Being able to solve NP hard optimization problems would enable progress in many areas of science and technology. For example it would allow us to find poly-sized Lean proofs for theorems efficiently, since proof verification can be done in polynomial time.

It would also be amusing to annihilate nearly six decades of proofs that assume P!=NP.

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manquer an hour ago | parent | next [-]

Could also break the basic principles underlying most encryption approaches. I would rather have my bank account not stolen and internet working

	▲	echelon 40 minutes ago \| parent [-]
		I've had enough Internet for one lifetime. As long as we also get low order polynomial solutions to important problems, it'll be worth it. Besides, unencrypted wifi was funny.

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charcircuit an hour ago | parent | prev [-]

Even if P=NP it doesn't mean that the P approach will be better than the heuristic approach we already do today.

	▲	adrianN 32 minutes ago \| parent [-]
		Of course, if we get ridiculous polynomials it doesn't mean much in practice. People who hope for P=NP generally hope for nice polynomials O(n^3) or something like that at worst.