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I have searched and examined legendary stories of the problem-solving skills of von Neumann in mathematics.

  1. With George Polya

  2. With Dantzig

Maybe there are other stories showing that he is a great problem-solver, but I think these two are well-known.

I know that he wrote many papers in pure mathematics (mostly developing new concepts), but with his talented problem-solving skills, didn't he write any paper on solving unsolved problems in mathematics? Maybe I haven't searched enough?

Just because he was not interested in publishing a paper on that subject?

Or, even for him, it is not easy solving problems that are worthy of publishing. What are your thoughts?

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  • $\begingroup$ Are you asking whether von Neumann solved any (previously) unsolved problem in math? $\endgroup$ Commented Sep 1, 2022 at 3:45
  • $\begingroup$ @J.W.Tanner Yes, maybe my writing was vague...? $\endgroup$
    – SG Kwon
    Commented Sep 2, 2022 at 5:45

2 Answers 2

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John von Neumann (partially) solved Hilbert's fifth problem.

Plus: he is one of those that contributed to solving Russell's paradox by building the axioms of maths.

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One guess: There was a question from physics on how to formulate quantum mechanics. Von Neumann proposed doing it using operators on Hilbert space. (1927-1929)

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    $\begingroup$ Which is part of Hilbert's sixth problem. $\endgroup$
    – Mauricio
    Commented Aug 31, 2022 at 19:45

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