From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5405 Path: news.gmane.org!not-for-mail From: Zinovy Diskin Newsgroups: gmane.science.mathematics.categories Subject: Re: A well kept secret? Date: Tue, 22 Dec 2009 23:31:10 -0500 Message-ID: References: Reply-To: Zinovy Diskin NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1261577433 31210 80.91.229.12 (23 Dec 2009 14:10:33 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 23 Dec 2009 14:10:33 +0000 (UTC) To: zoran skoda Original-X-From: categories@mta.ca Wed Dec 23 15:10:25 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 1NNRuz-00073o-06 for gsmc-categories@m.gmane.org; Wed, 23 Dec 2009 15:10:25 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NNRTB-0003eB-9f for categories-list@mta.ca; Wed, 23 Dec 2009 09:41:41 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5405 Archived-At: 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. I'm not going to defend the market metaphor -- it's doubtful anyway. Still, I'd like to clarify a couple of points. 1) I think that both sources of mathematical development, the internal one based on aesthetic criteria and consistency, and the external one based on applications, are equally important and mutually beneficial. Apart from posing interesting problems, applications provide novel interpretations of formal constructs, which is always fruitful. After all, effectively applicable mathematics turns out to be aesthetically appealing as well (Eugene Vigner wrote a famous paper about this "On inaccessible effectiveness of mathematics in natural sciences") 2) The problem of "category theory vs. mathematics" is beyond mathematics as such. A lot of problems could be avoided if a taste for categorical thinking were cultivated in high school, and the basics of category theory were taught to mathematicians, scientists, engineers at the undergrad level. But education is one of the most conservative social institutes with a huge inertia. Turning mathematical education towards category theory needs financial and administrative support, and an external demand. Applications of category theory to engineering problems would be beneficial in this respect too. Z. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]