User talk:Arcfrk/Archive2

Book recommendation

In Abstract Algebra, you wrote that "Numerous textbooks in abstract algebra start with axiomatic definitions of various algebraic structures and then proceed to establish their properties, creating a false impression that somehow in algebra axioms had come first and then served as a motivation and as a basis of further study. The true order of historical development was almost exactly the opposite." I'm a hobbyist who's thinking of getting into abstract algebra. Do you know of any books that more accurately reflect how the field was developed historically? Thanks. 81.94.82.39 15:03, 13 July 2007 (UTC)

Prüfer domains

Hi, Arcfrk. Thank you for your contributions to the article on Prüfer domains; I'm more of an analyst than an algebraist myself, so I'm a little out of my depth there. Is the distributivity property that you quoted [(I ∩ J)K = IJ ∩ IK] really correct, or a typo? I would have guessed (I ∩ J)K = IK ∩ JK, but that's just my naïve inexpert brain talking... :-) Sullivan.t.j 22:23, 22 July 2007 (UTC)

Hi TJ, being an algebraist, I try to contribute my ε (ε² = 0) every now and then . You are completely right about distributivity, I've noticed it but didn't get around to correcting it, so feel free. Incidentally, Bourbaki allegedly contains 14 different characterizations of Prüfer domains (although some of ours are not even included!), but I don't have it close at hand to check. Best, Arcfrk 22:46, 22 July 2007 (UTC)

Geometry article

I remembered I protected the Geometry article in May, so I went back to look to see if more protection was needed. The article looks very quiet in July. If vandalism starts again once the U.S. school year starts (mid August to September), let me know and I'll protect the page again. — Carl (CBM · talk) 17:02, 23 July 2007 (UTC)

Thank you for remembering! It is amazing what a difference the summer makes, isn't it? Very moderate volume of vandalism, indeed, but unfortunately, no improvements to the article, either. And it's too bad that we may lose the Calabi-Yau image, as it seemed to fit the lead so well. Arcfrk 23:20, 23 July 2007 (UTC)

If someone is willing to put in a little work, it may be possible to recreate a similar figure.

• Begin with "Calabi-Yau Cross Sections" on Hanson's home page.
• Read "A Construction for Computer Visualization of Certain Complex Curves" (from, e.g., cp2-94.pdf here).
• Get the Mathematica notebook he provided at MathSource.
• Optionally, consider the Live3D variation found here (under "Fermat").

I've only skimmed these, but it looks like the Mathematica notebook does 95% of the work already. Alternatively, contact Andy at Indiana, flatter him with the world-wide exposure of Wikipedia's geometry article, and ask him very nicely if he could provide a beautiful large freely licensed image for us.

Another possible contact for a vast assortment of appropriate images is Paul Bourke, who has his own take on Calabi–Yau.

I'm not sure of platform support, but Chandrajit Bajaj while at Purdue created the Ganith software to help visualize algebraic surface patches.

Other do-it-yourself options are:

1. POV-Ray, a general-purpose package which renders algebraic surfaces of degree up to seven;
2. surf, which is specialized for algebraic curves and surfaces;
3. surfex, which is built on top of surf.

In summary, there is no shortage of possibilities for great images! --KSmrq^T 14:49, 24 July 2007 (UTC)

Sorry/Coincidence

Hi,

In one of those weird happenings, I remembered to unprotect the article about 3 seconds before I got your message! A clear lapse on my part, perhaps motivated by having had to protect several articles on AfD for BLP disputes recently, which is unfortunately now common practice for those sensitive cases. Anyway, fixed. :)

Talk page undeleted also. I don't automatically undelete them -- as they sometimes confuse folks on AfD -- but I'm happy to do so on request. Best wishes, Xoloz 05:22, 11 August 2007 (UTC)

Current AfD discusion

The deleted article has been relisted at AfD: Wikipedia:Articles for deletion/Infinite monkey theorem in popular culture (second nomination). There you can express your opinion on whether to keep it or delete it. You should not just say keep or delete but also explain your rationale. Michael Hardy 18:28, 11 August 2007 (UTC)

