a book should fix his use unambiguously. However, I think it is not the mission of an encyclopedia to fix conventions. Rather, to inform about different conventions and to highlight the differences implied; this helps users to avoid confusion.

Note that this approach is common on Wikipedia in all cases where different definition or viewpoints or theories exists.

And the article does in my opinion a good job to explain the differences of the two definitions; not only in the section 'definition' much care is taken to explain both versions, also in numerous other places, for example where the different ranges of validity of representations is stated.

To help the user to distinguish different viewpoints and to enable him to draw his own conclusions about the relative merits of different conventions is an important point of a good article; not only in an encyclopedia, but in an encyclopedia in particular.

Maybe you can reconsider your reversion? (talk) 19:29, 12 May 2011 (UTC)

You seem to be rather confused. I am not using the convention B1=1/2, but am using the same convention B1=−1/2 as Neukirch, and almost everyone else such as the standard references Abramovich-Stegun and Olver. The article should use this standard convention, which is now used almost everywhere in number theory, and make a passing mention of the fact that a few authors use other conventions. r.e.b. (talk) 19:57, 12 May 2011 (UTC)
On checking Neukirch I see that he uses B1=1/2 (not −1/2 as stated in your message), but says that this is an unusual convention. Maybe you switched +1 and −1 in your message. r.e.b. (talk) 23:06, 12 May 2011 (UTC)

Weil conj.

A colleague of mine lauded Weil conjectures. I was not surprised to see your name in the history. Keep up the good work! Jakob.scholbach (talk) 13:57, 18 May 2011 (UTC)

Various conjectures

Quillen-Lichtenbaum conjecture is promising, but what with various reformulations it is not easy to see the relationship to the original Lichtenbaum conjecture (zeta-values up to powers of 2, as I understand it). On googling "Lichtenbaum's original conjecture" it seems clear that there is a relationship; as there is to the Birch-Tate conjecture. What quite "Lichtenbaum conjecture" means to the experts now I'm not so sure: without saying that things have got out of hand, some consolidation of what the literature says would be welcome. Charles Matthews (talk) 13:02, 20 May 2011 (UTC)

Heckman–Opdam polynomial(s)

I have proposed elsewhere, and I think it got mentioned in a style manual, possibly as a not-universally-agreed rule, that an article about a sequence of polynomials should usually have a plural title as in Hermite polynomials, on the grounds that it's about a set of things rather than about the individual things. Thus, for example, no same person would call an article Maxwell's equation, and even though Sir Paul McCartney is a former Beatle (and thus that word is used in the singular, the article title is nonetheless plural. That much I think is prescribed in WP:MOS. Last I checked (three or four years ago?) there was not yet an infallible decree from the Roman Pontiff or Oprah Winfrey or Miss Manners or whoever that we should do the same with polynomial sequences. Do you have any particular opinion on this one? Michael Hardy (talk) 22:44, 12 June 2011 (UTC)

de minimis non curat praetor. r.e.b. (talk) 22:51, 12 June 2011 (UTC)
Well, I guess I'll never win a Fields Medal by being a grammar-nazi...... Michael Hardy (talk) 03:33, 13 June 2011 (UTC)

TeX usage

It looks as if you wrote \mathrm{max} rather than \max in TeX. These don't always give identical results. Thus, \mathrm{max}_{a \in A} yields this:

whereas \max_{a \in A} yields this:

The latter is standard TeX usage.


\left\{ \begin{matrix} etc. etc. \end{matrix} \right.

is more complicated than

\begin{cases} etc. etc. \end{cases}

and I think in some instances that also gives different results, and is also standard for certain situations. Michael Hardy (talk) 17:29, 15 June 2011 (UTC)

You may have confused me with someone else. I do not recall using any of these constructions on wikipedia. r.e.b. (talk) 17:42, 15 June 2011 (UTC)
I see what happened now: I was copying a paragraph written by someone else (as my edit summary says). r.e.b. (talk) 17:44, 15 June 2011 (UTC)
I see. Michael Hardy (talk) 20:55, 16 June 2011 (UTC)

Frederick J. Almgren, jr.

