alt Hacker NewsOh it would change a lot. It would be an enormous psychological boost for everyone to find a practical algorithm.
In any case, I think it's better to read PP as somebody would find a practical, albeit incomprehensible, algorithm for solving NP complete problems.
Although I probably disagree with PP, because even a candidate algorithm that mysteriously works without proof would have practical value, so this case is not predicated on proving.
I think a better example of genuinely practical but rather uninteresting (YMMV) mathematical proofs are proofs of convergence of numerical methods, FEM for example. (I have been through it in school, it was a torture.)
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> a practical, albeit incomprehensible, algorithm for solving NP complete problems.
It would not not necessarily be practical, even if it ran in polynomial time. It may have cost O(n^c), with a totally out of order exponent like c=A(5,5) or whatever.
> > If a magic oracle tells you p=np, that's useless. How would that change anything?
> Oh it would change a lot. It would be an enormous psychological boost for everyone to find a practical algorithm.
OK, I tell you that P=NP, and that I am a magic oracle. So, you have you psychological boost for finding a practical algorithm for free. :-)