There is the "prove this conjecture I have" part, which I think will be taken over by machines rather soon (say, within my lifetime). I cannot imagine there is something extra-ordinarily hard that mathematicians do, that is somehow not captured by how a Go player approaches the game.
There is also the "come up with an interesting conjecture" part, which I think is a lot harder. It is extra-ordinarily hard to specify what exactly makes some conjectures more interesting than others. So I reckon this part of math will be much harder to automate in the long run. It will probably require a lot of cross-contamination from AI that manage to write interesting books for example.
> I cannot imagine there is something extra-ordinarily hard that mathematicians do, that is somehow not captured by how a Go player approaches the game.
It's not "extraordinarily hard" but the issue is that math does not have a well-defined search space. A lot of times, proving statements requires quite a lot of intermediate results, additional tools and definitions... There is more creativity in math proofs that people think, and I don't think ML algorithms will be able to reproduce that. At most I see specific algorithms for limited purposes.
