User talk:Arcfrk

Hi there. I saw your reply to my expert request on the Artin reciprocity page and I look forward to any insight you might be able to add. Welcome to Wikipedia. You may want to drop by Wikipedia:WikiProject Mathematics and see what other mathematicians are talking about around here. VectorPosse 10:49, 16 March 2007 (UTC)[reply]

Welcome!

Hello, Arcfrk, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or ask your question and then place {{helpme}} after the question on your talk page. Again, welcome!

I was also very impressed by your comments on Hilbert space. Welcome indeed! Geometry guy 11:43, 16 March 2007 (UTC)[reply]

Welcome from me too. Oleg Alexandrov (talk) 15:33, 16 March 2007 (UTC)[reply]

The English-language Wikipedia mathematics community tends to be a blissfully quiet backwater compared to the turbulence of the mainstream. Our articles are numerous, but vary widely in age, thoroughness, accuracy, and so on. Some of our editors are multilingual, but the typical Yank is not. Many of our editors have some level of university training, usually enough to help settle technical disputes. Good help is always appreciated, as is good company. Welcome. --KSmrq^T 17:27, 16 March 2007 (UTC)[reply]

Function

Fabulous edit to function (mathematics)! The article finally has a proper lead! You may face resistence from existing editors there, but I will back you up 100% and I hope others will too. Your edit shows great mathematical insight and the breadth of interpretation and knowledge that I believe such a general article should articulate. (See also my comments on the talk page of the article.) I wish I had had the courage to make such an edit myself - the article desperately needed a breath of fresh air. Thanks for bringing it. Geometry guy 22:07, 19 March 2007 (UTC)[reply]

Thank you for your kind words! As a matter of fact, as I explained on the talk page, I was very much inspired by your very well thought-out comments. Arcfrk 22:57, 19 March 2007 (UTC)[reply]

Been there, commented briefly, and made a few minor edits to your contribution (I hope correctly). I was very happy to hear that my comments inspired your efforts. Geometry guy 23:05, 19 March 2007 (UTC)[reply]

Differential calculus

It sounds to me like you might also care (and know in some detail) about the category differential calculus. This category desperately needs help. At the moment the main article is Derivative: this is a nice introduction, but only covers derivatives in one variable. The calculus article is not as good, and there is essentially no introductory article on calculus in many variables. Your comments and edits would be very welcome. Geometry guy 23:34, 19 March 2007 (UTC)[reply]

If you have any comments on my edits to Derivative let me know. I replied to your question on my talk page. Geometry guy 01:57, 29 March 2007 (UTC)[reply]

I just noticed your very sensible restructuring of derivative (generalizations). The next stage in my plan for derivative is to add an elementary section on vector-valued derivatives and derivatives in higher dimensions. Geometry guy 02:50, 29 March 2007 (UTC)[reply]

You are too kind to my edits. The "generalizations of derivatives" article still needs a lot of work, probably, summarizing some content and moving it out to separate articles, it's a big hodge-podge with lots of bold font at the moment. I indeed looked at the Derivative, it's in much better shape than before thanks to your efforts. We are on the same wavelength concerning this whole topic, I especially liked your comment about "derivatives of functions of one variable and Banach space derivatives - some reality check needed".

Arcfrk 03:37, 29 March 2007 (UTC)[reply]

Well, I realised your edits were just a start, but we've got to start somewhere, and preferably in the right direction! I'm very glad that I am not the only one who has noticed the strange dichotomy between the elementary and inaccessibly advanced in the differentiation articles: if you want to know the pain I feel as a geometer, take a look at chain rule ;-) Geometry guy 19:18, 29 March 2007 (UTC)[reply]

I've now completed the main work to revise Derivative and have added a section on higher dimensional derivatives. I hope this will help in refocusing Derivative (generalizations) and several other articles. I think I will move onto other things for now, but if you or other editors take this forward I will almost certainly be reinspired to join in the fun. Thanks for all your encouragement to date, anyway. Geometry guy 20:45, 31 March 2007 (UTC)[reply]

