I would love to know the true unsubsidized cost of all of this. How many grad student-years did this cost?

I've been mentoring (or so I'd like to think) a very bright undergraduate mathematician, in fact he was the one who pointed out the final irreducible flaw in my proof last summer. And I am extremely curious to see what he does and if he even finishes his degree in mathematics. He had already expressed to me some dismay that his summer undergrad research program with several Ivy-league math majors got blown out of the water by a few hours of a frontier model. It's making everyone question what the future will look like and what education and training and certification will even look like.

But the future belongs to those who show up. Maybe this is the beginning of a mass democratization of scientific and math research, maybe we are going back to the gentleman-scholar model of amateur researchers and Twitter will be the new Journal of the Royal Society.

You may achieve far more than you plan on and it may come years and years after you think it should happen. You probably haven't met the right problem yet. You will.

I think something like the Collatz conjecture will be solvable not as number theory or ergodic theory but some other completely wacky environment that humans haven't even sniffed at.

Also, once upon a time I wanted to be a patent lawyer. It's incredibly hard to sit for the patent bar if you have a pure math degree and don't have an engineering degree. Thankfully New Hampshire lets anyone sit for the FE exam.

But also I am excited to be living through this new era of programming and new era of mathematics. I'm still saddened that I couldn't be the one to solve this old problem, but now I realize that my personal approaches were really solving a level of this problem even stronger than the original conjecture, and I'm energized to tackle those (in my free time between being a solo founder and father of 3, etc.).

Humans are the same way sometimes but I guess there's romance in that. If a human had solved it a la Kekulé and said "it came to me in a dream" I would at least understand that.

I imagine the same will be true of AI, but I'll say that in the short term AI is going to make mathematicians better because it solves the breadth problem. Again, I feel like this Barnette conjecture got solved (if it is solved) because of some clever partition function sums which are intellectually tractable but simply too far out of anything I'd seen before (I see the apparition of my GT combinatorics professor intoning gravely that "everyone knows that, Jake, you're an idiot"). Maybe AI will help identify common threads far greater than Google and journal search.

I think if I had ChatGPT when I was 20 and working on this problem for the first time I might not have solved it, but I would have learned every angle and facet of it far more quickly. But then again I would not have spent so many late nights staring at the Országház across the Danube and letting my mind drift and bump against the problem like spilled cargo in the river.