Hi R.e.b., I have reworked a bit the entry about Frederick J. Almgren, Jr., and since you are one of the latest contributors, I thought it was a nice thing to ask for your opinion. If you do not like its present shape, please feel free to change it. Daniele.tampieri (talk) 19:57, 20 June 2011 (UTC)

Your changes look fine. r.e.b. (talk) 21:45, 20 June 2011 (UTC)

Wiener's thms


as far as I understand, Wiener's 1/f theorem and Wiener's tauberian theorem are the same fact. Do you think they should be united?

Sasha (talk) 06:09, 28 June 2011 (UTC)

PS I have posted the same comment at Talk:Wiener_algebra.

They are related but not the same. I do not think Wiener algebra and Wiener's tauberian theorem need to be merged. r.e.b. (talk) 13:13, 28 June 2011 (UTC)
well, there are many formulations of the Tauberian theorem, 1/f being one of them (the one which appears in the article can be deduced from it and vice versa). That's what I mean by "the same". Anyhow, thanks for your comment -- I think I will follow your advise. Sasha (talk) 17:10, 28 June 2011 (UTC)
hmmm... I have had another look, there are more serious problems in the Tauberian article. For example, it is not clear from what is written there that the theorems in L1 and L2 are different statements, which do not follow from one another (or have I gone crazy)? The L1 statement is what I thought is called the Wiener Tauberian theorem, and it is obviously equivalent to the 1/f thm. The L2 thm is also true and also due to Wiener, but I am not sure it even appears in the same paper of Wiener.
Sorry for bothering you again, I just do not want to change anything before I understand the rationale of what appears in the two articles now. Sasha (talk) 17:22, 28 June 2011 (UTC)
A good rule of thumb is to have one wikipedia article for each named concept. So it would be reasonable to have separate articles on Wiener's tauberian theorem, Wiener's 1/f theorem, and Wiener algebra. (If articles on closely related topics were always merged, wikipedia would end up with just one vast article.) Though merging some of these articles is also fine as they are short and closely related. r.e.b. (talk) 18:03, 28 June 2011 (UTC)

Nagata ring question

Hi. I had a question about Nagata ring, to which you seem to have been the earliest contributor. I'm kind of confused by this phrase: " integral domain A is called an N-1 ring if its integral closure in its quotient field is a finite A module." Should "finite A module" be "finitely generated A module"? Rschwieb (talk) 11:10, 12 July 2011 (UTC)

Yes. The terminology is confusing: an algebra over a ring is called finite if it is finitely generated as a module. r.e.b. (talk) 13:40, 12 July 2011 (UTC)
How widespread is the terminology "finite algebra"? It doesn't seem to be explained in wiki, and the only hits I can find online give the (obvious) interpretation that the underlying set is finite. If less than three references use this term, we should consider not propagating it. Rschwieb (talk) 14:07, 12 July 2011 (UTC)
It is (unfortunately) standard in commutative algebra and algebraic geometry. Check any commutative algebra textbook. r.e.b. (talk) 14:09, 12 July 2011 (UTC)
OK thanks for clearing that up then. This usage really should be clarified within wikipedia somewhere, though. It seems that it will trip up anyone without a commutative algebra text! Rschwieb (talk) 14:39, 12 July 2011 (UTC)
For an even worse abuse of the word "finite", see finite von Neumann algebra. r.e.b. (talk) 15:02, 12 July 2011 (UTC)

Question about old edit

In this long ago edit to Cluster expansion, you wrote that "It is only defined for field theories on a lattice, and not field theories on a continuum.". Do you remember why you said that? Glancing thru a textbook on statistical mechanics, I see that it assumes a continuum. Cardamon (talk) 23:08, 11 July 2011 (UTC)

