"Euler proves you can be a great mathematician even if you calculate a lot. Gauss was good at calculating too, but kept it hidden as if ashamed".
The 2019 course of Don Zagier has started today!
Great geometry moment: M_{1,1}=H/SL(2,Z) described as "toothpaste tube"
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And when calculation leads to this feeling that the rules of the game itself are somehow biasing play in a certain way, rewarding some choices and punishing others, then the activity takes on a tantalizing fascination. One struggles to hear the subtle guidance it is offering.
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According to the eminent mathematician-historian Jeremy Gray, "[Gauss] himself said that many of his best discoveries were made at the end of lengthy calculations, and much of his work on elliptic functions moves in a sea of formulae with an uncanny sense of direction."
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