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Kevin comments on Formalizing Newcomb's - Less Wrong
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All universities that I know of only grant PhDs based on prior work to their own previous students who've already taken a Masters there. If there is any university that just grants PhDs for sufficiently good prior work, do let me know.
For a certain definition of sufficiently good prior work, universities will grant PhDs. When I was in high school, I took a summer program at CMU and the professor Steven Rudich said that if we were to prove P=NP or P!=NP or prove it undecidable or whatever, that would be good for an instant PhD from CMU. I'm pretty sure the problem he referred to was P/NP, but it's been a while and it may have been another Millennium Problem.
So if you happen to have a proof for P/NP sitting around, let me know and I'll introduce you to Dr. Rudich.