Either mathematical progress helps advance society, in which case progress is a good thing.
Or mathematics is more like a hobby, and while ai may spoil their fun, they need to move on like chess and go players.
Or mathematics is more like a hobby, and while ai may spoil their fun, they need to move on like chess and go players.
Mathematical progress does (quite obviously, on the whole) help advance humanity, so progress is a good thing. The problem is that defunding mathematicians and handing over control to AI and the companies that create them will cause the subject to stagnate. Sure, for a while we might get progress on existing questions using (perhaps quite novel) combinations of existing techniques, but, so far, given the character of the results we’ve seen, there’s no indication that it will continue indefinitely. Even if it did, what would be the point? Huge textbooks full of work no one can understand or benefit from?
One possible analogy is that humans work to add new points to the space of mathematical knowledge, and AI then fleshes this out to attain the ‘convex hull’ of these points. Essentially, humans ‘invent’ the definitions and pose the questions and AI does the grunt work as well as some creative exploitation of known results and tools to bring down all the low-hanging fruit that follows (important note: what appears to be non-low-hanging fruit to us may in fact be technically low hanging once AI is involved; we saw this for example with the Jacobian conjecture). This seems to be the current situation, and to argue that humans are fully replaced it is necessary to argue that AI is adding points outside the convex hull of human mathematics. A sufficient example would be a first-principles AI proof using alien techniques, and this we haven’t seen so far.
The mathematics-chess comparison is, to put it bluntly, nonsense. I see where it comes from, but, as absolutely anyone with any research experience will tell you, mathematics is orders of magnitude (and this really isn’t strong enough) more open-ended, and doesn’t consist of a game one is seeking to ‘win’. The goal is understanding itself.
That’s like saying ‘what about the fact that a man has to walk up to his ex wife to shoot her in the head’ as an attempted criticism of walking.