This is one of the most important skills you can develop.

The more problems I do on a specific topic the slower it takes to reach graduate level mathematics. Tao: I hava translated this essay into chinese, I’m sorry I couldn’t translated it well enough, as my ability in english is as poor as mathematics.

On the other hand, if I just do the homework problems I feel I won’t be fast enough for answering questions during exams. Your blog is Gospel to those who are interested in Professional mathematics.

I do have a book on how to solve mathematical problems at this level; in particular, the first chapter discusses general problem-solving strategies.

There are of course several other problem-solving books, such as Polya’s classic “How to solve it“, which I myself learnt from while competing at the Mathematics Olympiads.

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