tag:blogger.com,1999:blog-80627546517646688652020-11-28T04:41:39.242-04:00Stop Timothy Gowers! !!!Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.comBlogger55125tag:blogger.com,1999:blog-8062754651764668865.post-55724583655726948872016-02-17T05:31:00.002-04:002016-02-17T14:09:23.557-04:00A comment from Timothy GowersPrevious post: Self-revealing truths? - Part 1
Let me try to dispel the mystery about my views. I share your distaste for incomprehensible proofs that merely certify the truth of a statement...
Next post: To appear Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com2tag:blogger.com,1999:blog-8062754651764668865.post-16187564645577434372016-01-24T00:33:00.000-04:002016-02-17T05:33:08.866-04:00Self-revealing truths? - Part 1Previous post: Mathematicians are human and want to be famous
There is an apparently unnoticed class of truths, which I call “self-revealing” - statements which may be trivial, may be unexpected, but which are reveal themselves as true after being stated. They may require some thinking over, but they do not require arguments.
Or, may be, there is no such thing as a universally self-revealing Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com1tag:blogger.com,1999:blog-8062754651764668865.post-52277828527005112982015-11-20T00:21:00.000-04:002016-01-24T00:37:25.905-04:00Mathematicians are human and want to be famousPrevious post: Where one can find an autobiography of Alexander Grothendieck? Part 2
A draft of this post was written quite a while ago. It was intended to be an opening of a series of posts. These posts may be written soon, or may never be will be written. Anyhow, I decided to post it "as is". The original title of the post was the following.
"Mathematics is a human activity."
This used to Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com12tag:blogger.com,1999:blog-8062754651764668865.post-4037969351429304392014-11-22T01:55:00.000-04:002015-11-20T00:22:23.425-04:00Where one can find an autobiography of Alexander Grothendieck? Part 2Previous post: Where one can find an autobiography of Alexander Grothendieck? Part 1.
A few years ago Grothendieck himself complicated the matter a lot. Note that this happened decades after his texts were rejected by all publishers.
Grothendieck contacted one or two of his former students and demanded that his works published without his authorization were removed from circulation, Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com10tag:blogger.com,1999:blog-8062754651764668865.post-80908133101135751962014-11-22T01:11:00.000-04:002015-11-19T23:14:21.907-04:00Where one can find an autobiography of Alexander Grothendieck? Part 1Previous post: Alexandre Grothendieck passed away yesterday, November 13, 2014.
michal2602 asked this question in a comment to the previous post. The short reply would be "I have no idea". This post and the next one are devoted to a long reply.
I don't know, and by good reasons.
First of all, autobiographical and philosophical texts of Grothendieck were never published. They were offered (IOwlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com12tag:blogger.com,1999:blog-8062754651764668865.post-49968749036734533212014-11-14T20:19:00.000-04:002014-11-22T02:14:44.024-04:00Alexandre Grothendieck passed away yesterday, November 13, 2014Previous post: And who actually got Fields medals?
Alexandre Grothendieck, the greatest mathematician for the twenties century, passed away on November 13, 2014 at the Saint-Girons hospital (Ariège) near the village Lasserre.
Alexandre Grothendieck spent about the last 24 years of his life in this village in Pyrenees range of mountains in a self-imposed retirement avoiding all contacts with Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com7tag:blogger.com,1999:blog-8062754651764668865.post-72875707407971872742014-08-13T09:19:00.001-03:002014-11-14T21:22:53.679-04:00And who actually got Fields medals?Previous post: Who will get Fields medals in less than two hours?
Of course, if you are interested, you know already: Artur Avila, Manjul Bhargava, Martin Hairer, Maryam Mirzakhani.
I named in my previous post all except Martin Hairer, who is working in a too distant area in which too many people are working. I was put off tracks by the claim that M. Mirzkhani definitely will not get the Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com77tag:blogger.com,1999:blog-8062754651764668865.post-145414006640390922014-08-12T22:25:00.000-03:002014-11-14T21:24:28.712-04:00Who will get Fields medals in less than two hours?Previous post: About expository writing: a reply to posic
At 10:30 p.m. US Eastern Summer time, the winner of this (2014) year Fields medals will be announced in Seoul.
I would like to post my current guess, mostly to have a record of it with the date and time stamp from Google, at least for myself.