If you have a problem with me

..I suggest you discuss it with me, at the time. Instead of bringing it up 2 1/2 months later in an unrelated discussion. I left that article entirely, disregarding the total idiocy that some editors decided to insert by deliberately choosing the wrong words. I'll thank you not to seek out opportunities to harp on it. Good day and good riddance. --Cheeser1 12:03, 31 August 2007 (UTC)

I thank you for stopping by and validating my observation concerning your Neanderthal manners. Contrary to your assertion, it is still very much relevant. Arcfrk 18:52, 31 August 2007 (UTC)

And I thank you for going out of your way to do nothing but attempt to incite personal conflict virtually unrelated to the matter at hand. I'm glad to see that you have chosen to contribute so positively to Wikipedia. --Cheeser1 22:11, 31 August 2007 (UTC)

If I may intervene (and I hesitate to enter the fray for obvious reasons), it is clear that Arcfrk's purpose was not, in fact, "to incite personal conflict." I believe that he is pointing out the fact that Trovatore has a very good record of making positive contributions, so there is very little reason for the community to believe your outrageous claims. You, on the other hand, have a history of bad behavior, and that is the point that Arcfrk is trying to make. The whole community can read your arguments and Trovatore's arguments. The fact that very few people have commented is an indication that the issue is largely irrelevant to most of us. But if you continue to push the issue, you may see more disinterested parties (like myself) joining Trovatore to condemn your irresponsible posts. VectorPosse 02:41, 1 September 2007 (UTC)

Trovatore's contributions are not in question. If he makes a million good edits, and then one bad one, it's still just as bad as any. If I've been such a horrible Wikipedian, then why does the issue of my "manners" only come up during content disputes? I've never been warned, chastised, banned, blocked, anything. But when I say that Trovatore's edits are arbitrary, and when Trovatore himself admits to refusing to compromise because he doesn't like me, it's my "manners" that are the center of attention?? And not just my manners in this dispute, but in a completely unrelated dispute MONTHS ago, in which I was hardly the one at fault (in my opinion and that of the administrators on the AN/I, to whom I reported the conflict). I never questioned Arcfrk's purpose - I'm sure he intends nothing but the best for Wikipedia. But since he considers me a cave-man, chasing me off with insults and intimidation relating to irrelevant past conflicts seems to be his idea of how to lend a hand. What other purpose could his insights about my manners serve? Trovatore made a sweeping and unjustified edit. I disputed it. No one else cares. And since they don't care but like Trovatore better, and because I refuse to let him push me around, this is what I get? Disinterested third parties taking Trovatore's side and coming down on me because he's been their Wikipedia-pal for a while? And now I get people jumping in because they're friends of Trovatore's friends. Sorry if I haven't proven myself to Wikipedia yet, or if you don't appreciate my tone of voice, but last time I checked, content disputes are content disputes, not contests of popularity, notoriety, or "manners." I'm the one who sought compromise. I'm the one who requested for comment. I'm the one who suggested a course of action when no consensus was reached. And when it came down to it, Trovatore insisted on making his edits. When I refused, he botched the article so that looking up large set will never get you to large set (Ramsey theory). Tell me I'm rude, persistent, annoying, or whatever else, but it appears that I'm the only one interested in fixing the disambig. instead of fixing my "manners." --Cheeser1 03:47, 1 September 2007 (UTC)

re: Typo fixing

Hello, I've restored a formula at Lie algebra which you have "corrected". According to the rules of mathematical syntax, every opening bracket must be complemented by a closing one, and vice-versa. Your efforts at fixing typos are appreciated, but, please, make sure you do not spoil mathematical formulas that you do not understand. Thanks, Arcfrk 19:04, 31 August 2007 (UTC)

Good catch. I'll be more careful. ssepp^(talk) 19:09, 31 August 2007 (UTC)

Von Neumann

It's not clear from your comment in the discussion over on User talk:Mathsci that your "always" in "the article in von Neumann's name is always lowercase" means, as you see it, when the word "von" starts a sentence, which is the issue under discussion. Read in the affirmative, your assertion agrees with Mathsci's, but it's not clear to me why this usage, which has apparently evolved in the mathematical community, contradicts the standard usage, i.e., capitalization of the V when it begins a sentence. Robert K S 00:43, 25 September 2007 (UTC)