Sorry, I can't remember offhand. My guess is that there are several different things called cluster expansions, some of which only work for lattices, and some for continuums. You may remove my comment if you think it is misleading. r.e.b. (talk) 23:53, 11 July 2011 (UTC)
I moved it to talk. Cardamon (talk) 21:53, 12 July 2011 (UTC)

p-adic group

Well, it would seem that after my edit to Andrei Zelevinsky, p-adic group appears in that article as a red link. Who'd'a thunk it? (I'll mention this at Wikipedia talk:WikiProject Mathematics unless someone does something about it in the next two seconds.) Michael Hardy (talk) 04:39, 15 July 2011 (UTC)

Favard's theorem

You wrote:

Suppose that y0 = 1, y1, ... is a sequence of polynomials where yn has degree n, and let Λ be the linear functional with Λ(1) = 1, Λ(yn) = 0 if n > 0. Favard's theorem states that if these polynomials satisfy the 3-term recurrence relation

then the polynomials yn form an orthogonal sequence for Λ; in other words Λ(ymyn) = 0 if m ≠ n.

From the relation Λ(y2
) = dn Λ(y2
), it follows that the functional Λ is positive definite if (and only if) the numbers cn are real and the numbers dn are positive.

Could it be that meant something like the following? For some particular values of cn, dn (which normally one would specify in the statement of the theorem) the sequence is orthogonal with respect to that particular linear functional, and then the general case is readily reducible to that? Michael Hardy (talk) 22:30, 8 August 2011 (UTC)

No. The numbers c and d are not specified in the theorem, though they are determined by the sequence yn. I dont know what you mean by the "general case". r.e.b. (talk) 03:28, 9 August 2011 (UTC)
It says "let Λ be the linear functional with Λ(1) = 1, Λ(yn) = 0 if n > 0." That identifies one particular linear functional. I'd have thought that the theorem says that if there is some such three-term recurrence, then there is some linear functional for which the sequence is orthogonal; not that if there is some such three-term recurrence, then the sequence is orthogonal with respect to that particular linear functional. Michael Hardy (talk) 13:48, 9 August 2011 (UTC)
You could phrase it like that, but it is trivial to see that any linear functional for which the sequence is orthogonal must be the functional Λ. r.e.b. (talk) 13:54, 9 August 2011 (UTC)

Rook polynomial

What's the rook polynomial-orthogonal polynomial connection? I didn't see anything in the rook polynomial article to suggest a link. --Joel B. Lewis (talk) 14:23, 14 August 2011 (UTC)

Rook polynomials are Laguerre polynomials up to change of variables, which are orthogonal polynomials. r.e.b. (talk) 14:52, 14 August 2011 (UTC)
Cool, thanks! --Joel B. Lewis (talk) 21:32, 14 August 2011 (UTC)



a couple of questions:

a) I saw you switched notation from theta to z in the generalisation, so I did the same in the Legendre part -- I hope you don't object.

b) A more conceptual q-n: to the best of my understanding, Mehler-Heine is a complement to simpler asymptotics (Laplace-Heine for Legendre and Darboux for Jacobi pol-s). Returning to even more basic stuff, I did not find a single wiki-article on asymptotics of OP (even in the classical case!) So the missing Laplace-Heine is perhaps not the major problem, and I do not even know where to start. If you have ideas how this should work, perhaps we can discuss it a bit and then start filling the gap.


Sasha (talk) 01:35, 20 August 2011 (UTC)

a) I have no preference for θ or z and have no objection to your change: I was only changing notation to fix a minor misprint.
b) If you are looking for things to write about related to orthogonal polynomials, Szego's book has lots of stuff that is not yet on Wikipedia, and there are still plenty of red links at Askey scheme. r.e.b. (talk) 05:02, 20 August 2011 (UTC)
well, I guess wikifying all of Szego's book is a project I won't finish in my lifetime, so I will start with more modest goals.
Sasha (talk) 15:45, 20 August 2011 (UTC)

Mourad Ismail


if you would like to add secondary sources to the article, perhaps this would help (p.466).

