From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3201 Path: news.gmane.org!not-for-mail From: jim stasheff Newsgroups: gmane.science.mathematics.categories Subject: Re: WHY ARE WE CONCERNED? I Date: Fri, 31 Mar 2006 09:30:58 -0500 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 1241019152 7678 80.91.229.2 (29 Apr 2009 15:32:32 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:32:32 +0000 (UTC) To: Categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Mar 31 19:32:29 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 31 Mar 2006 19:32:29 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FPT5p-0005Mu-8Q for categories-list@mta.ca; Fri, 31 Mar 2006 19:31:49 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 147 Original-Lines: 41 Xref: news.gmane.org gmane.science.mathematics.categories:3201 Archived-At: Proofs may be of ultimate importance but a lot can be accomplished at the penulitmate level or even sooner jim Colin McLarty wrote: >> 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. > > > This, and much else about Lefschetz has to tell us a lot. As to proof, > Lefschetz also never published a theorem without a purported proof, and > he often came to feel very strongly that his proofs were not good > enough. He wrote two long books on topology in the attempt to repair > the bad proofs in his influential booklet on cohomology in algebraic > topology, L'Analysis situs et la Topologie Algebrique. It was so > important to him that he enlisted many others. Notably for us, he > asked Eilenberg and Mac Lane to contribute an appendix to his 1942 > TOPOLOGY. This was their first published collaboration "On homology > groups of infinite complexes and compacta" and pursued the questions > that quickly led to category theory. > > Lefschetz had encouraged work on solving specific problems just over > the edge of what well-understood foundations for homology could > handle. Apparently he believed such solutions would lead to > significantly deeper understanding. He had encouraged Steenrod to work > on p-adic solenoids because existing methods did not seem adequate to > it. But whatever his motive, he was determined to see rigorous > solutions to quite specific problems. > > Colin > >