tag:blogger.com,1999:blog-8062754651764668865.post8643824179246007372..comments2023-12-09T04:56:42.838-04:00Comments on Stop Timothy Gowers! !!!: Guessing who will get Fields medals - Some history and 2014Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.comBlogger21125tag:blogger.com,1999:blog-8062754651764668865.post-28988031528972834672013-12-08T01:06:01.925-04:002013-12-08T01:06:01.925-04:00Dear Xiao-Chuan Liu,
Your comment is very cryptic...Dear Xiao-Chuan Liu,<br /><br />Your comment is very cryptic. What exactly I got wrong? Do you mean the mistake in spelling? Probably, I copy-pasted it from somewhere; anyhow I will correct it in a moment.Owlhttps://www.blogger.com/profile/13083493391293465339noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-25979188563743587482013-12-07T10:34:27.806-04:002013-12-07T10:34:27.806-04:00I think you got Artur Avila's name wrong.I think you got Artur Avila's name wrong. Anonymoushttps://www.blogger.com/profile/06665949421066135469noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-87400917959240260052013-08-16T17:33:33.411-03:002013-08-16T17:33:33.411-03:00Hi!
Thanks for commenting and paying attention t...Hi! <br /><br />Thanks for commenting and paying attention to small details. Actually, I did not write that Manjul Bhargava is from a developing country, but I could (and should) write that paragraph more clearly. I tend to write in a more or less German and a partially Russian style; this was noticed and discussed a little in the comments to the Gowers's blog (to the post about this year Owlhttps://www.blogger.com/profile/13083493391293465339noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-5203721028302528682013-08-16T09:17:28.311-03:002013-08-16T09:17:28.311-03:00Just to clarify, Manjul Bhargava is not from a de...Just to clarify, Manjul Bhargava is not from a developing country, he is from America.Siddharthahttps://www.blogger.com/profile/13445999321678627749noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-64799439664894493902013-08-04T23:55:47.886-03:002013-08-04T23:55:47.886-03:00Dear Tamas Gabal,
My reply is in the next post Di...Dear Tamas Gabal,<br /><br />My reply is in the next post <a href="http://owl-sowa.blogspot.com/2013/08/did-j-lurie-solved-any-big-problem.html" rel="nofollow">Did J. Lurie solved any big problem?</a>.Owlhttps://www.blogger.com/profile/13083493391293465339noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-48711331759691180192013-08-04T20:34:41.171-03:002013-08-04T20:34:41.171-03:00Dear Sowa,
I heard a criticism of Lurie's wor...Dear Sowa,<br /><br />I heard a criticism of Lurie's work, that it does not contain startling new ideas, complete solutions of important problems, even new conjectures. That he is simply rewriting old ideas in a new language. I am very far from this area, and I find it a little disturbing that only the ultimate experts speak highly of his work. Even people in related areas can not usually Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-18685185899512861402013-08-04T19:59:07.679-03:002013-08-04T19:59:07.679-03:00Dear Pete,
Thanks for a great comment!
I still ...Dear Pete,<br /><br />Thanks for a great comment! <br /><br />I still would like to give some specific examples. My problem is that I am not sure what counts as an example. Ideally, it would be an important result with a short and reasonably elementary, but not conceptual proof, which stimulated a successful search for a conceptual proof, no matter how long it is. But it seems to me that such Owlhttps://www.blogger.com/profile/13083493391293465339noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-79218486969911862732013-08-04T19:19:34.641-03:002013-08-04T19:19:34.641-03:00Dear Robert Walters,
It even may be the case that...Dear Robert Walters,<br /><br />It even may be the case that all expository papers by D.S. Freed are very poor. Frankly, I did not read any of them. But this one is on my reading list. It seems to me that this one is fairly understandable and fairly short (especially compared to Lurie's own texts). I suggested it as an <i>accessible introduction</i> and a place where one may find further Owlhttps://www.blogger.com/profile/13083493391293465339noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-59866015096895507612013-08-04T18:48:45.744-03:002013-08-04T18:48:45.744-03:00I am surprised you recommend the Freed paper which...I am surprised you recommend the Freed paper which seems to me very poor. It promises much but leaves the reader with no precise or useable idea. Anonymoushttps://www.blogger.com/profile/11168659017114792898noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-48338734487717305252013-07-30T22:28:19.335-03:002013-07-30T22:28:19.335-03:00Sowa, by the way, thank you for mentioning the pla...Sowa, by the way, thank you for mentioning the plays of Eugene Ionesco. I read two and really enjoyed them.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-59445599209151895552013-07-30T20:15:44.751-03:002013-07-30T20:15:44.751-03:00Ben Green will give a plenary lecture at ICM 2014....Ben Green will give a plenary lecture at ICM 2014. Considering an impressive list of past awards, he could be a strong candidate. By "strong" I mean in terms of likelihood. It does not hurt to be so closely linked to Gowers and Tao.