Magnus Carlsen plays fellow humans at the game because people still care about human competitions. What motivation would a mathematician have for solving already solved problems by hand? Can you imagine someone spending years working on a proof for an already-proved theorem just in case it leads to new insight?
Of course not. I'm so tired of the chess analogy. It was always a game and it was always performative.
Research is fundamentally different. We are seeing the erosion of specific needs for thinking at depth. AI is the automobile for the mind. There will 100% be undesirable consequences and selective atrophy of cognitive abilities once prized. This is a loss. There's no getting the cat back in the bag at this point so long as the objective dimension of work, as in object opposed to subject, is held as the most important.
SWEs felt this same crisis late last year. Now it's the mathematicians. They won't be the last.
If insights and human understanding are more important than specific results, I don't see why people should stop producing insights and human understanding. "Working on a proof" in today's sense of trying to come up with a proof before others probably stops being useful, other ways of working will be needed