From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4584 Path: news.gmane.org!not-for-mail From: David Spivak Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Mon, 15 Sep 2008 11:51:24 -0700 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v753) Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241020041 13944 80.91.229.2 (29 Apr 2009 15:47:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:21 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Mon Sep 15 19:26:52 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 15 Sep 2008 19:26:52 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KfMPb-0003q1-93 for categories-list@mta.ca; Mon, 15 Sep 2008 19:19:15 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 54 Original-Lines: 101 Xref: news.gmane.org gmane.science.mathematics.categories:4584 Archived-At: I agree with Andre. Encapsulating a group of mathematicians inside a =20= single named entity fosters a kind of collaborative spirit in which =20 good ideas are not kept for personal use later but are shared amongst =20= the community. When ideas are shared in real time, good mathematics =20 can be produced faster. Anyone who wants to join the collective can =20 do so, and the collective produces highly useful material. Of course =20= such an enterprise is orthogonal to name-recognition, and maybe to =20 getting tenure! But there is certainly something good about it, as =20 there is about wikipedia and the open source movement. I also agree that the internet could be used in a better way to =20 transfer knowledge of mathematics. Math papers are written linearly, =20= in the bottom-up (Euclid/Bourbaki) style, to some extent. Whereas =20 words on paper are in this sense one-dimensional, computers offer =20 many more dimensions for knowledge transfer. Even more interesting to me would be a kind of zoom-feature on =20 proofs. Proofs are in the eye of the beholder: for example it has =20 been debated as to whether Perelman's 70 pages was a full proof of =20 geometrization. Given a proof with a statement which one does not =20 understand, a mathematician may find himself reproving something that =20= was obvious to (or wrongly assumed to be obvious by) another =20 mathematician. The community could benefit if a mathematician who =20 proves such a statement then uploaded the proof, even in rough form, =20 to some kind of math wiki. If it were well-organized, this math wiki =20= could revolutionize how mathematics is done. In fact, choosing the =20 "right way" to organize such a site may itself be a problem which =20 could produce interesting mathematics. Whatever the case may be, I am all for the idea of a new Bourbaki-=20 style enterprise in some form or another. I think it may first =20 require interested parties to get together at some physical location. David On Sep 13, 2008, at 10:17 AM, Andre Joyal wrote: > Dear Colin, Zoran, Robert, Eduardo and All, > > I find the present discussion on Bourbaki and category theory very =20 > important. > I recall asking the question to Samuel Eilenberg 25 years ago and =20 > more recently to Pierre Cartier. > If my recollection is right, Bourbaki had essentially two options: =20 > rewrite the whole treaty using categories, > or just introduce them in the book on homological algebra, > The second option won, essentially because of the enormity of the =20 > task of rewriting everything. > Other factors may have contributed on a smaller scale, like some =20 > unresolved foundational questions. > In any cases, it was the beginning of end for Bourbaki. > > Bourbaki was a great humanistic and scientific enterprise. > Advanced mathematics was made available to a large number > of students, possibly over the head of their bad teachers. > It defended the unity and rationality of science in an age > of growing irrationalism (it was conceived in the mid thirties). > > I have personally learned a lot of mathematics by reading Bourbaki. > Everything was proved, and the proofs were logically very clear. > It was a like a continuation of Euclid Elements two thousand years =20= > later! > But after a while, I stopped reading it. > I had realised that something important was missing: the motivation. > The historical notes were very sketchy and not integrated to the text. > I remember my feeling of frustration in reading the books of =20 > functional analysis, > because the applications to partial differential equations were not =20= > described. > Everything was presented in a deductive order, from top to down. > We all know that learning is very much an inductive process, from > the particular to the general. This is true also of mathematical =20 > research. > > Bourbaki is dead but I hope that the humanistic philosophy behind =20 > the enterprise is not. > Unfortunately, we presently live in an era of growing irrationalism. > Science still needs to be defended against religion. > Civilisation maybe at a turning point with the problem of climate =20 > change. > Millions of people need and want to learn science and mathematics. > > Should we not try to give Bourbaki a second life? > It will have to be different this time. > Possibly with a new name. > Obviously, internet is the medium of choice. > What do you think? > > Andre > >