As I wrote about one year ago, I believe that I would be able to predict the actual winners Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com4tag:blogger.com,1999:blog-8062754651764668865.post-25618989838763127342014-03-07T03:45:00.001-04:002014-11-14T21:26:53.241-04:00About expository writing: a reply to posicPrevious post: Graduate level textbooks: A list - the second part
In the post Graduate level textbooks I I mentioned an advice given to me by a colleague many years ago:
"Do not write any books until you retire". posic commented on this:
"Do not write any books until you retire"?! One is tempted to generalize to "do not do any mathematics until you retire". Or, indeed, to "do not do anything Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com4tag:blogger.com,1999:blog-8062754651764668865.post-65729423404278388112014-01-02T09:25:00.003-04:002014-11-14T21:28:02.123-04:00Graduate level textbooks: A list - the second partPrevious post: Graduate level textbooks: A list - the first part
N. Koblitz, p-adic number, p-adic analysis, and zeta-functions. GTM. Perfect in every respect.
N. Koblitz, Other books. It seems that all of them are also excellent, but I am less familiar with them (the previous one I read from cover to cover).
K. Kunen, Set theory: an introduction to independence proofs. This is the best Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com17tag:blogger.com,1999:blog-8062754651764668865.post-84914226630401072802014-01-02T09:00:00.001-04:002014-11-14T21:29:11.723-04:00Graduate level textbooks: A list - the first partPrevious post: Graduate level textbooks II
The following list includes only the books which I read from cover to cover or from which I read at least some significant part (with a couple of exceptions); the books which I just used in my work are not included, no matter how useful they were.
This list includes almost no recent titles; I am planning to compile a list of more recent titles laterOwlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com2tag:blogger.com,1999:blog-8062754651764668865.post-72963883289980630842014-01-02T02:47:00.000-04:002014-11-14T21:33:53.371-04:00Graduate level textbooks IIPrevious post: Graduate level textbooks I
I would like to start with something at least a little bit shocking.
My first list will consists of books by two excellent authors who wrote many books each. These two authors are as different as one can imagine. I will say also few words about a third author, who worked nearly three hunderd years ago. The books mentioned in this post are not Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com0tag:blogger.com,1999:blog-8062754651764668865.post-89636598766682894652014-01-02T02:21:00.000-04:002014-11-14T21:31:42.234-04:00Graduate level textbooks IPrevious post: The role of the problems
Back in August Tamas Gabal asked me about my favorite graduate level textbooks in mathematics; later Ravi joined this request. I thought that the task will be very simple, but it turned out to be not. In addition, my teaching duties during the Fall term consumed much more energy than I could predict and even to imagine.
In this post I will try to Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com2tag:blogger.com,1999:blog-8062754651764668865.post-13213862968309276742013-08-23T22:07:00.001-03:002014-01-02T02:22:57.904-04:00The role of the problemsPrevious post: Is algebraic geometry applied or pure mathematics?
From a comment by Tamas Gabal:
“I also agree that many 'applied' areas of mathematics do not have famous open problems, unlike 'pure' areas. In 'applied' areas it is more difficult to make bold conjectures, because the questions are often imprecise. They are trying to explain certain phenomena and most efforts are devoted to Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com14tag:blogger.com,1999:blog-8062754651764668865.post-27150812572301932072013-08-23T21:56:00.000-03:002013-08-24T20:09:06.802-03:00Is algebraic geometry applied or pure mathematics?Previous post: About some ways to work in mathematics.
From a comment by Tamas Gabal:
“This division into 'pure' and 'applied' mathematics is real, as it is understood and awkwardly enforced by the math departments in the US. How is algebraic geometry not 'applied' when so much of its development is motivated by theoretical physics?”
Of course, the division into the pure and applied mathematicsOwlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com11tag:blogger.com,1999:blog-8062754651764668865.post-66424557179935710452013-08-21T22:03:00.001-03:002014-01-02T03:58:19.327-04:00About some ways to work in mathematicsPrevious post: New ideas.
From a comment by Tamas Gabal:
“...you mentioned that the problems are often solved by methods developed for completely different purposes. This can be interpreted in two different ways. First - if you work on some problem, you should constantly look for ideas that may seem unrelated to apply to your problem. Second - focus entirely on the development of your ideas Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com7tag:blogger.com,1999:blog-8062754651764668865.post-17252160215054425552013-08-20T20:41:00.000-03:002013-08-23T22:56:20.030-03:00New ideasPrevious post: Did J. Lurie solved any big problem?
