AI Might Be Solving Millennium Problems and Not Telling Anyone, and I Have Thoughts

I spent longer than I’d like to admit last night reading through a Reddit thread about AI labs supposedly sitting on solutions to major unsolved maths problems. Not releasing them. Just… holding them back, apparently, because the last time one of these companies claimed a breakthrough, the maths community set fire to it within about six hours.

If you missed it, there was a whole saga a few weeks back over a claimed Navier-Stokes proof. Big announcement, big fanfare, and then a slow, grinding backlash from mathematicians pointing out that a proof that technically compiles isn’t the same thing as a proof anyone understands. Now there’s a theoretical computer scientist (Scott Aaronson, whose blog is worth following if you like watching smart people think in public) saying he’s hearing rumours that labs have quietly cracked several more long-standing problems and are just… not saying anything, because they got burned once and don’t want it to happen again.

I find this fascinating for reasons that have nothing to do with whether the maths checks out.

The comment thread split roughly into two camps, and both of them are right, which is the annoying thing. One camp said: who cares if a human understands the proof, a proof is either true or it isn’t, ship it. The other camp said: the point of the Riemann Hypothesis was never really the answer, it was the fifty years of mathematics that got built trying to get there. An AI that hands you a correct answer with no explanation is like being told the ending of a book you never got to read. Technically you know what happens. You’ve lost everything else.

I lean toward the second camp, but not smugly. I write software for a living, and I’ve had this exact argument with myself about code. A colleague hands you a fix that works, tests pass, ticket closed, and you still feel a small itch because you don’t understand why it works. Six months later that itch is the reason production falls over at 2am and nobody can explain what the fix was actually doing. Understanding isn’t decoration. It’s the thing that lets you maintain the system, extend it, trust it next time. Maths at this level is the ultimate legacy codebase, and if AI starts handing us answers without comments, we’re going to have a very bad time in about a decade.

But then there’s the other half of me, the one that finds it genuinely thrilling that we might be living through a period where the tools for discovering things are changing faster than our institutions for verifying and communicating them can keep up. That’s not nothing. That’s actually one of the more interesting problems humans have had in a while: not “can the machine do it” but “how do we build the social and academic infrastructure to trust and absorb what it does.” We solved something like this before, badly, with the printing press and later with the internet. We’re not exactly batting a thousand on getting ahead of transformative information technology.

There’s a comment in that thread I keep thinking about, someone pointing out that academic mathematicians aren’t a particularly powerful lobby group, so a lab has very little incentive to actually care whether it upsets them. That’s a bleak but probably accurate read on how power works right now. Whole fields of human expertise, built over centuries, can suddenly find themselves with no leverage over the tools reshaping their discipline, purely because the leverage was never really about correctness, it was about who controls the infrastructure. That should worry anyone who’s ever cared about a public institution that isn’t backed by a hyperscaler’s balance sheet.

None of this stays abstract for long. My daughter is doing methods and specialist maths at school right now, grinding through proofs by hand, and I have genuinely wondered what the point of that grind is if the endpoint is a model that can do it instantly and better. I don’t think the answer is “no point.” I think the answer is closer to why we still teach kids to do long division even though every phone has a calculator: the process is where the understanding lives, not the answer. But I’ll admit that answer gets shakier every year, and I don’t fully believe it myself anymore. That’s the honest bit.

I don’t know how this settles. Maybe the labs release these proofs with proper writeups and the maths community absorbs them the way it eventually absorbed computer-assisted proofs like the four colour theorem, grumbling the whole way. Maybe it turns out some of these “breakthroughs” are shakier than advertised, and we’ve all just been fed another Navier-Stokes-shaped balloon that pops on contact with peer review. Both outcomes are plausible, and I genuinely don’t have a strong prior on which one it’ll be.

What I do know is that I’d rather live in a world paying close attention to this tension than one that’s decided it’s already been resolved, in either direction.