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Revision of Mathematicians need to be metamathematicians from Sun, 14/12/2008 - 15:17

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If you want to prove a theorem, then one way of looking at your task is to regard it as a search, amongst the huge space of potential arguments, for one that will actually work. One can often considerably narrow down this formidable search by thinking hard about properties that a successful argument would have to have. In other words, it is a good idea to focus not just on the mathematical ideas associated with your hoped-for theorem, but also on the properties of different kinds of proofs. This very important principle is best illustrated with some examples.

What a lower bound can say about the proof of the upper bound

When does reformulating a problem count as progress?

If you are getting stuck, then try to prove rigorously that your approach cannot work

Parent article

General problem-solving tips


"Think about the converse"

"Think about the converse" should be added as a link in this article.