Tamas Gabal asked:
“Dear Sowa, in your own experience, how often genuinely new ideas appear in an active field of mathematics and how long are the periods in between when people digest and build theories around those ideas? What are the dynamics of progress in mathematics, and how various areas are different in this regard?”
Here is my Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com7tag:blogger.com,1999:blog-8062754651764668865.post-55025356534798057372013-08-04T23:54:00.000-03:002013-08-23T22:55:38.305-03:00Did J. Lurie solved any big problem?Previous post: Guessing who will get Fields medals - Some history and 2014.
Tamas Gabal asked the following question.
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 Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com16tag:blogger.com,1999:blog-8062754651764668865.post-86438241792460073722013-07-29T06:50:00.002-03:002013-12-08T01:07:25.061-04:00Guessing who will get Fields medals - Some history and 2014Previous post: 2014 Fields medalists?
This was a relatively easy task during about three decades. But it is nearly impossible now, at least if you do not belong to the “inner circle” of the current President of the International Mathematical Union. But they change at each Congress, and one can hardly hope to belong to the inner circle of all of them.
I would like to try to explain my approach Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com21tag:blogger.com,1999:blog-8062754651764668865.post-56776085192249425252013-07-28T05:11:00.001-03:002013-08-23T22:54:51.254-03:002014 Fields medalists?Previous post: New comments to the post "What is mathematics?"
I was asked by Tamas Gabal about possible 2014 Fields medalists listed in an online poll. I am neither ready to systematically write down my thoughts about the prizes in general and Fields medals in particular, nor to predict who will get 2014 medals. I am sure that the world would be better without any prizes, especially without Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com4tag:blogger.com,1999:blog-8062754651764668865.post-17418791004312012932013-06-11T03:23:00.000-03:002013-07-28T05:15:30.312-03:00New comments to the post "What is mathematics?"Previous post: What is combinatorics and what this blog is about according to Igor Pak.
There is a new thread of comments to the post "What is mathematics?" started by Sandro Magi. The post is dated April 3; this thread started on May 31. The thread is concerned with only one claim in that post: proofs are not needed at all for applications of mathematics.
Unfortunately, the very first Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com8tag:blogger.com,1999:blog-8062754651764668865.post-24530591619875281242013-06-01T03:09:00.000-03:002013-06-11T03:26:25.462-03:00What is combinatorics and what this blog is about according to Igor PakPrevious post: About Timothy Gowers.
I came across the post “What is Combinatorics?” by Igor Pak. His intention seems to be refuting what is, in his opinion, a basic fault of my notes, namely, the lack of understanding of what is combinatorics.
“While myself uninterested in engaging in conversation, I figured that there got to be some old “war-time” replies which I can show to the Owl blogger.Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com0tag:blogger.com,1999:blog-8062754651764668865.post-44895056409436364152013-05-19T02:25:00.000-03:002013-06-01T03:10:21.253-03:00About Timothy GowersPrevious post: The conceptual mathematics vs. the classical (combinatorial) one.
This post was started as a reply to a comment by vznvzn. It had quickly overgrown the comment format, but still is mostly a reply to vznvzn's remarks.
Gowers did not identify any “new mathematical strand/style”, and did not even attempt this. The opposition “conceptual” mathematics vs. “Hungarian” combinatorics Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com2tag:blogger.com,1999:blog-8062754651764668865.post-29551990432099220552013-04-07T23:23:00.000-03:002013-05-19T02:26:41.435-03:00The Hungarian Combinatorics from an Advanced StandpointPrevious post: Conceptual mathematics vs. the classical (combinatorial) one.
Again, this post is a long reply to questions posed by ACM. It is a complement to the previous post "Conceptual mathematics vs. the classical (combinatorial) one". The title is intentionally similar to the titles of three well known books by F. Klein.
First, the terminology in “Conceptual mathematics vs. the Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com32tag:blogger.com,1999:blog-8062754651764668865.post-45268466703982250822013-04-05T00:43:00.000-03:002013-05-29T04:08:34.989-03:00The conceptual mathematics vs. the classical (combinatorial) one.Previous post: Simons's video protection, youtube.com, etc.
This post is an attempt to answer some questions of ACM in a form not requiring knowledge of Grothendieck ideas or anything simlilar.
But it is self-contained and touches upon important and hardly wide known issues.
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It is not easy to explain how conceptual theorems and proofs, Owlhttp://www.blogger.com/profile/13083493391293465339noreply@blogger.com4