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Will research-level math become a sport akin to chess before 2035?
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2034
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Will there be competitions of people doing phd-level math research without ai help before 2035?

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I'm not sure what you mean. Surely you don't mean that this sport would be as popular as chess. That seems very unrealistic. However, there are already math championships and competitions. Naturally, these work differently than chess compatitions based on chess matches. Do you mean that a kind of match-style format could be created for math research?

I get the impression that you have something very specific in mind, and I'm curious to know what that might be.

I'm sure there are things like a math world championship at the moment, it's like an exam with questions hard enough that the best mathematicians in the world cannot answer all of them.