From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3185 Path: news.gmane.org!not-for-mail From: Graham White Newsgroups: gmane.science.mathematics.categories Subject: Re: WHY ARE WE CONCERNED? I Date: Thu, 30 Mar 2006 09:13:52 +0100 Message-ID: <1143706432.8570.16.camel@localhost.localdomain> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019142 7609 80.91.229.2 (29 Apr 2009 15:32:22 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:32:22 +0000 (UTC) To: Categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Mar 30 18:52:09 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 30 Mar 2006 18:52:09 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FP5uo-0006Jy-O6 for categories-list@mta.ca; Thu, 30 Mar 2006 18:46:54 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 131 Original-Lines: 37 Xref: news.gmane.org gmane.science.mathematics.categories:3185 Archived-At: > jim stasheff wrote: > > > now for a mathematical subject a math proof is sometimes but not always > > necessary > There's a saying about Lefschetz that he "never wrote a valid proof, and never made a false conjecture". Now it's not an attitude that want to encourage, but if you have great mathematicians who are like that (and Lefschetz was not just a good mathematician, but a great mathematician, without whom a good deal of modern algebraic geometry would be unimaginable), then this ought to tell us something. What it tells us is, of course, not easy to formulate: it's an example that causes severe problems for almost every philosophy of mathematics that I know. But it ought to stop us saying things of the form "if we don't do category theory in such and such a way, then it won't be mathematics at all". (Of course we'll all keep saying this, because we all have a secret fear that, if we aren't really careful about what we do, the grown up mathematicians will kick sand in our face, but that's a psychological problem and not a mathematical problem.) -- Dr. Graham White Lecturer Department of Computer Science Queen Mary, University of London Mile End Road London E1 4NS http://www.dcs.qmul.ac.uk/~graham (+44)(020)7882 5242