From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4588 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Tue, 16 Sep 2008 01:57:50 -0700 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241020043 13953 80.91.229.2 (29 Apr 2009 15:47:23 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:23 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Sep 16 21:16:23 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 16 Sep 2008 21:16:23 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KfkcR-000403-I0 for categories-list@mta.ca; Tue, 16 Sep 2008 21:10:07 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 58 Original-Lines: 46 Xref: news.gmane.org gmane.science.mathematics.categories:4588 Archived-At: Bourbaki redone as Bourwiki (thanks, Dusko!) with the benefit of category theoretic insights will hopefully clarify some segments of mathematics. What troubles me in this discussion however is its assumed scope of "some." I get the sense that there are people who want it to be mandated as "all." Perhaps it should be. Just now I looked through an issue of American Mathematical Monthly that came to hand to get a sense of the likely alignment of Bourwiki with what the mathematical community generally regards as the scope of its subject. Actually I do this periodically, and I don't see much change between the issue I picked up just now and any of the other issues I've looked at in the past with just this question in mind. If the subject Bourwiki is proposing to serve is mathematics, then perhaps it is time that the American Mathematical Monthly, along with the Putnam Mathematical Competition, the International Mathematics Olympiad, and the Journal of the AMS, abandon their pretense of being about mathematics and come up with a suitable name for their subject. Not only do categories, functors, natural transformations, adjunctions, and monads go unused in these 20th century icons of mathematics, they go unacknowledged. Clearly they have not gotten with the modern mathematical program and fall somewhere between a throwback to a golden age and a backwater of mathematics. When they die off like the dinosaurs they are, real mathematics will be able to advance unfettered into the 21st century and beyond. Judging from the talks at BLAST in Denver last month (B = Boolean algebras, L = lattices, A = (universal) algebra, S = set theory, T = topology), at least the algebraic community is moving very slightly in this direction. Things will hopefully improve yet further when algebraic geometry gets over its snit with equational model theory. Meanwhile if you need a witness for seven degrees of separation, look no further than AMM and CT. (I confess to being an unreconstructed graph theorist and algebraist myself. I may have to preemptively volunteer myself for re-education before it becomes involuntary.) Vaughan Pratt