alt Hacker NewsIt 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