A suggestion for a linear algebra lead has been put on my user page. I'm not sure about it: I would emphasise linearity rather than vector spaces and axioms. What do you think? Geometry guy 00:08, 3 April 2007 (UTC)[reply]

It was not I who put it! I have looked at it, and I do not like it for the same reason as you: it seems strange to emphasize axioms over the idea of linearity. In almost all these subjects (topology, Hilbert spaces, differentiable functions, linear algebra) the axioms came last, yet some people editing the corresponding articles on Wikipedia insist on "explaining the axioms" instead of explaining the intuition behind the notion or how it is used. Arcfrk 01:47, 3 April 2007 (UTC)[reply]

Inner product space

Thanks for your comment. I responded on my talk page. Hopefully, I didn't make the article worse.--CSTAR 01:20, 21 March 2007 (UTC)[reply]

reverts

We have both been spending too much time recently on rewriting or reverting each other's contributions. Perhaps it would be more productive if we both agree just to add to the other's work, and not remove or revert it (except as necessary for corrections). R.e.b. 13:49, 26 March 2007 (UTC)[reply]

I completely agree. As you might have guessed from my earlier comments, I am a bit picky about the accuracy issues, which, on the other hand, can lead to unnecessary haisplitting. Arcfrk 17:06, 26 March 2007 (UTC)[reply]

Attitude adjustment

I felt I should pay a visit and offer some guidance, based on comments you left on my talk page and elsewhere. To say what I have to say, I must speak plainly; I hope you will not be offended.

As I mentioned in my previous welcoming message, many of us who contribute to mathematics articles here bring professional training and experience. However, we prefer to base our discussions on sound arguments and facts, not background and status. In fact, this is the professional way to behave, and tends to expedite our path to quality results.

Although I don't enjoy it, I can handle an occasional insult or slight. And I do understand that the Wikipedia process can be frustrating, even infuriating, and that we are all human beings with egos and emotions and other forces in our lives. But I think you will find it counterproductive to bristle if you are questioned, and very counterproductive to "throw your weight around".

I like to encourage an environment that is forgiving of mistakes, so long as someone does not make it a lifestyle. That includes emotional outbursts as well as errors in fact or blunders in copyediting. For example, I have quietly corrected mistakes that could have been caught by careful proofreading in edits you have made. Others have done the same for me.

If you have expert knowledge and experience to contribute, it won't take long for you to establish credibility and a good reputation in this community. I notice you do not state credentials on your user page; neither do I. I am satisfied — in fact, prefer — to have my contributions speak for themselves. And it rather forces me to convince with compelling arguments, not bluster.

I get the impression that you think a lot of your own opinion. Maybe that's justified. Maybe in time we'll come to think so, too. But if we do, it will be because of what we see for ourselves. So far, most of what I see is good; the rest, I hope, can be adjusted. --KSmrq^T 16:51, 27 March 2007 (UTC)[reply]

P.S.: You can reply here, if you like. --KSmrq^T 17:25, 27 March 2007 (UTC)[reply]

"Apology" accepted. Arcfrk 20:53, 27 March 2007 (UTC)[reply]

Reply

Thank you! I replied on my talk page. BTW, welcome to wikipedia, hope you enjoy your time here! linas 21:14, 30 March 2007 (UTC)[reply]

Err, I finally thought about what you wrote on my talk page. There was actually one more relation, that perhaps wasn't clearly stated, so its not just the free product of Z2 and Z. Although the Artin group looks intriguiging, I can't quite squeeze either my group M or the Heisenberg group H into the form of an Artin group. Can I convince you to take another look? linas 00:15, 31 March 2007 (UTC)[reply]

IMA

Hello. I am not doubting that the IMA is notable, or that the current article asserts it. What I inserted myself into was a situation where a user I know was being called an idiot for applying a speedy deletion tag 4 months ago. It was completely uncalled for. That's what deletion review is for. Perhaps if the initial response wasn't so caustic I wouldn't have even been interested. Leebo ^T/C 11:47, 31 March 2007 (UTC)[reply]

Welcome

Hi Arcfrk, welcome to the project. I have noticed your good work here and there. I thought you might be interested in adding yourself here. Regards, Paul August ☎ 21:39, 31 March 2007 (UTC)[reply]

elementary math articles

Thanks; for some reason you are turning up on many of the articles I'm working on. Good luck with improving some of the basic math articles: I gave up on this some time ago, as they all have a thermodynamic equilibrium state to which they gradually return. In particular, if they have archived discussion pages then any changes you make to the introduction will probably not last long.

