From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4956 Path: news.gmane.org!not-for-mail From: Paul Taylor Newsgroups: gmane.science.mathematics.categories Subject: Famous unsolved problems etc Date: Tue, 9 Jun 2009 10:52:20 +0100 Message-ID: Reply-To: Paul Taylor NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v624) Content-Type: text/plain; charset=US-ASCII; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1244547675 1824 80.91.229.12 (9 Jun 2009 11:41:15 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 9 Jun 2009 11:41:15 +0000 (UTC) To: Categories list Original-X-From: categories@mta.ca Tue Jun 09 13:41:13 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 1MDzhV-0000Us-8y for gsmc-categories@m.gmane.org; Tue, 09 Jun 2009 13:41:09 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MDyyt-0000pC-Vc for categories-list@mta.ca; Tue, 09 Jun 2009 07:55:04 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4956 Archived-At: I had wanted to give more careful consideration to this question before posting about it again, but an emergency has arisen: My website (paultaylor.eu) is likely to be out of action for the rest of this week. Apparently the hosting company was badly hacked, and even their own webpage doesn't exist at the moment. However, email gets through to me by a backup route, so please do not try to second guess my email address. You can access my papers etc by adding site:paultaylor.eu to a Google query and using their cached versions. The version of my diagrams package on CTAN was out of date (sorry). I have uploaded a new release (V3,93) and asked them to install it quickly. The package now automatically recognises when it is running under XeTeX, as it has done with PDFTeX for some time. I would like to thank Apostolos Syropoulos for his help in implementing this, which he wanted to use to combine my diagrams with Greek text in Unicode. --- I would like to thank all of the people who sent supportive responses to my autobiographical comments. However, it seems that people read these rather more literally than was intended, whilst incorrectly interpreting the "inappropriate boyfriend" as a metaphor. I was certainly not suggesting that I had a relevation about constructive categorical logic during puberty (which would have coincided with the invention of elementary toposes) and that this was suppressed by my mathematical teachers until my rebellion! Of course, this was exactly my point: conceptual and constructive thinking (which are by no means coincident) require mathematical and personal maturity. My reaction to Ellis Cooper's question about "Fundamental Theorems" was that Ronnie Brown and others had answered this question under the "famous unsolved problems" heading. Notwithstanding the occurrence of the phrases "fundamental theorem of algebra" and "fundamental theorem of interval analysis" on my (dormant) website, I would say that they demonstrate a fundamental lack of appreciation of the breadth of mathematics, and are only appropriate for schoolteachers to shoehorn the subject into a restrictive curriculum. The adjoint functor theorem and the Yoneda Lemma are the two obvious candidates for the title "fundamental theorem of category theory", but I have to say that I am somewhat alarmed by prospect that the apparent consensus about this might become "legislated" into someone's lecture notes, curriculum or textbook. I think that Ronnie Brown and other people have given the right answer to the question about famous unsolved problems. Category theory is not a collection of miscellaneous problems like combinatorics, but a way of thinking about mathematics. Rafael Borowiecki, alias Hasse Riemann, did not seem to be satisfied with these answers, so what I said to him privately is this: It would help people to give better answers if he, along with students and non-academics who ask questions on "categories", gave some clearer indication of their mathematical background. If you read the archives of "categories", you will find that people discuss topics from many areas in mathematics, physics and computer science. You may find amongst this something that interests you, in which case you should look up the web pages and papers of the people who post on that topic. Academics are not very responsive to completely uninformed questions, but they usually are very happy to help if you show some background. It is also a good idea to flatter them by indicating that you have looked at their papers. Finally, Rafael queried some of the technical points about "illegitimate presheaves on locales" that I made at the end of my "autobiography". I will publish my private reply another time, as I have some other things to say about locale theory. Sorry for the hurried response. Paul Taylor [For admin and other information see: http://www.mta.ca/~cat-dist/ ]