Thanks for stopping by! Like many other things about the language, use of capitalization is evolving with the time and is highly idiosyncratic. In German all nouns are capitalized; the same was almost universally true in English only a century and a half ago, and even as recently as 50 years ago, you could see sentences full of capital letters. Nowadays this practice is mostly confined to the headings of various sorts. I am not sure whether the character "v" in the name of von Neumann, the man, is capitalized or not in mathematics literature. But I know that it isn't in expressions "von Neumann algebra", "von Neumann entropy" and alike, regardless of their position in the sentence. A quick check of NY Times archives indicates that other than in the headlines, his name would always be preceded by a title (e.g. Dr von Neumann), so the point is a mute one.

I wanted to explain to you why MathSci became a bit upset over your insistence on capitals. He apparently spent quite a bit of time carefully assembling the evidence of prevalent use in mathematics literature. To most people in the subject, there is no question what is right, it's almost second nature, yet he was willing to engage you and demonstrate how things are done in mathematics. Rather than dismissing him and then adding a frivolous comment, it would have been better to thank him for the effort. Arcfrk 19:00, 25 September 2007 (UTC)

Thanks for the reply. There's a difference, though, between being dismissive and being challenging. I am thankful for, but disagree with, Mathsci's selection of references. I can supply an equal number of references from "mathematical community" sources that capitalize the V when it starts a sentence or a title. There still seems to be no explanation as to why the lowercase-v usage would have evolved to become accepted (if not standardized) in one particular field. I haven't seen any evidence against my working hypothesis that, like most mutations, it is merely an error that has caught on. Robert K S 19:21, 25 September 2007 (UTC)

Re: Function and Paolo

I'd prefer to focus the article talk page on improvements (it's bloated enough!), so I'm responding to your request that I "stop insulting Paolo" here.

I speak bluntly about Paolo because I have tried other means privately and on two article talk pages with no success. How many times will he try to introduce "reverses and is reversed by" or "undoes and can be undone by" or the like (see Inverse function and its talk page, as well as Function (mathematics) and its talk page)? How many times will he write as if all inverses are two-sided, despite being told and shown otherwise? (I have a longer list of complaints, but this should suffice to illustrate.) I say things about Paolo's behavior that are not flattering, true; if that seems insulting, I'm sorry, but my intent is to correct, not insult. He presents himself as a polite supplicant, but he will not learn. I believe a language barrier is part of the problem, both in his understanding and in his writing; but that is no longer a sufficient explanation. Patient explanations were already provided, by me and others. Enough! --KSmrq^T 07:52, 6 October 2007 (UTC)

On the other hand, imagine that Paolo is a precious young daughter of yours. Would you then behave in such an irritable way? I am not aware of the situation at the Inverse function, but after a cursory glance at your talk page, it appeared to me that Paolo was trying to learn from you, and instead of responding in a positive way, you were just curtly dismissing him. A couple of things struck me as particularly unhelpful: your edit summary "Paolo, PLEASE STOP" from October 3, 2007 wholesale reversion at Function, without any explanation of what you meant by that (I had to scratch my head in vain trying to understand your point) and, if you forgive my imagery, the childish competition between you and Paolo about "who knows English best". By the way, my impression is that Paolo is behaving politely, not merely "presenting" himself in this way. And given your comment that "this is all a tempest in a teapot", is there a good reason to generate bad feelings by overdramatazing the situation?

You see yourself as a guardian of Rome against roaming barbaric hordes. I certainly commend you for watching over an incredible number of article, trying to ascertain that good quality text is not replaced with nonsense. However, it is not so clear to me that your concerns are always valid, especially, in Wikipedia's context, where anyone can edit according to their own plan, even if it goes against your understanding of the topic or dissonates with your preferred language. Perhaps, after a few rounds these edits will lead to a genuine progress, by opening up new directions of expression or by attracting other editors who will improve the text? In many cases, it is more helpful to raise specific objections on the talk page, in as direct a way as possible. On many points you will find that others agree with you, but almost certainly not in every instance; besides, this will keep us focused on improving the presentation (if it is confusing some editors, than it will surely confuse many readers!) One of my tactics in dealing with confusing points with the potential for a revert war based on a misundertanding of the issue by some editors is to leave a commented out notice right in the text of the article which succintly explains why this is so and so. Cheers, Arcfrk 22:50, 7 October 2007 (UTC)

I finally lost patience for this "inverse" question when Paolo drove away a new and more valuable editor, user Jim.belk (talk · contribs). Many of the discussions were with Jim, not me, but the patient explanations had little effect. (Happily, Jim just moved on to other articles, rather than giving up on Wikipedia.)