Hodge structure could do with more expansion, and sounds like something you know about. R.e.b. 18:17, 1 April 2007 (UTC)[reply]

scholarpedia

I'm sorry if I offended you. In retrospect, yes I guess I was a bit robust. I hope the rewrite is more acceptable. And for your curiosity, no I have no links with Scholarpedia - I'd never heard of them before it came up here. Cheers, Jheald 15:09, 18 April 2007 (UTC)[reply]

Orthogonality relations

I see that you changed the name from "great" to "Schur" orthogonality relations, why did you do that? I can cite several textbooks in which it is called "great" and after 40 years of experience with group theory I wouldn't know any textbook that calls these relations after Schur. Further you say that (irreducible) representations of finite groups are unitary. This is outright WRONG. A well-known example of a non-unitary (non-orthogonal) irrep of a finite group is Young's semi-normal irrep of the permutation group S_N (N finite). So, I would suggest that you study a bit more group theory from the physics point of view before you continue changing this article. Thank you.--P.wormer 07:52, 4 May 2007 (UTC)[reply]

Calm down a little bit, will you, please? Stress is bad for your health. I thank you for your advise. Unlike you, I cannot cite forty years of experience with group theory. However, I did study group theory, and I can assure you that the vast majority of mathematical sources does, indeed, refer to the orthogonality relations as 'Schur'. Moreover, I cannot recall seeing 'great' being used at all in this context, but I am really not all that familiar with chemical literature, and would not be surprised if that term is occasionally used. Now, if you care to look up the definition of a unitary representation, you will see that it is defined relative to an invariant hermitian form. Thus a representation is unitary (or not) irrespective of a particular choice of basis. And yes, all finite-dimensional representations of finite groups are unitary. The proof is given by the construction of Maschke theorem, namely, the averaging over the group. The same construction extends to all compact groups, once the existence of Haar measure is known. Cheers, Arcfrk 08:06, 4 May 2007 (UTC)[reply]

Chemists like to call it "great". Physicists and older mathematical text (Boerner, Weyl, Miller, etc.) don't use any adjective. They simply use "orthogonality" relations. With regard to unitary: again a difference between perspective. You are saying in effect that every finite dimensional linear inner product space has an orthonormal basis (which is true, of course) and you being a mathematician couldn't care less about a choice of basis. However, physicists must compute numbers to compare with experiment. So for a physicist a matrix representation is crucial and therefore I wrote about MATRIX representations, not about GL(V). A matrix representation, as you will agree, is unitary only if its matrices are unitary. But I know, mathematicians don't like matrices any better than bases. However, I consider it very important that this article also caters for physicists (and even for chemists). When you continue on it, please make the step from endomorphisms to matrices by choosing bases which may or may not be orthonormal.--P.wormer 08:37, 4 May 2007 (UTC)[reply]

Actually, in a couple of standard math textbooks that I've checked in the meantime, such as Lang's Algebra, the adjective 'Schur' is not used. The definitive sources would be Jacobson's Algebra, Serre's Linear representation of finite groups (based on the lectures to chemists!) and Curtis and Reiner, none of which I have close at hand. However, I have confirmed that there are other types of orthogonality relations (e.g. Brauer orthogonality relations for modular representations), so it stands to reason that whenever confusion might arise, some authors (and my impression is, the majority of authors) call them Schur orthogonality relations. As an ultimate test, I've put both 'Schur orthogonality relations' and 'grand orthogonality relations' in google, the former had a few hundred references, the latter zero.

