Comments on: Dipoles http://www.arsmathematica.net/archives/2005/09/22/dipoles/ Dedicated to the mathematical arts. Fri, 05 Dec 2008 14:16:47 +0000 http://wordpress.org/?v=2.5.1 By: sigfpe http://www.arsmathematica.net/archives/2005/09/22/dipoles/#comment-138 sigfpe Mon, 26 Sep 2005 19:11:17 +0000 http://www.arsmathematica.net/?p=57#comment-138 The subject matter of GRR is the bread and butter of physics - vector bundles over manifolds. But I can't really say more than that. Presumably there <em>is</em> a way to visualise it that doesn't require you to read several hundred pages of densely written material on on commutative algebra and schemes, but people don't talk much about how they visualise things :-( The subject matter of GRR is the bread and butter of physics - vector bundles over manifolds. But I can’t really say more than that. Presumably there is a way to visualise it that doesn’t require you to read several hundred pages of densely written material on on commutative algebra and schemes, but people don’t talk much about how they visualise things :-(

]]> By: Walt http://www.arsmathematica.net/archives/2005/09/22/dipoles/#comment-137 Walt Sun, 25 Sep 2005 06:42:53 +0000 http://www.arsmathematica.net/?p=57#comment-137 Do you know how they think of Grothendieck-Riemann-Roch? String theorists must have some sort of intuitive picture. Do you know how they think of Grothendieck-Riemann-Roch? String theorists must have some sort of intuitive picture.

]]> By: sigfpe http://www.arsmathematica.net/archives/2005/09/22/dipoles/#comment-136 sigfpe Fri, 23 Sep 2005 19:12:04 +0000 http://www.arsmathematica.net/?p=57#comment-136 <blockquote> the uninhibited way they use mathematics </blockquote> Try some String Theory seminars. When I was studying mathematics years ago I used to hang out with theoretical physicists. I couldn't believe the amount of high powered mathematics they'd throw around: algebraic geometry, esoteric (co)homology theories, modular forms, representation theory, category theory and so on. They'd use something like Grothendieck-Riemann-Roch as if they'd been using it since birth and yet they barely knew the foundations of algebraic geometry. I could never figure it out. In fact, I was never sure whether they really understood what they were talking about at all :-)

the uninhibited way they use mathematics

Try some String Theory seminars. When I was studying mathematics years ago I used to hang out with theoretical physicists. I couldn’t believe the amount of high powered mathematics they’d throw around: algebraic geometry, esoteric (co)homology theories, modular forms, representation theory, category theory and so on. They’d use something like Grothendieck-Riemann-Roch as if they’d been using it since birth and yet they barely knew the foundations of algebraic geometry. I could never figure it out. In fact, I was never sure whether they really understood what they were talking about at all :-)

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