You do know that Rome fell to the barbarians, right? ;-)

We must have similar tastes if you think I watch that many articles; actually, I couldn't stand to do so. I limit my watching, and usually avoid topics I'm close to, knowing what will inevitably happen.

Recently I told Jim something like what you suggest about progress, that it was akin to simulated annealing. --KSmrq^T 12:37, 11 October 2007 (UTC)

Jim abandoned the discussion on inverse functions after writing exactly what he wanted. He is a brilliant editor, I agree, but I did not like some of his edits and explained why in the talk page. In the heated discussion I was not polite enough and I apologized with him. You can measure the difference with KSmrq's behaviour. His justification is amazing. In sum, "Paolo did not eventually agree with Jim, even after patient explanations, that's why I revert all of his edits and don't bother to explain why". Or "this dog barked at my pupil; why shouldn't I bite him?". Very gracious indeed. And perfectly compliant with Wikipedia policies. Paolo.dL 18:50, 16 October 2007 (UTC)

Comment about KSmrq's behaviour

Dear Arcfrk, I say things about KSmrq's behavior that are true; if that seems insulting, I'm sorry, but my intent is to correct, not insult. I tried other means both privately and publicly. Several times I asked KSmrq to raise specific objections on the talk page or in edit summaries, "in as direct a way as possible" (as you wrote above). If he did that, he would very easily obtain what he wanted (an improvement in an article or the conservation of a text which does not need to be improved). He is a great editor and an expert mathematician, honestly I highly value his opinion, and I wrote that both privately and publicly.

The last time I tried was on Talk:Function (mathematics), on the 3rd of october. I explained with great care the rationale behind the edit of mine that he reverted twice without explanation. KSmrq's answer was a comment in which he used his outstanding writing technique to offend me, rather than to explain why in his opinion I was wrong. He wrote to you that he explained already that not all the inverses are two-sided. True, but in Talk:Inverse function he accepted the two definitions given by Jim Belk on inverse function, and both of them are two-sided, as I pointed out both at the end of Talk:Inverse function, and in my 3 october explanation.

My opinion is this: if you want to summarize the definition of inverse functions, either you decide to give the most widely used definition (in short: "g(f(x))=x and f(g(y))=y") or you write "g(f(x))=x, or f(g(y))=y, or both". This was pointed out by Jitse Nitsen on a recent editing summary on inverse function: KSmrq's "round trip" does not necessarily start from X. Writing just "g(f(x))=x" (as KSmrq did originally) or just a vague definition and a two-sided example (the conversion Celsius-Farenheit, as KSmrq did in his latest edit) is questionable. Am I wrong? Maybe. In this case, a few specific words written by KSmrq would be enough to convince me. Most likely, not as many words as those he used to offend me: "Paolo still struggles to understand the variations available for inverses, yet mangles the English language to explain them to the world. The results are not pretty, and definitely not helpful"! This answer was given after I explained, on my 3 October comment, that "...my edit is compatible with the two definitions given in the article inverse function".

In sum, he did not explain and he did not consider any of my explanations. So, how can you say that my behaviour is obnoxious? What else can I do? What would you do? Would you just accept unexplained edit wars and mocking comments forever? Somebody needs to explain publicly to KSmrq that he is violating Wikipedia editing policies when he decides to revert without accepting the ensuing discussion. He should either leave to others the task of reverting, or accept to do it properly.