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-61649597819893622462013-07-30T06:17:59.359-03:002013-07-30T06:17:59.359-03:00Maybe this is not so hard to understand. Ten pages...Maybe this is not so hard to understand. Ten pages of elementary proof might be a clear explanation of why some statement is true (or it might not, ten pages of calculation with matrices plucked from thin air can prove some types of theorem but still leave the reader no understanding of why the statement holds). But it is not too likely to be general, at least not at anything like the sort of Petehttps://www.blogger.com/profile/02123359695496629332noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-15968069876163296782013-07-30T06:12:18.349-03:002013-07-30T06:12:18.349-03:00Maybe this is not so hard to understand. Ten pages...Maybe this is not so hard to understand. Ten pages of elementary proof might be a clear explanation of why some statement is true (or it might not, ten pages of calculation with matrices plucked from thin air can prove some types of theorem but still leave the reader no understanding of why the statement holds). But it is not too likely to be general, at least not at anything like the sort of Petehttps://www.blogger.com/profile/02123359695496629332noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-77520270992014894542013-07-30T05:50:27.646-03:002013-07-30T05:50:27.646-03:00Well, perhaps I should say explicitly a couple of ...Well, perhaps I should say explicitly a couple of things I took for granted. Of course, I wanted to make a counterintuitive statement. I wanted to attract attention to some phenomena. Of course, nobody sets him/herself the goal of replacing a half-page proof by 500 pages long theory. Doesn’t make much sense, I agree. In your ideal imaginary example there is very little motivation to search for Owlhttps://www.blogger.com/profile/13083493391293465339noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-71269800141878695582013-07-30T03:36:32.133-03:002013-07-30T03:36:32.133-03:00Right now I will comment only about P. Cohen’s the...Right now I will comment only about P. Cohen’s theory, and only about the mentioned aspect of it. The first publication of Cohen’s results consisted of two 6 pages long notes in Proc. Nat. Acad. Sci. USA, a journal which never was intended for complete expositions of mathematical results. I never looked at these two notes; definitely, K. Gödel would be able to understand the proof from them (he Owlhttps://www.blogger.com/profile/13083493391293465339noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-26252536348765071492013-07-29T22:47:02.897-03:002013-07-29T22:47:02.897-03:00To add to my previous comment, an example that com...To add to my previous comment, an example that comes to mind is Paul Cohen's proof of the independence of the continuum hypothesis and the axiom of choice from the Zermelo–Fraenkel set theory. His original proof was perhaps 15-20 pages long and (please, correct me if I am wrong here) it is considered to be a perfect proof and has never really been improved. There must be more examples like Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-46425160770288448702013-07-29T20:51:28.240-03:002013-07-29T20:51:28.240-03:00"Why replacing 10 pages long elementary proof..."Why replacing 10 pages long elementary proof by a half-page long application of a theory requiring 500 pages for an exposition could be a tremendous progress?" <br /><br />This statement is extremely fascinating because it is so counterintuitive. What if a ten page proof is the only proof we have and, in addition to being elementary, it is built on very new and beautiful ideas? To my Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-9048061459095893362013-07-29T19:45:57.528-03:002013-07-29T19:45:57.528-03:00Yes, Arnold wrote this either in “The Mathematical...Yes, Arnold wrote this either in “The Mathematical Intelligencer”, or in the “Notices of the AMS”.<br /><br />Perhaps, the most accessible introduction to a part of Lurie’s work is a recent survey <a href="http://www.ams.org/journals/bull/2013-50-01/S0273-0979-2012-01393-9/" rel="nofollow">Daniel S. Freed, The Cobordism hypothesis, Bull. AMS, V. 50 (2013), 57-92</a> and his papers cited there. Owlhttps://www.blogger.com/profile/13083493391293465339noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-11738806546513886552013-07-29T19:05:56.419-03:002013-07-29T19:05:56.419-03:00In fact, mathematicians only rarely interested in ...In fact, mathematicians only rarely interested in the history of mathematics (apparently, this is true for most of other professions also). This is rather disappointing, because the true motivation for everything done in pure mathematics is the history of the question, and not the artificial motivations included in the textbooks (or posted on T. Gowers’s website). This very negatively affects Owlhttps://www.blogger.com/profile/13083493391293465339noreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-50363217854057290982013-07-29T11:54:56.688-03:002013-07-29T11:54:56.688-03:00The award stipulation is vague - in recognition of...The award stipulation is vague - in recognition of work already done, while at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others. Because of the diversity of mathematics, it impossible to make the rule precise. There is this popular division into theory builders and problem solvers, but I Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8062754651764668865.post-74633236341160516272013-07-29T10:33:50.153-03:002013-07-29T10:33:50.153-03:00Thank you for writing such an interesting post, So...Thank you for writing such an interesting post, Sowa! I am a mathematician at the beginning of my career, and this historical perspective is very hard to find. I think Arnold wrote somewhere that in 1994 three of the winners were noted "for the art of manipulation of inequalities".<br /><br />Here are some link for people to connect the dots in your story: <a href="http://Anonymousnoreply@blogger.com