I am a theorist (though not in complexity) so I agree with you that new math is never bad. I also agree that an very lucky P=NP result _may_ be implementable _a

I am a theorist (though not in complexity) so I agree with you that new math is never bad. I also agree that an very lucky P=NP result _may_ be implementable _at some point_ in the future, though to be honest I wouldn't put my money on that happening. As for more important problems-- I think it's more important to improve the specializations of NP problems, heuristically, for problem instances which arise in practice. A concrete example in my line of work could be improving the performance of SMT solvers on encodings of real programs. There's a lot of exciting work happening in this area and it's opening doors in program verification previously thought to be unrealistic. IIUC the formal methods team at AWS is putting a lot of work into memoized, distributed SMT solving, and are making meaningful gains over the current state of the art. I don't really care if we can solve the most general NP hard problems in O(bad*N^bad) only for N>bad. A) Even a getting result that weak seems to be too challenging to prove and probably not true, and B) trying to solve the most general problem is complete overkill for any problems that come up outside a complexity textbook.