From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6638 Path: news.gmane.org!not-for-mail From: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: Re: Explanations Date: Mon, 25 Apr 2011 09:51:59 -0400 Message-ID: References: Reply-To: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1303776571 5024 80.91.229.12 (26 Apr 2011 00:09:31 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 26 Apr 2011 00:09:31 +0000 (UTC) Cc: To: "Ronnie Brown" , "Graham White" Original-X-From: majordomo@mlist.mta.ca Tue Apr 26 02:09:27 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1QEVqJ-00010z-1d for gsmc-categories@m.gmane.org; Tue, 26 Apr 2011 02:09:27 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:35536) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QEVqF-0006lS-3D; Mon, 25 Apr 2011 21:09:23 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QEVqB-0002b6-Gb for categories-list@mlist.mta.ca; Mon, 25 Apr 2011 21:09:19 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6638 Archived-At: I cannot resist adding my grain of salt. =20 Maybe we should distinguish between a human proof and a mechanical = proof. The goal of a human proof is to convince other peoples of the = truthfulness of a proposition. It is by nature explanatory and it can lead to new insights. A mechanical proof can be checked by computer but may not produce new = insights. It is establishing a fact. Of course, it is better than none. Mathematics is above all a human activity. The value of a proof depends very much on its method. A new proof may suggest a new method. A method is a kind of toolbox for proving a large class of propositions. Commutative algebra is a method in geometry Category theory is a method in mathematics. proofs --->methods ----> proofs ----> methods ....... Andr=E9 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]