From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5367 Path: news.gmane.org!not-for-mail From: Andrew Stacey Newsgroups: gmane.science.mathematics.categories Subject: Re: A well kept secret? Date: Mon, 14 Dec 2009 19:41:51 +0100 Message-ID: References: Reply-To: Andrew Stacey NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1260845222 12785 80.91.229.12 (15 Dec 2009 02:47:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 15 Dec 2009 02:47:02 +0000 (UTC) To: "categories@mta.ca" Original-X-From: categories@mta.ca Tue Dec 15 03:46:55 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 1NKNR8-0003tK-Sc for gsmc-categories@m.gmane.org; Tue, 15 Dec 2009 03:46:55 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NKMzO-0001f7-JT for categories-list@mta.ca; Mon, 14 Dec 2009 22:18:14 -0400 Content-Disposition: inline In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5367 Archived-At: This discussion has been very interesting. I have a couple of comments and a request, but first a little background. I've only recently truly encountered category theory - I describe myself as a differential topologist and as yet see no reason to change that description, but I've increasingly needed to use at least the language of category theory to express some of the things that I come across in algebraic and differential topology and this has led to me learning some category theory at last. However, I sometimes feel as though I've stumbled into a party by mistake and can't find the way out. I'm quite enjoying being at the party, I ought to say, but every now and then I sit down in a corner and wonder how I got in, and also suspect that I missed the Big Announcement at the beginning that said what the party was for. All this discussion about a "well kept secret" has gone a bit over my head. I'm not sure what the secret is! My forays into the categorical landscape have been two-fold: understanding operations in cohomology theories and understanding smooth spaces. The first, paradoxically, relates to trying to un-categorify something ("decategorify" now has a mathematical meaning and I don't intend that); namely, the previous description of what we wanted to understand was extremely categorical and we wanted a much more "hands on" description, but that actually just led us from one categorical description to another (our own journey was quite tortuous, I should say). The second foray wouldn't have happened if those I'd been talking to hadn't already been speaking in categories - I had to learn the language just to join the conversation. So when you all talk of a "well kept secret" and something that "went wrong in the 60s" (didn't everything?), please remember that some of us weren't even born in the 60s, let alone thinking about mathematics, so haven't a clue what's going on. And, as I've tried to say above, I'm an outsider but one with a favourable view of category theory so if it's hard for me to figure out what the fuss is about, I'm not surprised that it's hard for anyone further out. Let me make these remarks a little more concrete with a request (or a challenge if you prefer). In my department, the colloquium is called "Mathematical Pearls" (gosh, I actually wrote "Perls" first time round; I've been writing too many scripts lately!). I'm giving this talk in January. My original plan was to say something nice and differential, with lots of fun pictures of manifolds deforming or knots unknotting, or something like that. However, the discussion here has set me to thinking about saying something instead about category theory. It is a pearl of mathematics, it does have a certain beauty, there's certainly a lot that can be said, even to a fairly applied audience as we tend to have here (it is the Norwegian university of Science and Technology, after all), even without talking about programming (about which I know nothing). But for such a talk, I need a story. I don't mean a historical one (I'm not much of a mathematical historian anyway), I mean a mathematical one. I want some simple problem that category theory solves in an elegant fashion. It would be nice if there was one that used category theory in a surprising way; beyond the idea that categories are places in which things happen (so perhaps about small categories rather than large ones). I'm not trying to get anyone to write my talk for me! It's just that as someone who only recently engaged with category theory then I'm aware - painfully aware - that I often miss the point. But to counter that, then as someone who only recently engaged with category theory then I can still remember fairly vividly why I like it and what convinced me that it was worth thinking about (and learning about), which will hopefully give the talk a little more omph. Thanks in advance for your suggestions, Andrew Stacey PS I just remembered something else I was going to mention. Someone else mentioned MathOverflow. Well, there was a question about what was missing from undergraduate mathematics. I said "category theory". It currently lies 5th in the list (out of 28, my other suggestion "how to write with chalk so it doesn't squeak" is 12th). More interesting than it's placing is the vast number of comments that followed, mostly saying that too much "abstract nonsense" would be off-putting to students. You can read it at: http://mathoverflow.net/questions/3973/what-should-be-offered-in-undergraduate-mathematics-thats-currently-not-or-isn [For admin and other information see: http://www.mta.ca/~cat-dist/ ]