Best, Sasha (talk) 15:44, 22 August 2011 (UTC)

OP versus classical COP


I have put an "underconstruction" template on the Classical OP page: obviously, it needs a major revision, but I am not sure I understand what to keep there and what to move to the OP page. Since you are still editing the 2 pages, I do not want to create a mess by simultaneous editing, so I won't touch either page for a few days.

Best, Sasha (talk) 15:25, 24 August 2011 (UTC)

I havn't yet figured out what to move to the OP page or how to organize the 2 pages either. Feel free to edit either page: your edits on OPs are fine. r.e.b. (talk) 15:50, 24 August 2011 (UTC)

Category:Mathematicians who committed suicide

Please note that I have done a procedural close to Wikipedia:Categories for discussion/Log/2011 September 9#Category:Mathematicians who committed suicide, and created a new discussion about the related category tree at Wikipedia:Categories for discussion/Log/2011 October 3#Category:Suicides by occupation. Feel free to express your opinion there. עוד מישהו Od Mishehu 09:48, 3 October 2011 (UTC)

Mysterious duality

Hi r.e.b., Mysterious duality is in immediate danger of being deleted without more references that substantially address the topic. I was hoping you might have better luck with this than I did. Happy editing, Sławomir Biały (talk) 18:56, 6 October 2011 (UTC)

My policy is to stay clear of the inhabitants of Boise, who unfortunately often try to delete articles they do not understand. If you want to keep the article, I suggest taking a copy, adding a couple more references, and recreating it when all the editors who know nothing about the topic have lost interest. r.e.b. (talk) 19:50, 6 October 2011 (UTC)


Interesting tidbit you added to the zero sharp article. I heard once in an offhand conversation that the original "oh-sharp" term derived from Kleene's O. Do you have any sourceable info on that? --Trovatore (talk) 21:11, 19 October 2011 (UTC)

No. r.e.b. (talk) 12:38, 20 October 2011 (UTC)

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I was very interested in the article 3-transposition_group but I failed to find a good definition for . Do you happen to know a good reference (here on Wikipedia) or a simple explanation, that might be suitable for inclusion in the article? Many thanks!

--Evilbu (talk) 19:59, 3 November 2011 (UTC)

p-core. r.e.b. (talk) 20:16, 3 November 2011 (UTC)



if you read German, [6] may be of help.

Best, Sasha (talk) 04:32, 4 November 2011 (UTC)

"Regular surface" redirect page

I noticed you were the editor who created the redirect page from "Regular surface" to "Irregularity of a surface". Would you mind explaining the rationale for this redirect? I created a talk page section at "Irregularity of a surface" for discussion. Thanks! Augurar (talk) 03:09, 14 November 2011 (UTC)

pronunciation of "Hermite"?

I've been accustomed to thinking of the "H" in "Hermite" as silent, so that one would write "an Hermite ring" rather than "a Hermite ring". Do you have strong feelings one way or the other concerning this? (I changed "a" to "an" in the article.) Michael Hardy (talk) 17:26, 24 November 2011 (UTC)


Hi R. Since the theory of Grunsky matrices involves interpreting them as operators, I will be making Grunsky matrix the main article and Grunsky inequalities a redirect. There are a series of articles to write including a conformal welding article (using the Cauchy transform for existence for sufficiently smooth curves/diffeomorphisms and the Beltrami equation more generally), and the Grunsky matrices fit into that, this time for a pair of univalent functions corresponding to the conformal welding of the diffeomorphism. In that context the Grunsky matrices become corners of a unitary matrix. They also appear as part of the smooth model of universal Teichmüller space, which is the same thing as a slight generalisation of Diff ( S1) that several authors have studied (including your friend from UCSC, who seems to have published a corrected version of the infamous paper that did not get slated in Maths Reviews). The matrix coefficient in the projective representation of Diff ( S1) is expressed as a Fredholm determinant which arises in geometric function theory (called Fredholm eigenvalues of a planar domain) and has been calculated explicitly. Anyway, just so that you are warned (I thought quite long about what title the article should have). I liked the bio on Grunsky, which I had contemplated writing myself. Regards, A. Mathsci (talk) 18:28, 8 December 2011 (UTC)

I have no strong feelings about this and only a passing interest in the topic, so feel free to do whatever you think is best. r.e.b. (talk) 19:34, 8 December 2011 (UTC)

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Marcel Riesz


I have expanded the Marcel Riesz article which you have edited once. Comments are welcome.

