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Oct 29, 2009 at 18:20 comment added Harrison Brown I mean, a lot of the time what you do at each step is improve the solution locally in a way so obvious as to be almost stupid -- the miracle that occurs/meta-algorithm to consider is that the small local improvements don't eventually start cancelling each other out. I don't see an easy way to fit the three-squares theorem into this paradigm, though.
Oct 29, 2009 at 18:01 comment added Qiaochu Yuan Right, but I don't have an intuition for any of those algorithms either, except the ones that boil down to the Euclidean algorithm.
Oct 29, 2009 at 17:57 history answered Harrison Brown CC BY-SA 2.5