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Every mathematician has only a few tricks - MathOverflow

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Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. In Gian-Carlo Rota's "Ten lessons I wish I had been taught" he has a section, "Every mathematician has only a few tricks", where he asserts that even mathematicians like Hilbert have only a few tricks which they use over and over again. Assuming Rota is correct, what are the few tricks that mathematicians use repeatedly? ∑ 𝑖=1 𝑚 ∑ 𝑗=1 𝑛 𝑎 𝑖,𝑗 = ∑ 𝑗=1 𝑛 ∑ 𝑖=1 𝑚 𝑎 𝑖,𝑗 ∑ 𝑖 = 1 𝑚 ∑ 𝑗 = 1 𝑛 𝑎 𝑖 , 𝑗 = ∑ 𝑗 = 1 𝑛 ∑ 𝑖 = 1 𝑚 𝑎 𝑖 , 𝑗 (and its variants for other measure spaces). I still get misty-eyed whenever I read something that capitalizes on this trick in an unpredictable way. A very useful generic trick: If you can't prove it, make it simpler and prove that instead. An even more useful generic trick: If you can't prove it, make it more complicated and prove that instead!

soft question - Every mathematician has only a few tricks - MathOverflow Every mathematician has only a few tricks Ask Question Asked 6 years, 1 month ago Modified 10 months ago Viewed 61k times 203 $\begingroup$ In Gian-Carlo Rota's "Ten lessons I wish I had been taught" he has a section, "Every mathematician has only a few tricks" , where he asserts that even mathematicians like Hilbert have only a few tricks which they use over and over again. Assuming Rota is correct, what are the few tricks that mathematicians use repeatedly? soft-question ho.history-overview big-list big-picture gm.gener

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