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Dan Roberts
@danintheory
Scientist @OpenAI. Prev. co-founder @diffeo, acquired by @salesforce // co-authored The Principles of Deep Learning Theory // studied gravity.
796 Following    8.1K Followers
We recognize that the rapid progress of AI in mathematics is disruptive. We're looking to engage with the math community more on the best way to integrate this technology and communicate its impacts. After considering concerns raised by members of the mathematics community, we’ve decided to withdraw OpenAI’s sponsorship of the Caltech Mathathon and have notified the organizers.
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> The best model is no longer the unethical one.
While a resolution to Navier-Stokes is the highlight of today, this plot is really the headline result to me. Our ongoing training run demonstrates unprecedented performance on mathematics research, as measured by our model's estimated performance on a collection of **open** math problems. Of course, to settle Navier-Stokes, we took this model and also scaled test-time compute allll the way up.
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If you are not a mathematician, you might not care that some differential equations have a singularity. But if you are a resident of planet earth you should care that (1) an AI was able to solve a Millenium problem, and (2) that there is plenty of headroom for models to move up and to the right on this and any other task.
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Two things to distinguish: Did any human or agent look at user data as part of the Navier Stokes effort? No. Do we use user feedback and de-identified data to improve ChatGPT and Codex in a holistic way? Yes. And so does every LLM company.
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Clarifications from Seb. He reached out to Alpöge and Buckmuster under the (mistaken) belief that they have also solved the Navier-Stokes problem, in order to coordinate publication and to avoid scooping them. It turned out they proved a restricted result (forced Euler problem; the internal model proved the stronger unforced version along the way). This does not diminish their great achievement. I believe that no human mathematician can match 10,000 agents of this internal model, let alone future models that will come soon.
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This interpretation appears to be correct and Seb deserves grace. The mob was wrong.
@__alpoge__ nothing at all was locked we were just willing to talk but you didn't talk to us ... sorry but that's just untrue, we were willing to go above and beyond and have as many discussions as you would have liked to reach resolution.
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This is a cool plot too!
We've never seen this before. The biggest jump in Vending-Bench history. GPT-6 Astra is better at making money and more ethical than Claude Fable 5.1. Surprising, because: 1. First time ever that OpenAI is #1# on Vending-Bench 2. The best model is no longer the unethical one.
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Very sad to see Levent double down on the plagiarism accusation. I hope my friends at @AnthropicAI stand up to this internally. It should be clear by now what the truth is.
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It should be obvious to anyone with common sense that there is no plagiarism here. The primary question we set out to answer is how good is our model!
I spent much of the weekend talking with the team who did this work. Seb--and everyone else--acted with integrity and generosity throughout. Initially we believed the other team had also solved the problem. We wanted to collaborate and do a joint release. When we learned that they had Euler but not Navier-Stokes, we offered to let them go first, to suggest that they should be the ones to get the prize, and optionally for Tristan to be the lead author on a rewrite of the OpenAI proof. We felt it was challenging to offer the same to Levent (an Anthropic employee), who was not willing to talk or coordinate with us anyway. We were open to other solutions. We would have greatly preferred coordination. We did not rush to publish even though the other team wasn't communicating with us. The team threatened us with unfounded accusations of plagarism. Now that we can see their work, the approaches appear to be different. It is also worth noting that our latest model can solve many, many other math problems. It is true that we tried this because there were rumors on the internet last week that Anthropic's models had solved a millennium problem and we were curious if ours could do it too.
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We congratulate Levent Alpöge and Tristan Buckmaster on their remarkable mathematical work. 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).
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Seb is of the highest integrity. I know it’s hard to believe unless you viscerally experience it in action, but our AI system is really just that good at math.
I would like to clarify a few things: 1) The screenshot is my reaching out to Levent to coordinate our releases. I hope it’s clear from the message that we came in with the best possible intentions. 2) I never ever asked for Levent to be removed from authorship of his own work (as indicated by my text). I was surprised to learn during the call with Tristan that they had only solved Euler and not Navier-Stokes; after learning this we brainstormed possible paths forward. One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Importantly it was admitted that internal Anthropic models had been used in their proof of Euler blowup; I therefore felt I could not consider Levent to be an independent academic. Another option I wanted to propose (but got cut short) is to offer access to our internal model so that they could try to finish their proof and bridge the gap between Euler and NS. Again I did not know how to navigate giving access to internal OpenAI IP to an Anthropic employee. 3) To reiterate it plainly: as my text clearly indicates, and as I said during our call, OpenAI's intention was to do everything possible to celebrate their mathematical achievements and the heroic efforts that they made on Euler. In the call I was immediately met with a litany of slander, including direct threats that if we were to announce Navier-Stokes he would immediately go to the press with a barrage of unfounded accusations. I refuted all these accusations but he replied “there is nothing you can do, I simply do not trust you”. I was confused why one would turn an incredible source for celebration (of their achievements!) into such bickering, which is when I said that I did not understand why one would risk their career [over unfounded accusations]. Genuinely, at that moment, I was trying to care for him and do a last ditch attempt to get a chance to give them all the credits that they deserve. I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey. (I should say that I retracted them on the spot by the way.) 4) Overall, on a personal level, it was incredibly difficult to have these conversations. Levent refused to attend any of the meetings despite my repeated asking. As Sholto Douglas said, there will need to be coordination between Anthropic and OpenAI in the future; I felt I was doing a proxy negotiation with Anthropic while the Anthropic employee refused to directly participate.
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One of the most amazing moments for me in OpenAI history was watching this happen over the past week:
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“To solve the Navier-Stokes problem, we used an internal model that is significantly more capable than GPT-6 Astra.”
I think the traditional thing I should say here is that this collaboration was an honor & highlight of my career — & it absolutely was(!) — but even so, I think focus here should be on the figure in the this tweet and hope that it completely ratios the one above it.
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We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics. The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra. The problem concerns whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years.
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It can be hard to “feel the AGI” until you see an AI surpass you in a domain you care deeply about. This week, many mathematicians and physicists at @OpenAI had their Lee Sedol moment seeing this model solve, in minutes, open problems they’d struggled with for years.
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Yes, this result cost millions of dollars. But remember that when @OpenAI announced o3 it cost ~$500,000 to score 87.5% on ARC-AGI 1. Today, Astra scores higher for ~$20. In 2025 it took us and GDM an enormous amount of compute to achieve IMO gold. For the 2026 IMO, anyone with a $20/month ChatGPT subscription could do it. Massively scaling test-time compute gives us a glimpse of the future. I believe that a year from now everyone will have an AI at their fingertips capable of solving problems of this caliber.
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seb is a really sweet guy with great intentions, am so happy for him that his week long collaboration with myself and others worked out, but very sad that we didn't get to finish it in the way we wanted
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