Thanks, Sasha (talk) 16:54, 21 December 2011 (UTC)


Can you say whetehr this edit is a correction or not? It's outside my field of knowledge. JamesBWatson (talk) 17:39, 24 January 2012 (UTC)

It is a plausible correction as the new matrix is skew symmetric (as it should be) and the old one was not. Whether the matrix is now correct I have no idea. It really needs a reliable source as checking it is tiresome. r.e.b. (talk) 18:31, 24 January 2012 (UTC)

Loeb space

Hi, I was looking at Loeb space and it seems to me that the passage from v to mu is not completely correct. Shouldn't there be an application of the inverse shadow somewhere? Tkuvho (talk) 14:48, 8 February 2012 (UTC)

I do not see anything wrong with the article, or why the inverse shadow is needed. r.e.b. (talk) 16:12, 8 February 2012 (UTC)
Consider the set of rational numbers. Its natural extension, the hyperrationals, contains the hyperfinite grid used in the definition of the counting measure v. Therefore the rationals would have full measure if the definition you presented is interpreted naively. What one has to do instead is the following. Given a real set X, we look at the inverse image of the standard part function restricted to the hyperfinite grid. Then we apply v to the inverse image of X, and take standard part to get the Lebesgue measure of X. Tkuvho (talk) 16:41, 8 February 2012 (UTC)
I was a bit sloppy in describing the construction. The measure v cannot be applied to the "inverse shadow" because the latter is not internal. Instead, we take an outer measure generated by v, and apply that. That's the best I can do without opening some books. Tkuvho (talk) 17:04, 8 February 2012 (UTC)
It is possible to construct Lebesgue measure on the reals using Loeb measures. In this case a subset of the reals is Lebesgue measurable if and only if its inverse shadow is (internal and) Loeb measurable, and then they have the same measure. Perhaps this is what you are trying to say. However this is not needed for constructing general Loeb measures. r.e.b. (talk) 17:30, 8 February 2012 (UTC)
The inverse shadow cannot be internal. Tkuvho (talk) 17:38, 8 February 2012 (UTC)
Correct. I was not thinking when I wrote that.r.e.b. (talk) 17:42, 8 February 2012 (UTC)

the sum is over _what_?

You wrote:

where the sum is over the points of intersection of C and L

I hit a mental speed bump and thought:

  • It means so "the sum is over the points x of intersection of C and L"

and then: wait a minute: it's a plane curve, so maybe

  • It means so "the sum is over the points (x,y) of intersection of C and L.

Then I thought the latter seems more plausible, so I changed it to:

where the sum is over the points (xy) of intersection of C and L

Is that the meaning you intended? Michael Hardy (talk) 04:50, 9 February 2012 (UTC)

It should be added that this should include all complex points of intersection. Tkuvho (talk) 13:16, 9 February 2012 (UTC)


Hi, could you comment at Talk:Manifold Destiny#Birman? Tkuvho (talk) 13:23, 22 February 2012 (UTC)

I prefer not to jump into cesspits. It would be better to delete this article, but there seems little chance of this. r.e.b. (talk) 14:58, 22 February 2012 (UTC)
It does seem to be "notable". However they are currently trying to add more scurrilous material. Tkuvho (talk) 15:01, 22 February 2012 (UTC)
Please comment at Talk:Shing-Tung_Yau#Birman if you get a chance. Tkuvho (talk) 10:34, 28 February 2012 (UTC)
I advise dropping the topic, even though I agree with you. Remember the old curse: "May you be involved in a lawsuit in which you know you are right". r.e.b. (talk) 14:57, 28 February 2012 (UTC)
Thanks. Tkuvho (talk) 15:32, 28 February 2012 (UTC)

New articles

Barnstar-atom3.png The E=mc² Barnstar
Thanks for creating the new mathematics- and mathematician-related articles, including Aldo Andreotti, Giovanni Sansone, Beez's theorem and others. Your efforts to improve the encyclopedia for the public are greatly appreciated. Northamerica1000(talk) 08:01, 3 March 2012 (UTC)

Abhyankar's inequality

I added Abhyankar's inequality to the list of inequalities. If you know of others that should be there but are not, could you add those too?

