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Navier-Stokes – Tristan Buckmaster [pdf]

cims.nyu.edu

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Re: Navier-Stokes – Tristan Buckmaster [pdf]

#51

lol and here I felt GPT Astra was a regression in coding quality. Crazy times

To be clear, Astra played little part in Buckmaster and Alpoge's work:

> We used several LLMs throughout: Anthropic’s Claude, OpenAI’s Codex, especially with GPT-5.6 Sol and, more recently, Astra. The latter was only used for writeups and auditing our arguments.

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#52
Can a mathematical person explain how the different "bits" of Navier-Stokes proofs fit together? How significant is it to have "Euler"? What is this "smooth forcing"? Which are the most significant steps to proving the whole thing?

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#54
post #36

"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." The money in nerdy frontier math is very little. The money in Big AI is very very much. So the deal is this: We will pay an army of you guys very well and you will get to work on your favorite problems. The o…

Yes, and this puts in check the credibility of everything they say their model "discovered". Who knows what is really behind these "discoveries", what kind of backroom deals they did with other researchers who didn't have a chance or desire to disclose what happened?

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#55

I'm not one to comment often but this really pisses me off. OpenAI looked at user data, stole world class researchers' work, and then tried to threaten those researchers to do what would make their corporation profit (which they would anyways!). Imagine you have been working on a terribly difficult math problem for a decade. This is a result you have spent years on, and what you will likely be remembered for. And to…

LLMs do nothing but steal, and the companies that own them are fully aware and eager to do it.

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#56
post #2

Full mastodon post: https://mathstodon.xyz/@tristanbuckmaster@mastodon.social/11... Mathematical explanation by Terrance Tao: https://mathstodon.xyz/@tao/117233527638291447 It seems there is much background drama behind this, and this is what I've pieced together of what happened: Over the past year, Buckmaster and Alpöge have been using AI to work on fluid dynamics maths problems. Alpöge works at Anthropic, which wi…

> A few days later, OpenAI gets back to him, and tells him an internal model found a counterexample for Navier–Stokes

Why is OpenAI chatting with him at all at this stage? Is the discussion along the lines of "hey we used the work you are famous for to do a bigger piece of work, just thought you should know" or "heyyy....so we kinda liked what you were typing in your private chat, and thought we'd develop those ideas a bit. and yeah we solved Navier-Stokes in the process. But it's our finding, so do you want like an honorary acknowledgement or do you want to go to court?"

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#57
So, leaving aside the idea that OA might've used data from the researchers Codex sessions: Do I understand correctly that the internal OpenAI work on the problems was probably started after they heard Alpoge and Buckmaster had made process by using their models? And they used the publicly available info about the researchers past work to prompt their models?

If compute is cheap, and the difficult thing with scientific discovery is now mostly in steering agents into promising areas, there's an obvious incentive for OA mathematicians to simply monitor closely which researchers are close to releasing exciting results, make some assumptions about their prompts based on their past work, and quickly prompt their own (stronger) model to look into the same areas.

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#58

I'm not one to comment often but this really pisses me off. OpenAI looked at user data, stole world class researchers' work, and then tried to threaten those researchers to do what would make their corporation profit (which they would anyways!). Imagine you have been working on a terribly difficult math problem for a decade. This is a result you have spent years on, and what you will likely be remembered for. And to…

I'm stunned that people are taking this accusation as a fact. OpenAI is no stranger to rivalry with Anthropic but 1. it's not like user data is sitting around on some kitchen table somewhere and 2. I consider OpenAI to be as economically motivated as any other actor in this space and playing around with user data like that would destroy their business. There are things that Buckmaster alleged and things that he specu…

They stole it.

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#59
The accused Sebastian Bubeck has denied the allegations on Twitter[0], and various other OpenAI employees[1,2] seem to be mocking another Anthropic employee voicing support for Levent[3]? Things are getting messy.

[0] https://xcancel.com/SebastienBubeck/status/20972141224714323...

[1] https://xcancel.com/polynoamial/status/2097215233119211902

[2] https://xcancel.com/danintheory/status/2097214838003138603

[3] https://xcancel.com/_sholtodouglas/status/209721833169057800...

Re: Navier-Stokes – Tristan Buckmaster [pdf]

#60
post #46

Earlier quoted context omitted.

I'm stunned that people are taking this accusation as a fact. OpenAI is no stranger to rivalry with Anthropic but 1. it's not like user data is sitting around on some kitchen table somewhere and 2. I consider OpenAI to be as economically motivated as any other actor in this space and playing around with user data like that would destroy their business. There are things that Buckmaster alleged and things that he specu…

He didn't even make that accusation! > 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. The shocking/interesting thing would be if it was trained on the sessions. I think it's very implausible tha…

It wouldn't be shocking at all. They stole human data to train the first models and they've been stealing it ever since to train new models. Stealing mathematicians private chats and private research and taking credit for it would absolutely be par for the course.

Enterprises are well aware of it and are fully on board. You didn't think every corporation in America has an OpenAI subscription because the models were good, did you?

The whole reason they have subs is to train them on YOUR WORKFLOWS lol

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