One of the mathematicians who came close to solving the Navier–Stokes problem publicly questioned the confidentiality of OpenAI products.
New York University’s Tristan Buckmaster said all working drafts of his research were stored in Codex sessions, and now the lab is reporting its own breakthrough on the same problem.
The Navier–Stokes problem is one of the Clay Mathematics Institute’s Millennium Problems, each of which has a $1 million prize for solving it. The equations themselves were written down back in 1822 and describe the movement of any fluid, from water and air to smoke, honey and oil.
These equations are used in everything from weather forecasting to airplane design, but mathematicians have yet to prove that the underlying mathematics works correctly in all scenarios. Because of turbulence in hydrodynamics, the basic question remains open whether the solution always remains smooth and physically meaningful, or at some point it breaks down and produces infinity.
Buckmaster, together with Levent Alpöge, formerly associated with Anthropic, published results on the so-called related equations. We are talking about proving sharpening in a finite time under a smooth external force for several systems:
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incompressible flow in a porous medium
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Boussinesq equations
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three-dimensional incompressible Euler equations
UCLA mathematics professor Terence Tao reacted to the work of colleagues:
A remarkable achievement, Alpöge and Buckmaster were able to develop one of the major promising approaches to the construction of blow-up solutions for the fluid dynamics equations, developed by Cordoba and Martinez-Zoroa, and establish finite-time blow-up for many key fluid equations…
Then the conflict part of the story begins. According to Buckmaster, he was contacted by OpenAI and told that their model may have solved the Navier-Stokes problem. The mathematician described this conversation in a recording in Mastodon.
I asked if the model had been trained in or had access to our Codex sessions, since that’s where we put all our drafts throughout this research. I was told that the model did not access user data. I asked again, this time about training, and received no answer.
In the discussion under the post, there were also harsher assessments from other users.
I have little doubt that they had access. These companies have no principles. You may not want to hear this, but this is the price of selling your soul to the devil. The devil will force you to fulfill the terms of the deal.
Formally, OpenAI claims that the model did not look at user data. At the same time, the laboratory has not yet separately explained whether these drafts were included in the training set, and this is precisely the question that remained unanswered.
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The situation arises as OpenAI prepares to go public, when high-profile scientific results act as an argument in favor of capitalization.
Codex users who upload proprietary research or commercial materials should consider this issue when choosing tools for working with sensitive data.