You wrote that "far from being dismissive of you, Ksmrq patiently worked to adopt some of your proposals, in spite of himself". "Far from being dismissive"? How can you objectively think this? He did not say that he adopted some of my proposals. On the contrary, he just kept attacking me using a generic offensive sentence. He just ignored my request for explanations. On the other hand, I had previously and patiently explained why his two sentences were, in my opinion, linguistically incorrect. This was not a childish war about "who knows English better", as you wrote above; it is obvious to everybody that KSmrq is a master in this field. I referred only to two specific sentences which he probably wrote in a hurry. It was just a due and sincere explanation of the reason why I decided to edit, without any bias against KSmrq; it was a first step to begin the discussion that he denied. The absence of bias and my honest intentions were shown in my previous comment. I publicly recognized on the 2nd of october that the rest of KSmrq's text (which he later called "verbal diarrea") was perhaps "unfocused and long" (as somebody else wrote) but excellent and compelling. Paolo.dL 09:11, 11 October 2007 (UTC)

I also would like to thank you for writing to me on my talk page. This is a situation in which I feel forced to do what I do not like to do: fight against someone who I have always held in high esteem. We first met when I used a comment of his to create the history section of Cross product. If you can suggest a different strategy, I would be happy to accept your suggestion. Paolo.dL 09:46, 11 October 2007 (UTC)

Thanks

Thanks for your kind comments at my RfA. It reminded me that we haven't interacted much recently. An obvious place would be Hilbert space, where we both see that the article needs improvement. I should have really delisted it by now, but that's not so important as improving it. Anyway, it is on my watchlist (and I expect it is on yours), so hopefully one of us will make a start at some point: if it is you, I promise to join in! Geometry guy 20:44, 16 November 2007 (UTC)

You are very welcome, and you have fully deserved all the expressions of support throughout your nomination. I remember the good vibes of support that you've transmitted when I was still making my first steps on Wikipedia, and I know of several other editors whom you have likewise strongly supported. Even though "administratorship" (if that's the term) is but the means towards the goal of building better Wikipedia, I am glad that so many people recognized your important work in bringing us closer to that goal. Alas, I have been too busy to keep up with Wikipedia in the past few months, so I've put on hold all major work on a number of articles, including e.g. Probability theory and Abstract algebra. You are most likely to meet me at Homotopy groups of spheres in the nearest future. I have been following closely all the recent developments, and I do not quite like the direction in which that articles has been developing, but I do not have sufficient time to participate in arguments over the best way to do this or that, or even to "defend" my edits (for example, once I had changed the lead in a way that was hopefully an improvement, making it more subject-specific but then it was summarily reverted to what I feel is more of a textbook style presentation inappropriate for the lead; additionally, a couple of sentences on connection with cobordism theory and Pontryagin's pioneering contribution have been completely purged from the text as a result). Congratulations on having been promoted and I am sure we'll have much constructive interaction in the future! Arcfrk (talk) 09:33, 17 November 2007 (UTC)

Thanks. I think I may have been partly responsible for removing some of your previous work on the HGOS lead. It is very difficult to steer the lead on a balanced course between being a good introductory summary and being authoritative. And also concise at the same time! There are some editors who lean towards the textbook style, others whose contributions are rather unforgiving towards the general reader. All such contributions can be valuable: integrating them into a coherent article can be difficult! Anyway, I liked your recent tightening of the lead, and appreciated your lucid comments about referencing on the talk page. Geometry guy 19:54, 17 November 2007 (UTC)

Categories of manifolds

Hi Arcfrk,

Saw your note on Categories of manifolds—you're right that it's a Frankenstein article, and confusing for that. It's a mix of "Diff, PL, Top and their relations" (which is a key part of surgery theory), and G-structures, and polynomial/complex structures. I'll rework the material, putting it onto appropriate pages. I think I'll leave the page as "categories of manifolds in geometric topology", and include a link to lists of manifolds.

The reason for a single such page was that I wanted to emphasize the relations between various notions of manifolds, and that there are forgetful maps (often forgetful functors) between them, and I didn't want to put an involved discussion on the main manifolds page, but also didn't want the overall geography of "notions of manifold" spread across myriad pages. This is partly addressed under G-structures (which should include a geography of G-structures, or a separate such page), but that doesn't address smooth algebraic varieties to complex manifolds, for instance, or $C^{1}\to C^{\infty }$ (higher smoothing): where would be a suitable place for "connections between different notions of manifolds"?