Concerning a point you have raised about mathematicians not caring about bases. First, the article had already said that a representation could be chosen to be unitary, so I merely clarified that statement. This is a nontrivial statement, and it does not follow from the existense of an orthonormal basis. For example, the natural representation of the group of triangular matrices or all matrices is not unitary, no matter how you choose a basis. Further, I think that you are a bit presumptious concerning 1) what mathematicians in general, and your humble servant in particular, do and do not care about; 2) who will be the principal users of this article, and what is the best form to present the formulas. Two comments:

Especially for people who need to do a lot of computations, good, meaningful notation is of great importance. Last thing anyone wants is to complicate an already complex procedure by arbitrary, complex notation. By that token, the article fails miserably in its choice of notation, in particular, for the representations.
There are many situations where non-orthogonal bases are used, and it makes sense (at least, to me) to state the orthogonality relations in any basis.

None of which, of course, has anything to do with what you call the orthogonality relations. Arcfrk 09:04, 4 May 2007 (UTC)[reply]

You say: This is a nontrivial statement, and it does not follow from the existense of an orthonormal basis. But it does follow for a finite group for which Maschke holds as you pointed out yourself, I was making this statement in the context of finite group representations. Further don't Google "grand" but "great" (and don't use quotes, you will see pages with the "great orthogonality theorem"). You say the notation is miserable, but again look into physics books: Wigner, Hamermesh, Cornwall, they all use this notation. Maybe we should write two articles: you do your math thing and I do my physics thing.--P.wormer 09:20, 4 May 2007 (UTC)[reply]

I gave it some more thought and I propose the following deal to you: you write "Schur's orthogonality relations" and I take care of "great orthogonality theorem". You use whatever notation you find beautiful and you leave mine alone (unless you spot errors, those must be corrected asap). Notation and nomenclature are very subjective and not worth quarreling about; one's taste depends on the "Kindergarten" one went to. When you are finished I will link to your article.--P.wormer 11:29, 4 May 2007 (UTC)[reply]

Because I still feel not good about your remarks:

temporary fix, mostly terminology and links; major overhaul of the notation and clean-up is necessary

and

Old title idiosyncratic. New title widely used in the literature,

I checked your "Kindergarten", namely the French translation of

М.А. НАЙМАРК (M.A. NAÏMARK) and А.И. ШТЕРН (A. STERN) (Theory of Group Representations).

I assume that the equation numbering is the same in the French as in the original Russian edition. If I combine Eqs. (1.3.1) and (1.4.1) of that book I find

{\frac {1}{N}}\sum _{k=1}^{N}t_{jk}^{1}(g_{k}){\overline {t_{pq}^{2}(g_{k})}}=0{\hbox{ if }}T^{1}{\hbox{not equivalent to }}T^{2}

{\frac {1}{N}}\sum _{k=1}^{N}t_{jk}^{1}(g_{k}){\overline {t_{pq}^{1}(g_{k})}}=0{\hbox{ if }}j\neq p{\hbox{ or }}k\neq q,{\hbox{ else }}={\frac {1}{n_{1}}},

which are called orthogonality relations by Naimark and Stern (no mention of Schur). Substitute $t_{jk}^{1}(g_{k})\rightarrow \Gamma ^{(\lambda )}(R)_{jk}$ and you have the result of the article. So even in the Russian mathematical literature you must deem "clean-up of notation necessary".--P.wormer 14:19, 4 May 2007 (UTC)[reply]

Well, I certainly have no objections to mentioning that the orthogonality relations are called Great orthogonality theorem in physics and chemistry literature. Indeed, I typed a wrong word in google, and with the correct phrase there is a comparable number of hits as for the Schur orthogonality relations. As I explained above, there is a good reason to include the attributive Schur, namely, to differentiate from other orthogonality relations, some of which occur in closely related contexts. For what it's worth, Google does not confirm great orthogonality relations. Naimark and Stern is a very respectable source, and I hope you would agree that their notation is cleaner, in fact, I suggest that you directly copy the formula above into the article, add it to the references and consistently change the notation throughout. In fact, I have no intention to push 'my favourite' notation down anyone's throat, as you seem to believe. To change the notation in developed articles is a very hard and thankless task. Serre's book is another very readable source, widely used, with excellent notation, you may want to adapt his notation wholesale.