The list of inequalities is organized by topic, and the only algebra section was labeled Linear algebra. I dealt with this one by creating an "Algebra" section with "Linear algebra" as a subsection. For now, Abhyankar's inequality is the only item in that section that's not in that subsection. Michael Hardy (talk) 00:13, 10 March 2012 (UTC)

Albert Eagle?

I have real questions about the notability of Albert Eagle. Sławomir Biały (talk) 02:20, 29 March 2012 (UTC)

His book has been called "the second major revolution in the history of the Elliptic Functions". The only problem is that the person who called it that was Eagle himself. So he is notable for being the world's first (and only) elliptic function crackpot. r.e.b. (talk) 02:47, 29 March 2012 (UTC)
While that's very interesting, I'm not sure it rises to the level of having an article about the person. (And after recently being subjected to a barrage of vixra and the "General Science Journal" as part of a couple of deletion discussions, I can definitively say that you perhaps underestimate the breadth of crackpottery: it's really a choose-your-own-adventure out there.) Anyway, I'm not going to make a big deal out of it either way, although if I were confronted with an AfD, I would probably vote delete. Sławomir Biały (talk) 11:31, 29 March 2012 (UTC)

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Thanks for your stubs on Polish mathematicians. May I suggest that you look at my edits to Zygmunt Zalcwasser and Zenon Waraszkiewicz, and consider incorporating them (adding categories, stub templates, talk page assessments) to your article creation process? Thanks! --Piotr Konieczny aka Prokonsul Piotrus| talk to me 15:19, 4 April 2012 (UTC)

Glossary of archaic terms in algebraic geometry


You have not answered to my post on the talk page: Many of the terms you have introduced in this page are not archaic at all. Several appear in the title of publications of XXIth century. What is your project? To rename the page glossary of algebraic geometry or removing the non-archaic terms? What about old terms which are still in use but rarely?

D.Lazard (talk) 14:39, 7 April 2012 (UTC)

It is a glossary of terms used in old (=pre-Grothendieck) algebraic geometry books. As you have correctly pointed out, some of them are still widely used, and so are strictly speaking not really archaic. I guess you could change the word "archaic" to "old" if it upsets you that much. r.e.b. (talk) 14:54, 7 April 2012 (UTC)
I understand that you consider as "archaic" or "old" the large part of algebraic geometry which does not use scheme theory. If I understand correctly, this is original research and does not correspond to the reality of modern research (see the list of text books in Algebraic geometry and their date of publication. I propose Glossary of classical algebraic geometry, but this implies to rewrite the lead and add the mention of "archaic" for the entries which really are. D.Lazard (talk) 15:21, 7 April 2012 (UTC)
I agree that "classical" is a better term. r.e.b. (talk) 15:41, 7 April 2012 (UTC)

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list of wave topics

I've added the new article titled wave surface to the list of wave topics. (I also added Category:Waves.) It seems possible that you know of other articles that should be listed there and are not. Michael Hardy (talk) 18:57, 11 April 2012 (UTC)

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Hesse's theorem

It seems to me that the phrase "conjugate with respect to some conic" ought to link somewhere. Whether the place it ought to link to currently exists is another question. I looked briefly at projective harmonic conjugate and at pole and polar, and I thought I could probably figure out where among several articles would be the best article or section to link to. But I haven't done so yet and maybe you already know. Or maybe not. Michael Hardy (talk) 16:27, 30 April 2012 (UTC)


