We conjecture and argue for the following resolution to the P vs. NP problem: that it is unprovable within constructive mathematics that P != NP, but that sufficiently good heuristics can be found in most cases of interest for powerful AI systems to solve any problem in NP given enough ingenuity applied to the algorithm design and training process.
We trust that the significance of this claim is clear, but in case it is not, we spell it out. The current boom in artificial intelligence can be expected to scale to solve any problem whose solution can be efficiently checked. There are no limits to what AI can achieve, for good or for ill. We make a plea for peaceful use of the technology that is currently changing the world under our feet.
There are no limits to what AI can achieve, other than the limits of math and physics. There are no computational problems that it cannot solve, because the only limiting factor is clever algorithms, and AI will soon surpass humans at devising those.
So, I agree. It (probably) won't make a perpetual motion machine. But I predict it will do everything that we ask it to, and more. That is why I was so desperate to include a message of peace in the draft; we must be wise in what we ask of the new race of genies that we must coexist with.
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[ 2.2 ms ] story [ 16.1 ms ] threadFor a good introduction to the P vs. NP problem, please see: https://www.youtube.com/watch?v=pQsdygaYcE4
We conjecture and argue for the following resolution to the P vs. NP problem: that it is unprovable within constructive mathematics that P != NP, but that sufficiently good heuristics can be found in most cases of interest for powerful AI systems to solve any problem in NP given enough ingenuity applied to the algorithm design and training process.
We trust that the significance of this claim is clear, but in case it is not, we spell it out. The current boom in artificial intelligence can be expected to scale to solve any problem whose solution can be efficiently checked. There are no limits to what AI can achieve, for good or for ill. We make a plea for peaceful use of the technology that is currently changing the world under our feet.
This is an absurd statement. AI is just as constrained by physics and math as everything else in this world.
AI won’t make a perpetual motion machine, and if wind solve NP problems in polynomial time if in fact NP != P
So, I agree. It (probably) won't make a perpetual motion machine. But I predict it will do everything that we ask it to, and more. That is why I was so desperate to include a message of peace in the draft; we must be wise in what we ask of the new race of genies that we must coexist with.