alt Hacker NewsOK, good to know (if they can be trusted - Altman clearly is a liar), but it doesn't really change the big picture much.
1) OpenAI by their own admission, only re-tackled Navier-Stokes because they heard it had already been solved (but not yet published). This isn't advancing science or helping the mathematical community, this is just being a dick.
2) OpenAI, specifically Sebastien Brubeck, then threaten to "not be nice" and "ruin the career" of one of the mathematicians whose work they had succeeded in duplicating, unless he agreed (which he refused to do) that his collaborator, an Anthropic employee, was not named. This is not only against mathematical norms of credit assignment, it is also being a pathetic human being.
OpenAI would have you believe this result shows how powerful their mystery better-than-Astra model is, but the reality here is that this model needed 10,000 agents, $20M of compute, and the assistance of a whole team of people at OpenAI, to replicate (then exceed) the work that just took two people, with some academic grants as an AI spending budget to achieve (a few $100K - listed below).
https://cims.nyu.edu/~tristanb/
I'd say advantage humans this time. Better luck next time OpenAI - and if you don't want unfavorable comparisons then maybe choose to work on problems that have not been solved yet, and that humans are NOT making nice progress on.
Replies
1. I would agree if the rumours were that some mathematician(s) had solved them, but the rumors alleged it was Anthropic. I don't really see what the big deal was. They had a new model that was going along great and wanted to test its mettle.
2. Yes Brubeck's comments were weird at face value. That said, Open AI's proof isn't a duplication of anything. Not only is Tristan's work a sub problem but the methods are different. And what OpenAI didn't want was Levant on the paper OpenAI authored not whatever they were working on (Euler). It's petty sure but it's fair enough. Tristan and Levant didn't have anything to do with the Navier Stokes solution, so it's really their call if they didn't want to collaborate on their own paper with the Anthropic employee.
>OpenAI would have you believe this result shows how powerful their mystery better-than-Astra model is, but the reality here is that this model needed 10,000 agents, $20M of compute,
$20M in approximated API prices doesn't mean they spent $20M worth of compute. The real number would obviously be substantially less.
>and the assistance of a whole team of people at OpenAI
You can't eat your cake and have it. What sort of guidance do you think is happening in a 10k agent, 320b token, 88 hour run ? AI did this one.
>I'd say advantage humans this time....to work on problems that have not been solved yet, and that humans are NOT making nice progress on.
Interesting way to frame progress that didn't move along till an LLM generated proof.
>Better luck next time OpenAI
Well it looks like they will announce at least one other millenium solution soon. In the same link they say they have "made substantial progress" on another millenium problem. The rumor mill before that statement was Hodge is done and Birch and Swinnerton-Dyer is on its way out.
"I'd say advantage humans this time." Well LLMs were instrumental in any account of what happened. It's just a question of which company's LLMs did the breakthrough, and most of us outside silicon valley don't care about that part so much. The NYU guy himself said without LLMs the solution is maybe 10 years away.
> and that humans are NOT making nice progress on
They've pretty much said their own work was heavily agent driven. Levent is in a particularly bad place here because while he probably had a lot of background in the Jacobian Conjecture problem, he made the solution to that one sound like someone asked the question and he just fed it to Fable during the world cup. Whether that nonchalantness was to just seem hip or was to promote Anthropic, which he has stock in, or was just the truth I don't know though. But it makes this one seem similar, when they might have had really had nearly a year of very valuable feedback to the models.
> OpenAI would have you believe this result shows how powerful their mystery better-than-Astra model is, but the reality here is that this model needed 10,000 agents, $20M of compute, and the assistance of a whole team of people at OpenAI, to replicate (then exceed) the work that just took two people, with some academic grants as an AI spending budget to achieve (a few $100K - listed below).
I think you have to work pretty hard to minimize what OpenAI achieved here like this.
The Navier-Stokes equations have been around since 1850. The smoothness problem has been well known for over a hundred years and has only gained importance. It's been a Millennium Problem since 2000.
Levent Alpöge and Tristan Buckmaster did great work to solve the related Euler problem, but didn't solve the Navier-Stokes smoothness problem.
The Navier-Stokes smoothness problem has previously had significant resources working on it. Computational fluid dynamics is one of the most important tools in modern engineering and is closely related.
You speak of 10,000 agents as though it is somehow extreme, and yet within the past month I've had a single task that used over 100 agents on a mere Anthropic team plan. I think two orders of magnitude more compute to solve one of the greatest unsolved physics problems[1] is nothing.
I don't excuse Brubeck behavior because of this, but that doesn't minimize the achievement here.
[1] Wikipedia quote: In particular, solutions of the Navier–Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering. https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc...