OpenAI says an AI-driven mathematics project like the Navier-Stokes proof effort it just completed could cost roughly $100,000 to run next year, down from approximately $10 million for the initial attempt. If the forecast holds, that would represent a decline of about 99% in a single year.

The projection came as the company continued to face questions from mathematicians over research priority and who deserves credit for the result.

What OpenAI says it did

On September 8, 2026, OpenAI announced results from an internal AI system that reportedly outperformed GPT-6 Astra, the company's flagship model. According to OpenAI, the system produced an analytical proof addressing the Navier-Stokes existence and smoothness problem, one of the best-known open questions in mathematics. It also produced a formalization of that proof in Lean, a software tool that checks mathematical proofs step by step.

The Navier-Stokes problem is one of the Millennium Prize Problems established by the Clay Mathematics Institute in 2000. It concerns the equations that describe how incompressible fluids move in three dimensions. OpenAI's result points to breakdown: according to the company, the equations can develop finite-time singularities starting from smooth initial conditions, while the total energy stays finite. A confirmed singularity of that kind would mean the equations cease to yield a smooth description of the flow beyond a certain point, which is why the smoothness question has long stood as a benchmark for the limits of these equations.

The compute bill

The effort did not come from a single chatbot session. OpenAI used a dynamic network of approximately 10,000 coordinated AI agents. Those agents worked for about 88 hours on the proof itself, and another 17 hours went to verifying the Lean formalization.

Estimates put the compute cost of the project between $10 million and $15 million, with OpenAI's own framing referencing roughly $10 million.

The company expects a similar project to cost around $100,000 next year. It attributes that projected decline to anticipated gains in AI efficiency. The word anticipated carries weight: the $100,000 figure is a forecast, not an invoice.

Leaving the prize money on the table

The Clay Mathematics Institute attaches a $1 million prize to the Navier-Stokes problem. OpenAI has said it will not pursue the award. Against a compute bill of $10 million or more, the prize would barely cover the electricity.

The Navier-Stokes problem is one of seven Millennium Prize Problems, each carrying the same $1 million award. In the quarter-century since they were announced, only one has been resolved: the Poincaré conjecture, proved by Grigori Perelman, who also declined the prize.

The credit question

The announcement has sparked a heated debate among mathematicians over research priority and how credit should be assigned. Some prominent figures have raised concerns that the proof may have drawn on unpublished methods or insights. As of mid-to-late October 2026, that discussion was still ongoing, and researchers continue to scrutinize OpenAI's claims and the mathematical approach behind them.

The Lean formalization helps on one front. A machine-checked proof is harder to dispute on correctness grounds than a long paper reviewed by a handful of experts. Precedent points the same way: the Kepler conjecture on sphere packing gained full confirmation only after a multi-year formal verification project checked it line by line. But correctness and credit are separate questions. Lean can confirm that each logical step holds; it cannot determine whose idea the key step was.

What this means

The most consequential number in the announcement may not be $10 million. It is $100,000. At $10 million, a run like this is a one-off demonstration that only a handful of well-funded labs could attempt. At $100,000, it starts to resemble a research budget line that a university department or a mid-sized company could plausibly justify.

Three questions stand out from here: whether independent experts endorse the result, how the Clay Mathematics Institute responds given OpenAI's refusal of the prize, and whether next year's runs actually land anywhere near the $100,000 mark.

Source: CryptoBriefing (edited by Diego Almada Lopez), October 29, 2026 — OpenAI says its $10 million Navier-Stokes proof could cost $100,000 next year