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Sep 6, 2010 at 21:05 comment added Gil Kalai And now, of course, we finally understand exactly what Gian-Carlo meant: A proof enlightens us if: 1) it is the first proof, 2) it is accepted, and 3) it has at least 10 up votes!
Sep 5, 2010 at 22:49 history edited André Henriques CC BY-SA 2.5
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Sep 5, 2010 at 15:26 comment added gowers That's a very interesting example, even if it is of the opposite of what I asked. My instinct is to think it's good that there's a proof, but I'm not sure how to justify that. And obviously I'd prefer a conceptual argument.
Sep 5, 2010 at 3:00 comment added Joseph O'Rourke Gian-Carlo Rota would agree, for he said (in "The Phenomenology of Mathematical Beauty") that we most value a proof that enlightens us.
Sep 5, 2010 at 1:17 history answered André Henriques CC BY-SA 2.5