I think you are reading too much into my edit summary, which merely serves a pragmatic goal of helping the editors, not passes a judgement on how well is anyone capable of writing. I do believe that both mathematics and physics can be treated in one article. Note, however, that currently there are no links to that article from any physics and chemistry articles, while representation theory part of Wikipedia is undergoing intensive expansion. In fact, at first I did not even realize that an article on the orthogonality relations already exists, precisely because of what I refered to as an 'idiosyncratic title'. Anyway, feel free to improve the article, and I will contribute in a little bit. Cheers, Arcfrk 19:38, 4 May 2007 (UTC)[reply]

OK, now that the dust is settling: (i) I like to know what your exact objections are against the notation. I myself would have written $D^{\lambda }(g)$ with the D of Darstellung and the g of group element. However, the Γ and the R were already chosen by a previous author of the article and because of Wikipedia politeness I kept it that way. (ii) With regard to unitarity: I noticed that Naimark and Stern also say that any finite group matrix representation is equivalent to (not is) a unitary one. Which I expressed by stating that one may choose unitary matrices to represent finite and compact groups. (iii) I agree that one article (plus possible redirects) that is readable across the whole of science would be best. However, I got the impression that you wanted to rephrase it in the condensed algebraic language of Curtis and Reiner (I once had to study parts of the 1962 edition of the book and found it very tough going). Look at Schur's lemma, this is written a language that is very hard to read for a non-mathematician. I added the paragraph "alternative formulation", which is more readable (I hope) for physicists and chemists. PS. We could have had this discussion, in a more friendly tone, if you had entered your objections on the talk page of the lemma before actually making major changes.--P.wormer 10:03, 5 May 2007 (UTC)[reply]

My primary objection to the present notation is its clumsiness. Further, I do not believe it to be standard in any way. Mathematicians (and many physists) like to denote their representations by small greek letters such as π, ρ, σ, τ; in the case of explicitly given matrices it may be t as in the example that you quoted, or in some contexts R or T. The superscript λ is employed for labelling the representations if the full set of irreducible representations is known. In this general context, it is not useful, rather, it is distracting and should be dropped. The elements of the group are commonly denoted by small latin characters, usually (but not always) corresponding to the name of the group, such as g for G, h for H, etc. There are lots of minor consistency issues, such as summation over g ∈ G as opposed to what's on the page now, etc, all of which require careful thinking through. Again, this is why it may be preferable to import the notation wholesale from a reputable and authoritative source known for its attention to details, such as the Serre's book.

Concerning unitarity, you probably realize that it is not required for the orthogonality relations, just replace the adjoint matrix with the matrix element of the inverse element. When the matrices are unitary, you can, of course, use either formulation. A more serious issue is that I believe that coordinate-free formulation of the orthogonality relations should be given (for me, it's the primary form, but I can see the utility of having an explicit formula with indices as well). The present text contains an error where it says that orthogonality holds if representations are different (should be inequivalent instead), and it is not helpful to hide behind notational gimmicks, such as superscripts λ.

You have a good point about Schur's lemma. That article is very spotty, and has to be rewritten. One of the most important parts of Schur's lemma is not addressed at all, namely, that if two irreducible representations are inequivalent then all intertwining operators between them are zero (this part of the Schur's lemma is used in the proof of the 'orthogonality' case of the orthogonality relations). Your edit is a good step forward, but far from sufficient. I have taken note of the problems, but do not have time presently to bring Schur's lemma to the proper level. Again, contrary to your supposition, I am not a great fan of Curtis and Reiner, nor of Bourbakist approach. However, I am very conscious of good notation clarifying conceptual understanding, and the other way around: profusion of indices masking the true meaning. And I believe the coordinate-free formulations to be greatly elucidating, even if you eventually want to get your hands dirty and do computations with concrete vectors and matrices. For the record, other than changing the name of the article, which you may consider a 'major change' (but there is still a redirect), I've performed some clean-up (link to compact groups is preferable in the lead, corrections of a few statements), but no substantial changes. You should stop being paranoid about mathematicians closing in on you and rewriting your favourite articles in the axiomatic fashion! Arcfrk 00:33, 7 May 2007 (UTC)[reply]

