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No matter how original you think you are, it's almost always already been done. You think you found a new theorem and then you check some old pdf from 20+ years ago and it's already been done.

If you can pull it off, and the result is actually novel and not trivial, you can get a PhD. that is how hard it is.

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The flipside of that is seeing hints of a result that would be really helpful. I still remember how excited I was to stumble on a book from 1931 (The Taylor Series by Dienes) since it had the only english-language proofs of some results by Szego and Polya that I felt could unblock my research. My hope is that this discovery problem can be largely solved.

This is also why I'm not as excited by the focus on pure reasoning and olympiad problem solving in the math and AI space. It's like the early career phase of trying to solve Collatz and Riemann but just repeating work from decades ago.

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