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RickSilver

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My question though involves math competitions. While I seem to definitely have some facility for proof based mathematics (I've done pretty well in the proof based courses at my local uni and I seem to manage to do most of the exercises in the math books I read) I seem to have a terrible time with problem solving especially at math competitions. I've never managed to move onto AIME from the AMC for example. The time constraints make me feel uncomfortable and while I'm interested in the topics covered on these tests (I'm hugely interested in geometry, less so in elementary number theory) I seem to not be able to solve these problems in the time constraints. Should I go back to basics and try to cultivate more skill in problem solving? is it really all that important a skill for a mathematician to cultivate?