In retrospect, my comment was unhelpful, since it is not known whether there are any algorithms than solve every instance of an NP-complete problem with high probability.
This is the key. If you had an algorithm that solved every instance of an NP-complete problem in polynomial time with high probability, you could generate a proof of the Riemann hypothesis with high probability! (Provided that the polynomial time algorithm is pretty fast, and that the proof isn’t too long)
This is the key. If you had an algorithm that solved every instance of an NP-complete problem in polynomial time with high probability, you could generate a proof of the Riemann hypothesis with high probability! (Provided that the polynomial time algorithm is pretty fast, and that the proof isn’t too long)