Edit conflicts

An easy way to avoid most edit conflicts is to edit just one section of an article at a time, as the wikipedia software is smart enough to notice when two people are editing different sections and does not flag this as a conflict. (Also you will lose less work next time wikipedia crashes.) R.e.b. 05:18, 10 May 2007 (UTC)[reply]

Mathematics CotW

Her Arc, I am writing you to let you know that the Mathematics Collaboration of the week(soon to "of the month") is getting an overhaul of sorts and I would encourage you to participate in whatever way you can, i.e. nominate an article, contribute to an article, or sign up to be part of the project. Any help would be greatly appreciated, thanks--Cronholm144 17:29, 13 May 2007 (UTC)[reply]

P.S. I hope the contentious nature of En.wiki hasn't turned you off to much. Most of us are trying to do the right thing;)

Category vs field

Hi Arcfrk,

Sorry to have disagreed with you recently at WT:WPM. It reminded me that we have not crossed paths for some time, which is a pity, and certainly my fault because you left some friendly invitations on my talk page which I did not get round to following up.

I'm also sorry I've not been a model of clarity at the discussion, as you seem to have missed my main point, which is that the field system is useless for evaluating context: it is much better to use categories. I claim that it doesn't make much difference whether algebraic geometry is separate or not: for instance, "Plane algebraic curve" and "Grothendieck site" would still be pretty incomparable, as would "cubic surface" and "Taniyama-Shimura conjecture". On the other hand, using categories, these concepts do no need to be compared directly. Geometry guy 01:52, 22 May 2007 (UTC)[reply]

Hi Geometry guy,

Wow! Thank you for such a thorough and fantastic reply! I hope you don't mind if I interleave my response.

Thank you for finding time in your busy schedule to address some of my concerns. Upon re-reading the discussion (which has grown quite a bit by now, as you know:-), I see that you brought in categories, as opposed to the field entry on the rating template rather belatedly. Many people who participated in discussion agreed that rating within a specific context is better than 'absolute' rating (although there is at least one vocal opposing view), and you can count me in this large group. What is at issue here is what constitutes the context. Jitse Niesen made a good case with pseudo-differentiable quasi-widgets that rating within a specific context makes ratings at different level of hierarchy rather incomparable, and I do not think you addressed the issue well in your subsequent comments. I think that interpreting the 'Field' as context makes a lot of sense, and it seemed to mesh well with your initial example of motives vs platonic solids, but you rather cursorily, and I would even say, arbitrarily, suggested that it's the categories that are of primary concern, and proceeded to ignore or brush aside all subsequent arguments, as if this were a self-evident truth not worth discussing. As a matter of fact, I was so surprised that I asked myself whether you, forgive me for the indecent thought, might suffer from a severe case of WP:OWN re math ratings! Please, reassure us that it is not so, and you can rationally and unbiasedly address the issues that were raised.

A true friend is the best critic, and there is clearly a point for me to answer and reflect on! I am certainly trying to be open to the issues: I would not have posted at all if I had no doubts or questions, and my POV has developed in response to the dialogue rather than as a prior agenda. However, at the back of my mind is not so much WP:OWN as WP:Who is going to do the work?, and I am aware that this might mean I am sensitive to some of the suggestions raised, especially considering that a month ago very few people seemed to be at all interested in maths ratings.

A significant expansion of the number of fields would require a lot of work. I take your point entirely about the benefits of such expansion, and in the long run, "geometry and topology" could be split into (e.g.) "general topology", "algebraic topology", "differential topology", "elementary geometry", "differential geometry" and "algebraic geometry".

