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Tangent:

> From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it.

Keep in mind those ~88 hours were spread across ~10,000 simultaneous agent instances.

So, roughly 880,000 hours of compute.

Assuming a fifty-year career, and forty-hour workweeks, a human mathematician's career is about 100,000 hours of "compute".

I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already.

The perverse incentives of academia mean this has never occurred.

The perverse incentives of industry mean OpenAI intentionally scooped researchers who were getting close (granted, with AI help).

I'm not trying to dismiss the achievement - if the proof turns out to be solid, it's quite impressive (though much less so if the training data included the recent human breakthrough, which seems pretty plausible).

I'm just pointing out that "88 hours" is a very misleading way of framing this.

> I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already.

> The perverse incentives of academia mean this has never occurred.

This. Mathematicians in their most energetic years are trying to get tenure or land a tenure-track job. They are disincentivized to go all-in on ultra high risk, high-reward problems. The potential downside is just too forbidding. It's much safer to develop a research program in a mainstream field that affords many opportunities for partial progress that can translate to a robust publication record.

ok I realize this is a tangent but you're saying my post is very misleading and then also saying that a human mathematician's career is about 100,000 hours of compute and that Navier-Stokes could've had a solution by now if not for perverse incentives. You may be right but I don't think this is a great argument because in a year I would bet that those numbers change since computing power tends to increase or get cheaper over time. So I am taking the stance AI can outdo people if not now, perhaps soon.

I wasn't trying to say that genAI won't beat humans. It arguably already has, much as that may fill me with horror and revulsion.

I'm just trying to point out that economically, we have not yet reached the point where AI mathematics research is a no-brainer hands-down win, no consideration required.

It might already be a win, and certainly the ability to compress those 900,000 hours of effort into an actual week of linear time is mind-boggling and potentially a huge game-changer for all kinds of open research questions.

It's not obvious that human math research is dead yet.

Maybe soon, but not yet.

"I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already"

There were more than six doing that and it's essentially why it was ripe for AI to finish it off. But the finishing off was quicker than anyone expected

I'm not a mathematician, nor do I know almost anything about the discipline, but it sounds like maybe you do.

What teams of people spent an entire career working together, focused entirely on Navier-Stokes or problems they suspected were related, without any "publish or perish" concerns?

I realize tenure is a thing, but my limited understanding is that a significant amount of time is spent earning it, once you account for Ph.D. program and the years of needed to be granted it.

> Would it be better to ask someone who has climbed Mt. Everest or someone who took a helicopter ride up near the top and then went to the peak?

Depends on if I want to go by helicopter myself.

I agree entirely with what you're saying, right up until your final question:

> why bother grinding through all the material of climbing Mt. Everest and then attempting it if the helicopter ride is how things are done now?

I think you answered this yourself earlier:

> I think progress is really measured by what humans are able to do and understand

People want to make this progress. Therefore people will "grind Everest" as a mathematical community, and that is maybe not so hugely different from a lot of previous mathematical work.

There's still ample room for creativity: simplifying, generalizing, asking new questions humans are interested in, ...

That grind is emotional. And it's something AI will never have. The desire to solve a problem.

Citation needed. Who are you to say large enough clusters of neurons can't develo emotions?

Who are you to say they can? I would think the burden of proof is on you to promote an inanimate object to an emotional entity.

Otherwise we are truly lost.

I think progress is really measured by what humans are able to do and understand, not machines.

Building a machine that solves Millennium problems is pretty cool too. You wouldn't know it from reading these stories, though.