http://acandystore.org/books/archives/2006/07/12/bourbaki-and-abstraction Overheard in a library Sun, 20 May 2012 06:46:30 +0000 http://wordpress.org/?v=2.0.3 http://acandystore.org/books/archives/2006/07/12/bourbaki-and-abstraction#comment-8 Tue, 08 Aug 2006 13:12:01 +0000 http://acandystore.org/books/archives/2006/07/12/bourbaki-and-abstraction#comment-8 "To do that we have to start with case 2, and fight our way through it using anything that comes to hand, however clumsy, before refining our methos into an elegant but ethereal technique which — without such preparation — lets us prove case n without having any idea of what the proof does, how it works, or where it came from." I have a hard time believing this. Surely the elegant but ethereal technique needed a couple of base cases worked out, at least in an unspoken and unwritten way, before it could be formed? You can /read/ math in the reverse order, learning and verifying the general proof, then never needing to work out any specific case by hand, and that can be very smart and efficient. But can you really /write/ it like that? “To do that we have to start with case 2, and fight our way through it using anything that comes to hand, however clumsy, before refining our methos into an elegant but ethereal technique which — without such preparation — lets us prove case n without having any idea of what the proof does, how it works, or where it came from.” I have a hard time believing this. Surely the elegant but ethereal technique needed a couple of base cases worked out, at least in an unspoken and unwritten way, before it could be formed? You can /read/ math in the reverse order, learning and verifying the general proof, then never needing to work out any specific case by hand, and that can be very smart and efficient. But can you really /write/ it like that?

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