It seems that AIs are really good at finding counterexamples now.
Even if progress by AIs in proving conjectures lags, it seems likely that AIs collectively will, in the next few years, find counterexamples to nearly all the Erdős (and other) conjectures that are actually false and also provably false.
That means we will able to assume that nearly all the remaining conjectures are either true or undecidable.
Surely, that's good for folks who just want to know where the truth boundaries in mathematics lie.
It's obviously causing a lot of soul-searching amongst professional mathematicians.
Arguably, they should have given less weight for the last 100 years to Hardy's view in 'A Mathematician's Apology' [0]:
> It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.
Rota takes a much more balanced view in 'Indiscrete Thoughts' [1].
"Problem Solvers" take Hardy's view:
> ... The mathematical concepts required to state mathematical problems are tacitly assumed to be eternal and immutable. Mathematical exposition is regarded as an inferior undertaking. ...
While for "theorizers":
> Mathematical exposition is considered a more difficult undertaking than mathematical research.
If professional mathematicians can reinvent themselves, there will be plenty of work left to do to explain the results of AIs to other humans.
There probably needs to be a new career path into professional pure mathematics other than doing novel research in a PhD.
[0] https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology
Counterexamples can be decidable and arbitrarily ugly or difficult to find. If you know anything about mathematics it's trivially simple things can yield extremely complex structures. And that can absolutely include terse conjectures whose solutions are in fact decidable but only with proofs that would consume more than a bit of memory for every particle in the universe. Not logically undecidable, but physically impossible to prove in our physical universe.
Further down the scale are ones that are decidable only by machines that we would never have the wherewithal to construct, even though they could physically be constructed with the material we have to work with.
I'm not sure we should take it as a given that AI will not also become better than humans at mathematical exposition.
> That means we will able to assume that nearly all the remaining conjectures are either true or undecidable
I mean, we could. But it doesn't really make sense to think that AIs are perfect at finding counterexamples, just because they are good (or even better than us). My general opinion is that they are orthagonally intelligent, that is, they are intelligent in an entirely different way to the way that people are. They are undoubtably clever, but the distance between when they are better than us at their best skill (or even most skills) and when they are better than us in all aspects is going to be MASSIVE.