We have machines that can crank out true theorems, rigorously proven, all day. It takes a mathematician to know what is worth working on. And that is fundamentally an intuitive decision. Computers don't care whether a proof is interesting or not.
It’s a bit tautological since we are defining interesting as what human mathematicians work on. Perhaps if computers ran the show they wouldn’t agree with our definition.
Maybe it is a feedback loop, rather than a tautology? The things many mathematicians find interesting are the things that the general mathematician community is working on. And the way you become a mathematician is by publishing things that the community finds interesting enough to let through the peer review process.
Ultimately though this is all funded by, in the end, the belief that they’ll be able to dumb down the good stuff for us scientists, engineers, and other folks who build actual physical things when we hit the point that we need it. (Of course it is an exploration process so not everything needs to be directly applicable).
If computers ran the show, we would probably stop plugging them in if they used more power than their theories saved us, or whatever.
Regardless of what computers find interesting, humans want to progress math in stuff humans find interesting. We can't fully rely on computers to do that yet since they can't seem to judge that very well rn as good as human mathematicians.
Think of pets. We, humans, run the show. There are some things the pets think are interesting because we humans are doing it, but by and large pets like what is dictated by their genes + individual preferences.
True. It’s also interesting to note that a lot of Newton and Leibniz’s original reasoning about infinitesimals itself went through the same sort of three step process: first it was accepted because it was all there was, then rigour became fashionable and it was thrown out. Finally, only last century, it was shown that such ideas can be made perfectly rigorous in the right setting [see: nonstandard analysis].
