| ▲ | ChadNauseam 4 hours ago | |
> One can explain it as the computer checked a bunch of cases and all maps reduce to one of these cases. It doesn’t take an expert to state this. Hmm, doesn't it take an expert to explain why those cases are exhaustive, and why the code that checked them is correct? Tangentially, I'm not a mathematician but I wonder if one "opaque" proof that is too complicated for anyone to understand, but that we know is correct via formal verification, might end up being built on with "transparent" human-understandable proofs. For example, it's my understanding that there are many conjectures that have been proven true conditional on the riemann hypothesis being true. In that case, an opaque proof of the riemann hypothesis would enable those conjectures to be known and built upon | ||
| ▲ | czgov 3 hours ago | parent [-] | |
That will certainly happen. Humans will extend AI generated results. But what will also happen is that AI can “think” much longer than a human can and can have a vastly greater base “knowledge” than humans can have and so there will be a bewildering amount of new results. Humans may not be able to keep up. To your first point. There a large number of cases that maps can be reduced to. Very few people have checked these reductions themselves. In 50 years there will be no human alive that will have checked the reductions by hand. Do we then discard the theorem? More importantly, do we trust the people that claim to have checked all the reductions? There are hundreds of cases. I trust a computer verification much more than I’d trust human verification. Humans will likely make mistakes due to the tedium. And some will claim understanding of all cases but be wrong in their understanding in some of the cases. | ||