"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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Even when whacking the ball around for the sheer fun of it, though, one still tries to avoid hitting the ball into the net, or outside the lines. And in this sense calculation is always constrained and structured, even if its purpose is not always perfectly clear.
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Often the play seems magically to organize itself, in some strange and surprising way. As one fiddles around, obeying the rules of calculation, one often starts to feel as though the rules themselves are somehow pushing one in a certain direction. As though they subtly bias play.
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