On the Navier–Stokes Millennium Prize Problem

I work at OpenAI, though not on the team that did this, and my understanding is:

- we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular individuals and we were looking at many problems beyond these)

- we did not read any private chats (but of course the model was aware of prior research literature published to the internet)

- the proof generated by our model was very different from theirs and also goes far beyond the published literature

- we made an effort to jointly announce rather than immediately scoop (I understand Tristan was unhappy with the conversations; I know zero details here and I hope more is shared today)

Edit: Here's is Sebastian's take: https://x.com/SebastienBubeck/status/2097379411691516310?s=2...

> We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).

Once again, I'm no closer to understanding what https://openai.com/policies/how-your-data-is-used-to-improve... actually means.

If I run Codex against a project that includes a private API key, is there a chance a future user of ChatGPT could ask for an API key and get back mine?

I've actually asked someone at OpenAI this question and they said that was the "regurgitation" problem and is something which they actively work to prevent happening.

That's reassuring, but I want to know more. I still don't have an intuitive understanding of what kind of data I should avoid sharing with a model if I'm worried about that data causing me problems when it's used for future training.

Is it safe for me to brainstorm future directions for my company with a model, or might that risk someone getting that information in response to a prompt like "What potential directions could company X consider in the future?" in six months time?

    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.