From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4578 Path: news.gmane.org!not-for-mail From: mjhealy@ece.unm.edu Newsgroups: gmane.science.mathematics.categories Subject: Re: Bourbaki and Categories Date: Sun, 14 Sep 2008 13:53:12 -0600 (MDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241020038 13918 80.91.229.2 (29 Apr 2009 15:47:18 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:18 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Sep 15 08:34:24 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 15 Sep 2008 08:34:24 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KfCG2-0001X6-55 for categories-list@mta.ca; Mon, 15 Sep 2008 08:28:42 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 48 Original-Lines: 48 Xref: news.gmane.org gmane.science.mathematics.categories:4578 Archived-At: Andre Joyal's message was inspiring. I think a new Bourbaki type of effort (this time with motivation and category theory) is called for. I would like a text on categorical algebra oriented toward those who have studied algebra and know enough category theory to use adjunctions, monad= s and the like. The same goes for categorical logic and model theory. I read Andre's closing remarks as a commentary on the emerging crisis in overcoming misconceptions about and outright hostility toward science and mathemtics. I have a current project, using my own meager funds and time= , to advance science teaching using a book available through the National Academies Press, "Science, Evolution, and Creationism". From the title, = I think you can see my motivation. In a similar (although less aprocryphal) vein, when I worked with compute= r scientists and applied mathematicians in industry ( and also when I've submitted papers to certain neural network journals) I encountered misconceptions about and outright hostility toward category theory. For example, in the dynamic systems community there seems to be a widespread myth that "category theory was tried and failed". I have followed this u= p to some extent and haven't found any basis for it. I am often told that the best way to counter skepticism is with a working application. Having tried that, and tried again, I've come to the conclusion that Yes, you need applications, but applications cannot by themselves counter a refusal to give a theory credit for being consistent with the data. You need a good, clear presentation of the theory couched in a language oriented toward the intended audience. As with biology teaching that shows clearly the importance of the theory of evolution, maybe mathematic= s teaching that incorporates category theory needs to begin in 6th Grade (i= n schools in the USA) if not sooner. Maybe a new Bourbaki project could have an extension into this level of instruction. Best Regards, Mike Please excuse my deviating from mathematics