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linhares 1347 days ago | link | parent

The problem with these grandiose statements is that they forget the word formal. You have to be searching on a space that's formally defined to make optimization=verification if P=NP. When we do art and creativity, the space is not formally defined a priori. Hell, even theorem-proving isn't. Look at the breakthroughs in mathematics and most of them, a really large majority, came from applying some new ideas or operations (e.g., ricci flows) to problems that all others simply could not see as applicable. There are no "profound philosophical implications" if P=NP (which I doubt) other than our universe lets us have polynomially bounded algorithms for a huge cluster of problems.



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