OpenAI新模型8天解千禧难题，引发学术诚信争议

The first Millennium Prize, Navier-Stokes, has fallen to AI.

A deeply unfortunate situation has arisen involving what should have been some combination of a positive story about new progress in AI-assisted mathematical research and yet another opportunity to freak out about rapid AI progress.

Or, as we call it around here, Tuesday.

The Real Story Is The New Model That Is Better Than Astra

Keep your eyes on the prize. There are three stories here.

The first story is much more important than the second story, which in turn is much more important than the third story.

• OpenAI’s next model took a week to get a generation ahead of Astra, and they are telling us this because everyone is totally freaked out about what is happening.
• Or, in official language: ‘We believe it is important to inform the world about the pace of AI progress and what to expect from upcoming models’ and that we ‘may require more deliberate choices about the pace of progress.’
• This new AI has, eight days after it started training, solved Navier-Stokes.
• A bunch of drama over who gets the credit for math involving Navier-Stokes.

Jeffrey Ladish: I haven’t looked into the human drama around the Navier–Stokes problem but sorry give me a minute because HOLY SHIT AI JUST SOLVED A MILLENNIUM PROBLEM.

I cannot emphasize the top story enough.

I am still going to tell all three stories, but again: Eyes on the prize.

Setting the Stage

The story on this particular Tuesday begins in the morning.

Tristan Buckmaster and Levent Alpoge had worked for a year and offer us a series of remarkable results: Finite-time blowup with smooth forcing for incompressible porous media, for Boussinesq, and for 3D incompressible Euler. They also believe they have a blowup for hypo-dissipative Navier-Stokes, but the Lean verification of that result is not finished.

Tristan Buckmaster: The program this fits into was not started by us nor was it proposed by a Large Language Model. The credit for the basic idea of this program goes to Diego Cordoba and Luis Martınez-Zoroa, who for several years have been

exploring the construction of forced blow ups. We took their work as a starting

point, using Large Language Models to push their program to completion.

Concretely, what Levent and I did was to take the Cordoba and Martınez-Zoroa program, which achieved blowup results with rough forcing, and, with a

great deal of help from LLMs, push it to smooth forcing and to the incompressible Euler equations. The ideas making this line of attack possible are due to

Cordoba and Martınez-Zoroa.

Let me make plain what I have said to colleagues in private: in view of this body of work, I believe Luis Martınez-Zoroa deserves a Fields Medal.

So far this is great. As he notes requires rethinking about how all of advanced math will function going forward. Terence Tao offers commentary on the underlying results.

The part that is not so great is where they felt forced to publish early, without the opportunity to spend the weeks necessary to make the proofs what passes among mathematicians as readable. Buckmaster outright apologizes for the way the reports look, comparing the Euler writeup in particular to AI slop.

What happened?

I Heard a Rumor

On September 1, OpenAI heard a (false) rumor that two Millennium Problems had been resolved. In response to the possibility that someone else might make the world a better place, OpenAI spent millions of dollars in inference to explore all the unsolved Millennium Problems, using an internal model stronger than Astra, and cracked the whole of Navier-Stokes in 88 hours, plus another 17 for Astra to do the Lean formalization and verification.

You can view this as ‘OpenAI got curious to see what their new baby could do’ or you can view this as ‘they spent millions trying to scoop what they thought was an Anthropic project.’ My money is on a little from column A, a little from column B.

All it took was the rumor.

Our Price Cheap

OpenAI: Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens. In the process of resolving the Navier–Stokes problem, the agents sent 2.7 million messages and used approximately 130 billion output tokens.

Depending on what costs you count, this would have cost a regular customer on the order of $22 million, or several million for internal marginal costs. A small price if it works, but also it is crazy how many people don’t think two steps ahead.

roon (OpenAI): like all other technologies your equivalent agent swarm will cost a buck fifty in like a year. all this stuff will mean an unprecedented Enlightenment no matter the costs today

I mean, no, maybe $150k or if you’re lucky $15k, but the point stands.

Sam Altman (CEO OpenAI): ugh AI is such a bubble, i heard they are selling tokens at a loss, did they know this was only worth $1 million?

A Millennium Prize result is worth vastly more than a million dollars. OpenAI does not intend to claim the prize money. This was never about prize money, for anyone. It was always about the credit.

An Accusation Is Made

After hearing internet rumors, Buckmaster reached out to OpenAI, and according to Buckmaster OpenAI’s Sebastien Bubeck said that an internal OpenAI model had produced a proof of finite time blowup for the forced Navier-Stokes equations over the past few days. Buckmaster claims that over the course of two calls, it became clear he had initially been misled and that an entire team had been working on the problem, using an ‘insane’ amount of compute.

Which we now know was 130 or 300 billion output tokens, depending on what counts.

If this part is true, it would be quite bad.

Tristan Buckmaster: Two proposals were offered to me.

The first was that we post our Euler result, and that OpenAI post its Navier-Stokes result the next day.

The second was that, after posting Euler, I alone write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic. It was also said that if OpenAI posted after us,

they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers.

I said that if OpenAI released its result in the way proposed I would go

public with what happened. The reply was, “Why would you ruin your career?”

I replied that I am an academic, and asked why he thought going public would

ruin my career. The reply was, “If you don’t want me to be nice, then I don’t

have to be nice.”

… I would like to be clear about what I am not claiming. I have not seen

OpenAI’s proof. I do not know what their model did, or how. I do not know

whether our data was used. I am not accusing anyone of anything. I am stating

what I was told, when, and what was proposed to me. I am stating it because

the alternative is to let a sequence of announcements say something I know to

be false.

Or here’s Levent Alpoge telling his side of the story, and Sebastien responding:

levent: “we cannot rule out that de-identified data derived from their usage of our products helped improve our models.”

i mean props to them for straight coming clean.

(so far the proof looks more along the lines of another euler blowup proof we had, off of whose ansatz naming we were making really stupid puns like “smooth criminale”, unlike the much better “ideal fluids explode”, Tristan)