From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5988 Path: news.gmane.org!not-for-mail From: Ronnie Brown Newsgroups: gmane.science.mathematics.categories Subject: Re: Are mathematical proofs incomparable with proofs in other disciplines? Date: Sat, 10 Jul 2010 17:10:20 +0100 Message-ID: References: Reply-To: Ronnie Brown NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1278971158 15539 80.91.229.12 (12 Jul 2010 21:45:58 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 12 Jul 2010 21:45:58 +0000 (UTC) Cc: Vaughan Pratt , categories list To: Michael Barr Original-X-From: categories@mta.ca Mon Jul 12 23:45:57 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OYQp1-0006D4-03 for gsmc-categories@m.gmane.org; Mon, 12 Jul 2010 23:45:55 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OYQA1-00002y-LY for categories-list@mta.ca; Mon, 12 Jul 2010 18:03:33 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5988 Archived-At: My suggestion is that mathematical proofs still require a mathematical landscape in which to find our way. Michael Barr points out the problems of finding a completely `logical' proof. I propose the analogy of giving directions to the station, such as `go out of the house, turn right, go straight on until ..., etc., etc.' We don't need to specify all the cracks in the pavement, but we may need to warn of holes due to roadworks! The aura of certainty in a mathematical proof is partly because the `conceptual landscape' has been worked up over centuries, in terms of convenience and usability, and tested by thousands. Hopefully, arguments come to be produced which seem inevitable, indeed aesthetic, rather than ad hoc. Are there computer theorem provers which can work at a `landscape level'? The assumption is also that there are no cracks in our mathematical universe. On the more general point, I did hear of a University Vice Chancellor who asked his staff for a series of lectures on `The notion of validity in my subject'. Ronnie Brown [For admin and other information see: http://www.mta.ca/~cat-dist/ ]