Notably, the NYU professors have made a statement. It has a few notable facts which do not reflect well on OpenAI They were not willing to give a direct answer as to whether or not their user...
Notably, the NYU professors have made a statement. It has a few notable facts which do not reflect well on OpenAI
They were not willing to give a direct answer as to whether or not their user prompts were used for training in the model.
They wanted Levent removed from the NYU paper, seemingly for the sole reason that Levent works at Anthropic.
They threatened Tristan with “ruining his career” if he didn’t give in to one of 2 options they proposed for him.
I think it’s fully possible that their user prompts had little realistic influence in the model, however the threats and random personal attack on one of the coauthors seemingly for just being associated with Anthropic look pretty childish regardless.
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).
This seems promising! It's always been unclear which problems in the world are "difficult" and which are "difficult for humans", so it's good to see empirical evidence of that here. It's...
This seems promising! It's always been unclear which problems in the world are "difficult" and which are "difficult for humans", so it's good to see empirical evidence of that here. It's unfortunate that many of our present day problems are caused by poor governance and resource allocation, rather than mathematics, so this doesn't seem like it necessarily helps a tonne. Still neat though!
Our system produced an analytical proof and a Lean formalization that an initially smooth fluid at rest can develop a singularity in a finite time. The fluid has a smooth force applied to it, and its energy remains finite through the entire dynamics, from rest to the formation of the singularity. This resolves the Navier–Stokes Millennium Prize problem by establishing statement “C” (and also “D”) in the official Millennium Prize formulation.
The solution is a vortex, a spinning swirl of fluid, that spirals inward and gets increasingly elongated, like spaghetti. This central region shrinks while it speeds up in such a way that its energy still stays finite, as required by the laws of physics. The technical challenge is for the equations to develop the breakdown through the motion of the fluid itself, rather than, for example, us putting in an infinite force by hand. More mathematically, the terms in the Navier–Stokes equations that describe the motion—acceleration, pressure gradients, momentum transfer, viscosity—must both become big yet cancel in a precise way. This detailed balance leaves a smooth external force even as the velocity of the fluid grows without bound.
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Since August 28 we have been training a new internal model that has exhibited unprecedented performance in our benchmarks, including mathematics. This model’s training is ongoing and its performance continues to improve.
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On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems.
We used a system of coordinating agents powered by our internal model. The agents had access to tools such as the ability to read from a cached version of the internet and the ability to run code. Agents were subdivided into groups with the ability to communicate within the group. The groups varied in size, and the group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents. At all times we maintained the same strict safeguards that we apply to all our frontier model evaluations, including monitoring and isolation.
For each problem, we prompted different groups of agents with different variants of the problem statement, covering all variants of the problem. For the Navier–Stokes problem, we suggested versions “A” and “B” (particular forms of the Navier–Stokes problem which would result in a proof) and versions “C” and “D” (which would result in a disproof) to separate groups of agents.
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The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched. Lean formalization and verification took an additional 17 hours via GPT‑6 Astra.
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.
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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.
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Our goal in releasing this result is to report on the substantial progress of our AI models. We do not intend to claim the Millennium Prize for this result.
Notably, the NYU professors have made a statement. It has a few notable facts which do not reflect well on OpenAI
They were not willing to give a direct answer as to whether or not their user prompts were used for training in the model.
They wanted Levent removed from the NYU paper, seemingly for the sole reason that Levent works at Anthropic.
They threatened Tristan with “ruining his career” if he didn’t give in to one of 2 options they proposed for him.
I think it’s fully possible that their user prompts had little realistic influence in the model, however the threats and random personal attack on one of the coauthors seemingly for just being associated with Anthropic look pretty childish regardless.
Yea, it’s a mess…
Here is an update from the OpenAI researcher.
They did write this in the blog post:
This seems promising! It's always been unclear which problems in the world are "difficult" and which are "difficult for humans", so it's good to see empirical evidence of that here. It's unfortunate that many of our present day problems are caused by poor governance and resource allocation, rather than mathematics, so this doesn't seem like it necessarily helps a tonne. Still neat though!
From the article:
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