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Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses and then start to reason. What you do is trial and error, experimentation, guesswork.
Our mission is to make the world more open and connected.
If you want to be given everything, give everything up.
It is always good to have a problem that you cannot solve. It means you have something to work on.