"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."

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Have confidence in your decisions. Make them expeditiously, and stay with them as long as you believe you are correct no matter what others say. However, when you conclude you were in error, do not hesitate to announce the error publicly and change course.

— Ed Koch