From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5414 Path: news.gmane.org!not-for-mail From: Ronnie Brown Newsgroups: gmane.science.mathematics.categories Subject: Re: A well kept secret? Date: Wed, 23 Dec 2009 14:35:54 +0000 Message-ID: References: Reply-To: Ronnie Brown NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1261595445 25606 80.91.229.12 (23 Dec 2009 19:10:45 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 23 Dec 2009 19:10:45 +0000 (UTC) To: Zinovy Diskin Original-X-From: categories@mta.ca Wed Dec 23 20:10:38 2009 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 4.50) id 1NNWbU-0005im-Tr for gsmc-categories@m.gmane.org; Wed, 23 Dec 2009 20:10:37 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NNWJs-0002Am-2I for categories-list@mta.ca; Wed, 23 Dec 2009 14:52:24 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5414 Archived-At: First a slight correction: The paper referred to was I think Wigner, E.P., The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Comm. in Pure Appl. Math. (1960), reprinted in Symmetries and reflections: scientific essays of Eugene P. Wigner, Bloomington Indiana University Press (1967). Here are some quotations from this article: ------------------------------------------------------------------------- ... that the enormous usefulness of mathematics in the physical sciences is something bordering on the mysterious, and that there is no rational explanation for it. Mathematics is the science of skilful operations with concepts and rules invented just for this purpose. [this purpose being the skilful operation ....] The principal emphasis is on the invention of concepts. The depth of thought which goes into the formation of mathematical concepts is later justified by the skill with which these concepts are used. The statement that the laws of nature are written in the language of mathematics was properly made three hundred years ago; [it is attributed to Gallileo] it is now more true than ever before. The observation which comes closest to an explanation for the mathematical concepts cropping up in physics which I know is Einstein's statement that the only physical theories which we are willing to accept are the beautiful ones. It stands to argue that the concepts of mathematics, which invite the exercise of so much wit, have the quality of beauty. --------------------------------------------------------------------------------- There is also a question of what is expected from a mathematical area. At a conference in Baku in 1987 I was asked `what are the big theorems in category theory? People sometimes want to know:`What are the big problems in category theory?' That these `big' things may not exist (comments?) does say something about the nature of category theory, and also of mathematical progress, and what this is conceived of by various groups of mathematicians.. Part of Grothendieck's success was his aims for maximum generality and for making things tautological. So some simple things (to category theorists) like `left adjoints preserve colimits' are very useful in a variety of fields, and make tautological some apparently difficult procedures. And also allow analogies between different fields. Hence my paper with Tim Porter: `Category theory: an abstract basis for analogy and comparison'. (Just one aspect, of course.) Ronnie Brown Zinovy Diskin wrote: > Dear Zoran, > > You misunderstood my posting, or I phrased it badly, because > > On Tue, Dec 22, 2009 at 11:59 AM, zoran skoda wrote: >> Dear Zinovy, >> >> I can say that I dislike your selling/marketing despair and do not share >> excitement in the existence of an easy niche market you propose. >> > > in the list "despair-excitement-easy niche", only the second term is > true. Building mathematical models for engineering problems is a hard > business, and the suggestion to view it as a fruitful area for > categorical applications stems from optimism about the power of > category theory, rather than from despair. > ... [For admin and other information see: http://www.mta.ca/~cat-dist/ ]