Well, if I were a mathematician, what I'd be noodling about with right now is a way to model the number of failed attempts that AI companies must be making for every success they report.
I guess you don't have to be a mathematician to do that sort of calculation, but I'm just proposing it as a way to lift mathematicians' spirits a bit.
Also pay attention to the fact that every time a new model is released there's a slew of new results and then they dry out for a while, which suggests a "throw stuff at the wall and keep what sticks" approach that's incompatible with a kind of system that can just magickally solve all maths right now.
I'm saying that because I get the feeling that mathematicians don't have a good model for the true capabilities of those systems and that can lead to an overreaction, like "woe is me, all of mathematics will be solved and my entire discipline will be rendered obsolete". Coming from an AI background I don't think that's right. I think because mathematicians are not AI researchers they simply don't have a very clear idea of what's going on with those systems. And tbf even many AI researchers (the ones who don't enjoy the benefits of a long tradition that goes back to the 1950's and basically only joined the field in the last 10 years or so) don't understand those systems very well either.
Nobody is in panic, but we are using these systems and seeing what are their capabilities and it's clear that their use has a big impact on the practice of mathematical research, probably far more impact than it has in other areas. Part of mathematics involves classifying structures - think of describing combinatorial objects - and this is a sort of game with which a well directed AI tool can be very effective. Part of mathematics involves being able to bring to bear on a problem a diversity of techniques, and AI is also very helpful in this regard.
The point is that people who spend their time classifying nilpotent Lie groups that admit structure X are out of work if they don't change their perspective. Maybe such problems were never really that interesting, although it was useful to have a group of people acting as human computers to work them out - but well used AI yields for such problems more complete and more reliable results - and so allows researchers to spend their time on other more interesting things. The problem for your run of the mill professional mathematician is that more interesting things are harder ...
I guess you don't have to be a mathematician to do that sort of calculation, but I'm just proposing it as a way to lift mathematicians' spirits a bit.
Also pay attention to the fact that every time a new model is released there's a slew of new results and then they dry out for a while, which suggests a "throw stuff at the wall and keep what sticks" approach that's incompatible with a kind of system that can just magickally solve all maths right now.
I'm saying that because I get the feeling that mathematicians don't have a good model for the true capabilities of those systems and that can lead to an overreaction, like "woe is me, all of mathematics will be solved and my entire discipline will be rendered obsolete". Coming from an AI background I don't think that's right. I think because mathematicians are not AI researchers they simply don't have a very clear idea of what's going on with those systems. And tbf even many AI researchers (the ones who don't enjoy the benefits of a long tradition that goes back to the 1950's and basically only joined the field in the last 10 years or so) don't understand those systems very well either.
Bottom line: don't panic.
Or, not yet :0)