Nbarth (talk) 02:58, 25 November 2007 (UTC)

Yes, it feels a bit like Borges's celebrated taxonomy of animals! I think that Classification of manifolds may be a good place to flesh out distinctions between smooth, topological and PL theories, and the interplay between smooth and complex structures on four-manifolds can be dealt with, for example, at Donaldson theory, but I remain unconvinced that functoriality should play any role in the discussion. Also, the whole enterprise appears rather a low priority to me. On the other hand, geometric topology is crying to be expanded, and if you can do it, that would be not just more valuable, it would be terrific!

After browsing over various manifold pages, I have two general comments on how to improve your contributions.

• It's important to source your statements, so that other editors and readers do not have to scratch their heads trying to decide whether they represent someone's original approach (as in original research) or the standard way of presenting the topic.
• Duplicating and multiplicating the same material over different articles complicates their maintenance (for example, if one of them is corrected or updated, not necessarily by you, then either the rest would have to be updated at the same time, or the discrepancies will detract from the reliability and will eventually require incredible amount of time and effort to reconcile). Try to find the most appropriate place for each kind of material, put it all in one place, and use the "main" template with minimal explanations in all the other places.

Happy editing! Arcfrk (talk) 08:22, 25 November 2007 (UTC)

I hadn't really appreciated the issue that "the notion of map between manifolds is not clear from the category". In some cases it is, but as you mention, maps between symplectic manifolds are subtle (and in geometric topology, there are the notions of embeddings, immersions, submersions).

Functoriality is clearly present and useful for algebraic -> analytic (GAGA), G-structure -> G'-structure, including Diff -> PL -> Top and $C^{\omega }\to C^{\infty }\to C^{k}\to C^{1}\to C^{0}$, and general statements can be made (notably in obstruction theory of reduction of the structure group), and functoriality is not irrelevant: not only is there the question of whether a given manifold admits a refinement of the structure, but also whether a given map of manifolds admits a refinement. For instance, is a $C^{1}$ map between manifolds homotopic to a $C^{\omega }$ map between manifolds/has a $C^{\omega }$ map as a limit? (This case is related to h-principles.) Or in defining the surgery set, one doesn't classify abstract objects, but manifolds with a given homotopy equivalence.

For Diff, PL, Top, that might fit on classification of manifolds; I think it will grow quite large, as each step has a theory associated to it (non-smoothable manifolds; exotic differentiable structures on manifolds; non-triangulable manifolds; exotic triangulations of manifolds; Kirby-Siebenmann invariant; plumbing), and it may be better to sketch it at "classification of manifolds" (which is broad) and link to a main article.

The overall geography of structures on manifolds is a high priority for me: my sense is that a newcomer is easily lost, and even semi-experts are confused (witness various Hermitian manifolds/almost-Hermitian/Kähler manifold/almost-Kähler definitions before I clarified the integrability conditions).

However, I think this can be addressed briefly on the main manifolds page or list of manifolds, and the detailed on specific pages (like G-structures, holonomy, smoothing).

Re: duplication—I was (as is clear) unclear on what general policy was suggested; there's the obvious trade-off between "everything in one place" and "jump through 20 links". I'll aim to err on the side of "everything in one place", though for instance in the case of Kähler vs. almost-Hermitian etc., it was clearly a confusing point so I wanted to front it.

Re: sources—guilty on that point; I've moved 3 times in the past 2 years (including across continents) so almost all my books are in storage on the other side of the world, and I haven't easy access to a good research library here. I'll try to add more references, though of necessity they'll be mostly online sources.

