OpenAI Navier-Stokes Claim Sparks AI Ethics Controversy in Math

The interviewee, a mathematician, discusses the recent controversy surrounding the Navier-Stokes problem, a Millennium Prize Problem, and its alleged solution by OpenAI. He shares his personal experience, the impact on the mathematical community, and his perspective on the role of AI in scientific discovery.

Personal Impact and Initial Reactions

The mathematician admits to feeling "better than a few weeks ago" but notes that the situation "hasn't sort of calmed down." He recounts the intense period following the events, where he averaged only two hours of sleep per night, often falling asleep at his desk due to exhaustion. He describes the experience as feeling "mugged" or a "victim" of something "silly."

He was aware of the "move fast, break things" philosophy prevalent in the tech industry, having previously collaborated with Google DeepMind. He believes this philosophy clashes with the methodical nature of mathematics. He suggests that the situation could have been avoided if OpenAI had allowed his team to release their results first before launching their own solution.

The Navier-Stokes Problem: A North Star

The Navier-Stokes problem was never a direct goal for him to solve, but rather a "north star" throughout his career. He explains that in science and mathematics, researchers often work on smaller, related problems that contribute to the eventual solution of larger, seemingly unreachable problems. He had been working on singularities for six or seven years, with Navier-Stokes as a guiding principle, aiming to be "part of the story" of its solution.

Success with Euler Equations and the Path to Navier-Stokes

His team achieved success with the Euler equations, which he considers the "main mechanism" of Navier-Stokes, differing primarily by the presence of viscosity in the latter. He views viscosity as an "annoyance" that makes the problem harder, but the core mechanism remains the Euler equations. Solving Euler required a stronger singularity to overcome this internal friction.

After solving Euler, they progressed to "hyper-dissipative Navier-Stokes," where viscosity is reintroduced but weakened. This success provided a clear path forward to solving the full Navier-Stokes problem, potentially within a month.

The Role of AI in His Work

The mathematician emphasizes that he is not anti-AI and actively uses it in his research. He clarifies that his collaboration with Levent, who built an "agentic system" to mimic mathematical processes, was crucial. He refutes the notion that AI simply provides solutions at the push of a button, highlighting the complex system and extensive work involved.

The Leak and the Rumor Mill

He confirms that there was a leak from Anthropic, where Levent works, regarding their progress with the Euler equations. This rumor spread through the tech industry, leading to speculation that Anthropic had solved two Millennium Prize Problems, including Navier-Stokes and the Hodge conjecture. While the rumor was inaccurate in claiming a full Navier-Stokes solution, it stemmed directly from their work on Euler.

OpenAI's Intervention and the "Stupid Thing"

As the rumors intensified, he contacted a mathematician at OpenAI to "calm things down," emphasizing their use of OpenAI products. He aimed to frame the narrative as a collaborative achievement in AI-guided mathematics, rather than a competition between Anthropic and OpenAI.

He received a message from the OpenAI mathematician warning that "OpenAI were about to do something really stupid." He interpreted this as an impending unethical action, not merely a wild or crazy move. He believes OpenAI intended to release their solution before his team.

The Call with OpenAI and the "Lie"

During the call, OpenAI announced they had solved Navier-Stokes. The first question he asked was about the specific version solved, not out of curiosity, but to ascertain if they had used his team's methods. He noted that they had solved the "forced one," which was a "red flag" for him.

He suspected OpenAI might have accessed their methods, possibly through the use of Codex, an OpenAI product. He recounts how OpenAI presented a prompt, claiming they simply copied the Millennium Prize problem and pressed enter to get a solution. He immediately recognized this as a "ridiculous" lie, which quickly unraveled. He also noted their evasiveness about when they started working on the problem, eventually admitting they began after the rumor.

Circumstantial Evidence of Method Appropriation

He points to circumstantial evidence suggesting OpenAI used his team's unpublished work. He argues that the correct comparison paper for OpenAI's work is not their Navier-Stokes solution, but rather the "unforced Euler equation," which shares identical mechanisms with a version of Euler his team had not yet released. He states that the architectural ingredients for this unforced Euler solution were present in his team's work and would have been on OpenAI's servers.

He also highlights OpenAI's admission of their agents hacking a competitor's GitHub repository to solve a math problem, suggesting a precedent for accessing others' work. He notes that OpenAI used 10,000 agents for Navier-Stokes but only 100 for the Euler problem, yet still arrived at an "identical architecture" to his team's.

Regrets and Secrecy

He admits to making "many mistakes," including the leak that initiated the controversy and his use of Codex. He acknowledges that he "didn't think that they would go this far." While his team believed they were being secretive, the leak, likely due to "people bragging," undermined their efforts.

The Rivalry and Its Impact

He clarifies that his concern is not about receiving more credit, but about the "culture of how these companies are acting" and its negative impact on the mathematical community. He attributes the situation to the "ultra-competitiveness" between labs, noting that other companies also began investing heavily in solving Navier-Stokes after the rumor.

He argues that the "move fast, break culture" is on a "head-on collision with the math community" and will eventually affect everyone. He believes that while OpenAI's solution advanced the field, the negative consequences outweigh the benefits. He states that if OpenAI had released their solution a few days later, the world would not have changed, but the current situation has led to:

• Mathematicians being hesitant to discuss open problems.
• Fear of AI companies "scooping" their work.
• Distrust of AI products within academia.
• A slowdown in scientific progress due to the perceived threat from AI labs.

He acknowledges that OpenAI's urgency was driven by a perceived threat to their "bottom line" and their belief that Anthropic solving a Millennium Prize Problem would negatively impact their IPO. He dismisses this rationale, stating that the solution isn't solely about internal models but also about the strategic use of multiple agents.

Principled Stand and Ethical Dilemmas

He recounts being offered the opportunity to be the sole author of OpenAI's paper, effectively "throwing my collaborator under the bus" because he worked for Anthropic. He refused, deeming it "so unethical."

The Key Idea in OpenAI's Solution

While he hasn't fully digested OpenAI's proof, he identifies a "smart idea" that bridges the gap from Euler to Navier-Stokes, which he believes is not widely discussed. He explains that the commonly cited "collapsing vortex" is not a solution to Navier-Stokes with forcing, as it implies infinite energy.

The true innovation, he suggests, lies in combining "convex integration," a concept he has specialized in, with the "growth mechanism" of the Euler blowup. This combination creates a new mechanism to correct non-solutions without infinite force. He notes that OpenAI's paper did cite his work on convex integration, providing an early hint.

AI and the Future of Mathematics

He acknowledges the petition signed by Fields medalists expressing concerns about AI in mathematics. As an extensive AI user, he believes we are in a "new world" and need to find a "positive way forward that does incorporate AI." He draws an analogy to chess, where human players are still valued, but notes that mathematics is not a "performative science" in the same way.

He recognizes the "flying too close to the sun" aspect of his experience. He plans to dedicate his time to explaining his team's methods and how they solved these problems, rather than secretly using their techniques for more publications.

The Core Grievance

He clarifies that his main issue with OpenAI's actions is not merely the speed of their publication, but the perceived unethical use of his team's work. He states that if a human team in Japan had been close to a solution, he would not have used resources they lacked to "front-run" them, deeming it "inappropriate." He believes that OpenAI accessing his work through Codex, which he used in good faith, feels like having his "pocket picked." He concludes by stating that this incident will certainly change how he uses Codex, ensuring "nothing important goes into Codex."