From the little I know about covariants and from the article you created on Hermite reciprocity, it seems like a G-covariant, in representation-theoretic terms, of a representation V of a group G is simply what we would nowadays call a G-equivariant map from V to some other representation W of G. For instance, the work of Davenport and Heilbronn studies binary cubic forms and their quadratic covariant, the Hessian. However, the entry for covariant in the glossary of invariant theory seems to have a much more restricted definition. I'm really unfamiliar with any texts relevant to the notion of covariant, so I was hoping you might be able to fix up the entry in the glossary. Thanks. RobHar (talk) 02:35, 9 May 2012 (UTC)

According to Sylvester, a covariant is "a function which stands in the same relation to the primitive function from which it is derived as any of its linear transforms to a similarly derived transform of its primitive". I hope this makes everything clear. r.e.b. (talk) 02:55, 9 May 2012 (UTC)
Crystal clear!! RobHar (talk) 03:48, 9 May 2012 (UTC)

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An appreciation of one of your recent works

Hi R.e.b.; I've just come across the "A priori estimate" entry you created, and I'm writing this just to say you that I'm positively impressed: it's nice work, precise, compact and well documented, and Wikipedia deserves such articles. Daniele.tampieri (talk) 09:46, 25 July 2012 (UTC)

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Proposed deletion of Inter-universal Teichmüller theory

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The article Inter-universal Teichmüller theory has been proposed for deletion because of the following concern:

WP:TOOSOON. None of this has been peer-reviewed, cited in Google scholar by anybody other than Mochizuki himself, reviewed in MathSciNet, or described in any other reliable secondary sources

While all contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the article to address the issues raised. Removing {{proposed deletion/dated}} will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. David Eppstein (talk) 15:55, 10 September 2012 (UTC)

Is there any chance at least one of the cited papers can be described as "to appear" or something like that? I suspect what might happen is the article gets deleted because the papers are not refereed, then in a few months one or more of the papers gets published and then we'll have to remember to un-delete it rather than creating a new one. Michael Hardy (talk) 16:49, 10 September 2012 (UTC)
An anonymous editor found a reliable source and added it to the abc conjecture article. So I added it as well to the inter-universal article and removed my own prod. —David Eppstein (talk) 17:58, 10 September 2012 (UTC)


I am sorry that the template posted a Teahouse link and treated you like a new user...I just wanted to drop by to tell you I'd added that tag. When it comes to BLP (I am not sure whether or not this is one based on the ref and my quick Google search), I probably apply tags a little more liberally. Thanks and once again sorry for the tone of the template. Go Phightins! 18:55, 20 October 2012 (UTC)

Ways to improve Chitikila Musili

Hi, I'm Go Phightins!. R.e.b., thanks for creating Chitikila Musili!

I've just tagged the page, using our page curation tools, as having some issues to fix. Judging from the only source, I'm not sure if this is a BLP or not, but nevertheless, additional sources and claims to notability would be helpful. Thank you. Feel free to contact me on my talk page with any questions.

The tags can be removed by you or another editor once the issues they mention are addressed. If you have questions, you can leave a comment on my talk page. Or, for more editing help, talk to the volunteers at the Teahouse. Go Phightins! 18:55, 20 October 2012 (UTC)

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hyper-finite fields

I haven't fully digested the definition of this concept yet . . . . Would I be right if I guessed that a hyper-finite field is any field satisfying the same first-order sentences in the language of fields that are satisfied by all finite fields? Michael Hardy (talk) 03:35, 11 November 2012 (UTC)

. . . . but provided it's not actually finite? Michael Hardy (talk) 03:40, 11 November 2012 (UTC)
Not sure offhand; I would have to look Ax's paper which I cannot be bothered to do.r.e.b. (talk) 14:50, 11 November 2012 (UTC)

Teichmüller space topology

Hi, thanks a lot for all your contributions! I have one request: could you write a little at Teichmüller space about how TX obtains a topology and a complex structure? Thanks and cheers, AxelBoldt (talk) 20:54, 19 November 2012 (UTC)

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Translation of german reference