I am not at all against this. I just think it might be premature to do it now, especially if Wikipedia:Category intersection gets implemented (which would change the whole framework for this discourse). In the meanwhile, it seems to me that splitting off one of these fields is rather an arbitrary thing to do. The remaining field "geometry (non-algebraic) and topology" seems rather artificial.

I will challenge your next paragraph, but I understand your general point.

Part of the problem with things that do not make sense is just that: they do not fit together. Thus it is frequently a futile task to try to explain why certain statements do not fit together, and is both easier and more constructive to attempt to emend them. Nevertheless, let me try to explain what I found self-contradictory in your statements. In one sentence you complain that the certain 'Fields', like Algebra and Differential geometry and topology, have grown too large for the purposes of rating; and then you proceed to ridicule a proposal of splitting off a rather large (at least 500 articles),

I ridiculed nothing (although you explain this below). I just made an alternative suggestion. Yes algebraic geometry is a large subfield, but if we want to split the field in two I would rather it were split "into two equal halves" (as my woodwork teacher used to say, to the hilarity of the class!) and I doubt algebraic geometry is more than a quarter, unless you include a lot of number theory and commutative algebra. As above, this idea has longer term potential, but it is not clear to me that it is the best current solution.

separate, and rather artificially embedded subfield of Algebraic geometry (you may disagree, but I personally feel that if you exclude the small overlap with elementary geometry, it's closer to algebra than geometry, certainly, in the techniques used, but to large extent, also in the direction of development).

I do disagree with this. There is a huge overlap with differential geometry (Calabi-Yau's, hyperkahler manifolds, symplectic techniques in Kahler geometry, the whole "stability and extremal/constant scalar curvature metrics" issue which is so hot right now, etc.).

I say 'ridicule', because I do not think your argument (if it may be called so) that algebraic geometry can be further split into arithmetic, algebraic, analytic, and geometric parts is of any relevance here,

Slightly straw-man. Algebraic geometry has a lot of coherence, but it is a coherence (and differential geometry is not so different) that has the potential to take over everything! If I were arguing that the best solution was to split off differential geometry, I would expect you to challenge it!

except to cloud the issue by bringing in a separate point of contention, 'Field' vs 'category'. Of course, what you wrote about different points of view in algebraic geometry is true, and likewise, geometry has algebraic, differential, analytic, topological and other sides; the only thing it proves is that we are looking at the top levels in the hierarchy of mathematical subjects. Entirely uncontroversial and utterly irrelevant.

Except that these sides overlap with other fields and there are possibly arbitrary decisions to be made.

As far the proper contexts for ratings go, and I sense that we may disagree here (although you didn't directly address the two bullet points I raised in the discussion), I believe that it's possible (and preferable) to compare the significance (not the notions themselves) of elliptic curve and Grothendieck topos, or of Plane algebraic curve and Grothendieck site within algebraic geometry; but it is rather more subjective to compare the importance of triangle and Grothendieck topos within geometry as a whole.

What about triangle and exotic sphere or Donaldson invariant or hyperkahler manifold?

Note that Taniyama-Shimura conjecture is number theory.

This illustrates my point: how to decide that a conjecture about elliptic curves is number theory rather than algebraic geometry? There is even trouble in the current system distinguishing between algebra and number theory.

To summarize, I thought that I completely agreed with some of your points, but then other things you said made me question whether I understood you at all. I conjectured (and, please, do not take it the wrong way) that a possible reason may be that you are attached too much to the rating project to have rational discourse, but based on your last comments about the CD version of Wikipedia you have a hidden agenda which you should state up front so that we understand what exactly is up for discussion. I read the discussion carefully, and quite liked many suggestions being made by various contributors, but, sadly, felt that you were mostly interested in promoting your POV. Best, Arcfrk 19:35, 22 May 2007 (UTC)[reply]

Alas, the discussion might have been simpler if I had had a hidden agenda, or if I had thought more about importance in context, the Wikipedia 1.0 CD point of view, and how importance in context might be implemented in practice. Instead I raised the question, because I discovered from rating articles that I did not have a clear idea how importance ratings are decided. My POV has developed with the discussion, and the category idea was indeed a belated one. However, I freely admit it is coloured by pragmatism, which editors who have not adjusted 1000 maths ratings might not appreciate.

