OpenAI is turning math into a pay-to-win game
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Last week, OpenAI announced a solution to one of the biggest open questions in mathematics. Hours earlier, a mathematician posted a result on a closely related problem — along with a statement implying that OpenAI may have based its solution on his work and may have tried to minimize the contributions of a colleague employed at Anthropic.
If the solution is confirmed, this is a big deal. And even if there ends up being a flaw in the proof, it's still a big deal. The implications go beyond any one math problem, and even beyond math. If you care about scholarship in the year 2026, it is worth understanding what happened and a few things it could mean.
The Navier-Stokes equations describe how fluids flow. These equations are pretty simple on the surface, but very hard to solve. The Navier-Stokes problem asks whether there are conditions under which these equations produce physically impossible behavior — "singularities" where an infinitely small patch of fluid flows infinitely fast. Last week, OpenAI claimed to have resolved the question by finding a solution to the Navier-Stokes equations that produces a singularity.
(Note: this doesn't mean physics is broken; the equations make some unrealistic assumptions, like assuming fluids are perfectly smooth rather than made of particles).
The Navier-Stokes problem is, quite literally, a million-dollar question. It is one of six remaining Millennium Prize Problems — major unsolved problems in mathematics attached to a $1 million prize. The Clay Mathematics Institute, which posed the problems and awards the prizes, describes them as historical achievements: "These are not arbitrary puzzles akin to fiendish crosswords. Rather, they are fundamental challenges that mark the frontier of human knowledge."
OpenAI burned millions of dollars to solve this fundamental challenge at the frontier of human knowledge in 88 hours, just under 4 days.
It began on August 28. OpenAI started training an internal model and realized it was outperforming its Astra LLM on math benchmarks. Then, on September 1, OpenAI heard rumors that mathematicians had made progress on "two Millennium Prize Problems" and started using their new internal model to try to solve all of them. They used teams of thousands of "agents" — programs that can autonomously perform tasks and operate other programs — powered by their new model. After 100 agents working for about 50 hours found a solution to a simplified variant of the Navier-Stokes problem, OpenAI decided to go all-in on Navier-Stokes and dedicate most of its resources there.
A team of about 10,000 agents working over 88 hours found a solution on September 5. It was announced on September 8 in a statement accompanied by a 166-page paper and a formal proof in the programming language Lean. The Lean proof shows that OpenAI's work is correct. But that doesn't mean that what OpenAI has shown is perfectly equivalent to the Navier-Stokes problem. The Clay Mathematics Institute is still evaluating whether or not the problem as originally formulated has truly been solved.
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