I'll ping you when I've fixed up "categories of manifolds" (meaning "moved and linked to relevant specialized articles, leaving either a deleted entry or an article narrowly focused on categories in geometric topology")—thanks for the assistance and concern! Nbarth (talk) 12:19, 25 November 2007 (UTC)

Your remarks

I suggest you do not make remarks like the one you made in the edit summary to Boundedly generated groups which I largely wrote. I have included 4 or 5 proofs that free groups (and related groups) are not boundedly generated, which have in fact been discussed with my colleagues Nicolas Monod, Andre Zuk, Derek Holt and others. It is very hard, if not impossible, to locate these in the literature, even if they are folklore. Even if you happened to be an expert on these matters yourself, you should be wary of making insulting remarks in edit summaries. Anyway your edit was lazy because you did not bother to find a proper wikilink for the congruence subgroup problem; nor did you provide a reference for the treatment of the congruence subgroup problem by this method (which is not at all immediate). You could have added the book by Lubotzky (for example). In its present form, I'm afraid what you have added is not particularly useful. --Mathsci (talk) 07:55, 25 November 2007 (UTC)

I am sorry that you feel insulted, that certainly wasn't my intention, and you may be just be a tad too sensitive having invested so much time in working on the article. You are right that I happen to know a bit about this topic, enough to spot errors, but I am far from an expert. However, I object to all your other comments, which are unnecessarily provocative and belligerent. Be advised that, contrary to your insinuations:

• I did consult the literature:
  • Lubotzky's book: boundedly generated groups get a one-sentence mention on p.128, and this is clearly inappropriate/insufficient as a reference for this article
  • Platonov—Rapinchuk: contains more details on the connection, but somewhat out of date

(The connection with the congruence subgroup problem is one of the original motivations for introducing the notion of a boundedly generated group and should certainly be mentioned in the lead, but it would require some time to properly source it or, better, give a self-contained explanation.)

• I did look up the congruence subgroup problem on wikipedia: it has no article of its own, and gets only minimal coverage at the congruence subgroup, so wikilink there would be more of a distraction. (Please, feel free to start an article on this rather important topic.)
• I would characterize my edit not as "lazy" but as consistent: I have corrected certain wrong statements and improved presentation of one part of the text, but deferred other tasks to a later time. There is nothing in my edit that would need to be redone, as would have been the case had I added inappropriate references or links.

You are fully entitled to your opinion on what should and should not be included in the article. However, I hope that you would agree that wrong statements should stay out. The text you had written failed to note that the infinite cyclic group and, more generally, virtually cyclic groups, are boundedly generated, and those cases have to be excluded from "free groups are not boundedly generated" and "hyperbolic groups are not boundedly generated" assertions.

I would like to point out that one of the key wikipedia policies is No original research. I am afraid that proofs that have been discussed privately with one's colleagues but are "very hard, if not impossible, to locate … in the literature" exactly fall into the category of original research, and constitute inappropriate content. Irrespective of verifiability and OR issues, I also think that four or five proofs that X is indeed an example of Y are not necessary for a general encyclopaedic article on Y, and present more of a liability than of an asset. One school of thought holds that in a case like that, they should be put into a separate article "Proof that X is an example of Y", which you may want to consider. Incidentally, you are quite deluded if you think that your several "proofs" contribute much to comprehension of the notion of a boundedly generated group: they are quite sketchy, too sloppy to be proofs in the standard mathematical sense, for the benefit of the experts in the area not yet familiar with them, and too technical for anyone learning about the subject for the first time. Your efforts at contributing to Wikipedia are appreciated, but let us not forget the reader!

With warmest greetings to your distinguished colleagues, Arcfrk (talk) 09:43, 25 November 2007 (UTC)

I left out Novikov also. But the Burnside problem is hardly the point here, because the proofs are long and hard, whereas Golod-Shafarevich or the Grigorchuk example can put on two sides, repectively one side, of paper. The other proofs are simple remarks, not original research, and are all in the literature: references have been given. The last is just a clarification of a remark by a reviewer in Mathematical Reviews.

I wonder whether you yourself might attempt to write a section on the application to the congruence subgroup problem. I think this task is rather non-trivial, although various survey accounts do exist (some of which I have glanced at).

Which mathematicians do you talk to? --Mathsci (talk) 11:12, 25 November 2007 (UTC)

While you're at it, please correct the article on periodic groups which does not mention Olshanskii in the section on automata. Again, it seems to be a question of bounded and unbounded exponent. The proof of Olshanskii is not easy: quoting it or Novikov's, is like using a sledge hammer to crack a nut. --Mathsci (talk) 11:23, 25 November 2007 (UTC)