Not to denigrate the moment (AI ingress into theory which this is a part of) or the result here, but these headlines are perhaps overstating the importance - some of the theories and conjectures are available for AI-assisted exploration because they are quite niche and not very important.

Maxwell's name being invoked here for instance implies a hundred year old foundational problem like Fermat, but it's just a recent conjecture that was inspired by reflections from the great man on his work.

They might be low-hanging fruit but two things immediately come to mind:

* As more of the small stuff is just proven for free, the more they can be used as a basis for other proofs. If you know something is true or false for certain, that can be a significant tailwind for the much harder, much more important problems. Fermat's last theorem looks deceptively simple and invited many failed amateur attempts at solving it, but Wiles' proof drew on a diversity of seemingly-distant subfields within mathematics that were better understood.

* What are aspiring math Phd's supposed to do, now that the bar is much higher these days? The net effect of this appears to be that we'll see far fewer, but far more elite math Phd's, potentially discouraging many young people from the field.

Yeah, the Jacobian conjecture counter-example was big news. In particular, it would have been news even if an AI hadn't done it. That's where the bar is now. Settling Erdős conjecture 7529 or whatever no longer qualifies as AI news.

I find them useful bellweathers of genuinely out of domain performance and capability, regardless of their theoretical importance. What I see is that performance trends are remarkably stable both upstream (miraculous scaling laws of pretraining on validation loss) and downstream performance (epoch capability index). We get the equivalent of a GPT4->GPT5 performance leap every ~16-18 months, and we are not hitting ceilings nor do we see any deceleration.

Today we can solve nontrivial open problems. What will we be able to do next year or the year after? 18months ago no one was using a coding agent seriously. Now for a large segment of the population you cannot do your job without them.

I'm not sure that's right. The conjecture is (claimed to be, by the people who explicitly made it) simply a reformulation of a claim made by Maxwell in his "Treatise on Electricity and Magnetism" of 1873.

It is much harder to prove these conjectures true than false. On some of these people had spent years of their life trying to prove them true. By showing they are definitely false that can be avoided.

some of the theories and conjectures are available for AI-assisted exploration because they are quite niche and not very important.

The fact this has gone viral, shows otherwise. It is important to apparently enough people that the story went viral.