The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys:

> 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.”

Threatening a research mathematician and dangling and $1M payday to dissociate from his research collaborators and to adopt OpenAI's narrative is bad stuff.

Buckmaster:

> "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer."

OpenAI (i.e. this OP):

> "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models ."

"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute had been used."

One of the interesting threads here that is certainly relevant to the OpenAI writeup is the human role in the process. Buckmaster clearly points out that (exceptional!) mathematicians at OpenAI were certainly involved in correcting and guiding the process - and that their path/strategy was no doubt influenced by Alpoge & Buckmaster's work. It is always in OpenAI's interest to de-emphasize the role of people in the process, as is clearly the case here. Indeed, given sufficient compute and resources, I suspect Buckmaster could have also extended their approach to N-S.

It reminds me of the Cognitive Dark Forest hypotheses recently shared here:

> “You are creating your cool streaming platform in your bedroom. Nobody is stopping you, but if you succeed, if you get the signal out, if you are being noticed, the large platform with loads of cash can incorporate your specific innovations simply by throwing compute and capital at the problem. They can generate a variation of your innovation every few days, eventually they will be able to absorb your uniqueness. It’s just cash, and they have more of it than you. So the safest bet again is to stay silent, or at least under the radar. Best bet is to not disrupt - succeed at all … ?”

https://ryelang.org/blog/posts/cognitive-dark-forest/

https://news.ycombinator.com/item?id=47566442

They do mention that in the "Concurrent Work" section.

    Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.

To my understanding, those mathematicians proved a subset of problems, not the Navier-Stokes problem itself. OpenAI used that subproblem in its proof of NS it seems.

The drama comes from where OpenAI got the idea to use that route to tackle NS, since the authors maintain that no one could have plucked it out of thin air like the OpenAI research claim to have done.

[1] - https://cims.nyu.edu/%7Etristanb/statement.pdf

[1] - "...I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute had been used. I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI.

I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.

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.”..."

This Tristan guy's statement reads like something a normal, reasonable human being would write.

Reading Sam Altman's and Sebastien's tweets reads like something written by people who know they did dirty shit and are willing to cross any lines to "win". https://x.com/sama/status/2097385167002415140

OpenAI's leadership just can't help to continue to disappoint everyone with their lack of ethics or integrity.

> The significance of this with respect to the way we train students, assign credit, referee, and decide what is worth one human life’s attention cannot be understated.

This. What is worth a human life's attention? As little as a month ago, mathematics was valuable in part because only a small number of people could possibly make progress on the frontier. We are confronting an existential moment for a 4000+ year-old human cultural endeavor. The assumption that "mathematical thinking is hard" has been built-in at a number of important points in how we support mathematics and mathematicians.

We need a different model, and fast. Already, the research community is feeling unable to digest proofs fast enough to keep up with the output of AI models. The paper is 165 pages, and the discovery was finalized two days ago. What this means is that nobody really understands it. Nobody would accept OpenAI's proof in this amount of time, except that they formalized it in lean. The formalization alone would normally be another years-long (or career-long!) effort if the world was the way it was one year ago.

So, again, what efforts are worth a life's attention today? It's a harrowing change.

I just want to add to this another update by the author as well:

https://mastodon.social/@tristanbuckmaster/11723647135247030...

Which seems to be very directly accusing OpenAI of plagiarism

A company who made their business out of stealing intellectual property from the entire mankind, stealing other researchers' unpublished work, how surprising, really.

Statements from OpenAI about it:

https://x.com/SebastienBubeck/status/2097379411691516310

https://x.com/sama/status/2097385167002415140

I tend to believe OpenAI on this. Their stated desires seem rational, and Buckmaster's account makes them sound like cartoon villains. It sounds like there may have been some things lost in translation along with some bruised egos. Seems like the most plausible explanation for what Buckmaster is claiming.

"When a further trained version of our internal model became available over the course of the effort, we updated our agents to that model."

woah, this gives some credit to the rumor that openai finetuned a model over the course of a few days for this task, and maybe trained on the Chatgpt/codex history of the authors, including drafts of this research.

Worth noting that Tao's post says the authors had "significant AI input" but are reworking them into "acceptable form". Either way, it seems AI was involved.

> A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774

Glad to see this is the top comment. There's also https://news.ycombinator.com/item?id=49605915 which links directly. Corporate talking points where they try to set the narrative are going to get the big press and most discussion elsewhere, which is gross. But inevitably the press will muddle the priority question, and even if they didn't.. as usual OpenAI will even benefit from the accusation of bad behavior. Sigh.

I like the 'cat > statement.tex' approach here. These guys dream macros.