I am reading the discussions with interest. The objections to assessment within context are from a very well qualified and insightful new editor, and even if assessment within context has consensus, there is room for compromise over what this means. The issue that makes me appear to have a strong POV is the implementation. If I saw some willingness from other editors to go through hundreds of articles altering fields, my point of view on pragmatism would be entirely different. Geometry guy 20:57, 22 May 2007 (UTC)[reply]

May I interject a brief observation? Until a day or so ago my only exposure to the project was seeing messages on WT:WPM, and seeing ratings appear on articles I watch. Now I have seen the scope of the undertaking, which is huge. (Per Douglas Adams: "Space is big. Really big. You just won't believe how vastly hugely mindboggingly big it is. I mean you may think it's a long way down the road to the chemist, but that's just peanuts to space.") In that light, I think the idea is to get any kind of toehold we can, questionable or not, and climb. In the time it takes for two or three editors to exchange a few words (or more) about the best way to proceed, we could instead make tangible progress on dozens of articles. The fields are only there to help organize and mobilize the rating effort. They have no importance beyond that. As I see it.

There is a different question about standards for ratings, so editors can have a reasonably consistent (modulo personal bias) criterion for assigning and interpreting them. Clearly a topic may have a different significance for one specialty than for another, and we should use categories and subject knowledge, not the "field" tag, to guide us. But that's another discussion. --KSmrq^T 22:53, 22 May 2007 (UTC)[reply]

Your queries about GA/R of Georg Cantor

Hi. I noticed you made some queries there, and I realized that not everyone, especially people only recently participating actively in Wikipedia (and participating at WT:WPM) will know the history. Our math A-class and scientific citation guidelines were partly created due to tensions and opposing viewpoints between the GA folk and sizable number of members of WikiProject Mathematics and various science wikiprojects. Your first query about referencing is a reasonable one, but I fear it will only exacerbate the people there. Same with your second query, which only served to point out to them that we created an A-class because we didn't think GA was good for our purposes. There's perhaps too much stuff to slog through, but if you look through the archives at WT:WPM, you will get a good idea of the (unfortunate) situation. --Chan-Ho (Talk) 13:10, 26 May 2007 (UTC)[reply]

Hello, and thank you for explaining the situation to me! I was somewhat aware of the tensions that you mention, but didn't realize that they were that bad. I hope that I didn't let the GA people loose with my queries; on the other hand, it is naive to think that they could miss not one, but four tags of A-class on the talk page. And given the completely public nature of Wikipedia, do you think they have not caught up with the separate math guidelines yet? My main reason for pointing out that Georg Cantor is in many respects is a model article is because I grew alarmed by their casual 'Yeah, needs a solid rewrite' attitude. If you followed recent edit wars on that article, you know what I mean! Best, Arcfrk 13:22, 26 May 2007 (UTC)[reply]

You raise some interesting points. Let me just say that perhaps it is not so obvious, but "Good Article" is in fact a WikiProject too. At some time some people suggested that perhaps the overall consensus on Wikipedia was against the GA guidelines on how a "good article" should look. The response to this by the GA folk was that it's their WikiProject and so they have no obligation to follow consensus from outside it. I think this answers your implicit questions. --Chan-Ho (Talk) 02:40, 28 May 2007 (UTC)[reply]

If that is the current and official attitude of the GA project, then I am somewhat relieved. I propose that we voluntarily withdraw all articles in the mathematics project from GA status and place them under a new "A−" class, and henceforth boycott participation in GA. I assume, however, that FA cannot be so dismissive of Wikipedia consensus. --KSmrq^T 09:54, 28 May 2007 (UTC)[reply]