Hi R.e.b. I really need an english translation of Homologie nicht-additiver Funktore by Dold & Puppe. Here's the link Seeing as you're the one who started that page I thought you might know if there exist an english translation. Thanks in advance for any help. Money is tight (talk) 11:31, 6 December 2012 (UTC)

typesetting details

Here's an oddity that became apparent in Parafactorial local ring: The "nbsp" non-breakable space prevents line breaks when it precedes and follows a minus sign, but not when it precedes and follows an en-dash. On the browser I'm using a minus sign does not otherwise look different from an en-dash, but there you have a reason to distinguish between them. Michael Hardy (talk) 22:09, 2 January 2013 (UTC)

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torsion-free module

A while ago I had been drafting an article for torsion-free module, but I did not find the time to finish it. I'm glad you dug into it. I was wondering: is the general definition using regular elements the one Matlis used? I know that most (all?) the theory works for a slightly more general definition that appears in Lam's Lectures on modules and rings. Rschwieb (talk) 20:36, 2 February 2013 (UTC)

Matlis in his book works only over integral domains, and uses the definition that does not generalize well to other rings. r.e.b. (talk) 20:57, 2 February 2013 (UTC)
Ah, ok well in that case, I think I will cite the general definition given in Lam's Lectures on Modules and Rings so that there is a reference for it. I'm curious about other places where similar definitions are given also. Rschwieb (talk) 15:26, 3 February 2013 (UTC)

Unipotent representations

I was reading the article on unipotent representations, where I came across the following:

Unipotent representations are supposed to be the basic "building blocks" out of which one can construct all other representations in the following sense. Unipotent representations should form a small (preferably finite) set of irreducible representations for each reductive group, such that all irreducible representations can be obtained from unipotent representations of possibly smaller groups by some sort of systematic process, such as (cohomological or parabolic) induction.

My understanding was that it was not unipotent representations, but cuspidal representations, which form the basic building blocks. For instance in the representation theory of , the unipotent representations are those that appear inside , and so unipotence is in some sense orthogonal to the notion of being a building block. Could you clarify what you meant; are there other induction processes at play?

Thanks for your time, and also for all the beautiful mathematics you've contributed to Wikipedia. --SamTalk 07:40, 15 April 2013 (UTC)

Cuspidal representations are the basic building blocks for parabolic induction. For more refined types of induction such as cohomological induction or Deligne-Lusztig's construction one expects the basic building blocks to be unipotent representations. r.e.b. (talk) 13:27, 15 April 2013 (UTC)

I have unreviewed a page you curated

Hi, I'm Ankit Maity. I wanted to let you know that I saw the page you reviewed, Admissible algebra, and have un-reviewed it again. If you have any questions, please ask them on my talk page. Thank you. Ankit MaityTalkContribs 16:40, 4 May 2013 (UTC)

May 2013

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June 2013

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Irreducible representation

Hi, many thanks for your edits to the article, it is spruced up nicely as others here have recognized.

However - at the points where I originally wrote "reducible/irreducible" and you changed to "decomposable/indecomposable", the inline citations (including Wigner) use the former terms and not the latter, unless I have somehow complete misread them (the books are not to hand right now). So, the terminology seems to be torn between the current refs and the article... I will not argue about or change any terminology, but it would be great if you added at least one ref using the term "decomposable", as well as more refs furthering the definitions of "reducible/irreducible representations" as opposed to "decomposable/indecomposable".

Many thanks again in advance. M∧Ŝc2ħεИτlk 12:27, 9 July 2013 (UTC)

File:Neighborhood graph of Niemeier lattices.jpg listed for deletion

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Was I correct?

I think there were typos in the list in Glossary_of_string_theory#C, so I have attempted to fix them. It involves CAR, CCR, and CCR and CAR algebras. Please confirm that I am either correct, incorrect, or "anticorrect". :-) Bearian (talk) 13:39, 19 July 2013 (UTC)

O'Nan–Scott theorem

I linked to O'Nan–Scott theorem from the list of permutation topics. If you know of any others that should be there and are not, could you add those too? Michael Hardy (talk) 03:05, 29 July 2013 (UTC)

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