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Can interesting mathematics problems be solved systematically?

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Solving a mathematics problem that is not a routine exercise can often feel more like an art than a science. Different people attack problems in different ways, and ideas can appear to spring into one’s mind from nowhere. I shall argue that solving problems is a much more systematic process than it appears, and shall also try to explain why, if that is the case, it has the features that make us think that it isn’t. For the bulk of the talk, I shall attempt, with help from the audience, to solve an Olympiad-style problem that I have not seen before, and to do so systematically rather than by waiting for a clever idea to appear out of the blue. The attempt is not guaranteed to succeed, but I hope that it will be informative whether or not it does.

This talk is part of the Trinity Mathematical Society series.

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