To be fair - there are statements in math that are independent of the axioms. For those statements, the universe you find yourself in can pick either version (true OR false) and still be consistent.
See also: noneuclidian geometry and axiom of choice.
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.
Leans proof checker is not polynomial time, unfortunately. It is super exponential. Basically, because it can verify the result of any function it can prove to be total.
It's math, the result shouldn't be different just because it's a different sim.
To be fair - there are statements in math that are independent of the axioms. For those statements, the universe you find yourself in can pick either version (true OR false) and still be consistent.
See also: noneuclidian geometry and axiom of choice.
Well if the fundamental constants or hidden variables of the universe are shifting because of his comment then it can change the outcome.
Depends how fundamental the variables are. If we can code a sim for a topos[1], why can’t we be in such a sim?
1. https://arxiv.org/pdf/1012.5647
unless mechanism behind our universe dynamically alters our logic on the fly to be artificially self-consistent
Why?
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.
Leans proof checker is not polynomial time, unfortunately. It is super exponential. Basically, because it can verify the result of any function it can prove to be total.
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Could also break the basic principles underlying most encryption approaches. I would rather have my bank account not stolen and internet working
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Even if P=NP it doesn't mean that the P approach will be better than the heuristic approach we already do today.
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