[schmuhblaster]

Mathematics has always been an experimental science to some extent. While Newton, Euler and Gauss would spend a lot time calculating numerical approximations by hand, modern mathematicians have been doing the same using computers and software. And once an a clear picture emerge about what’s going, you can start to formalize that and attempt to prove and communicate your results in the standard definition, proposition, lemma, theorem scheme. (Btw there is even a journal called Experimental Mathematics devoted to this approach).

I don’t see that LLMs will fundamentally change this, but rather accelerate the speed of mathematical research.

Some computer generated proofs might of course be hard to understand, but at least their existence gives another data point work with.

Doing Mathematics is more than proving something, that’s just the end of a long road spent pondering at one’s desk about how things could work out.