OpenAI’s maths breakthrough claim has become a fight over credit and trust

OpenAI’s claim that an artificial intelligence system solved a famous mathematics problem has triggered a wider dispute over credit, research data and corporate power. The claimed result has not completed independent mathematical review.

The immediate argument involves New York University professor Tristan Buckmaster, mathematician Levent Alpöge, who works at Anthropic, and OpenAI researcher Sébastien Bubeck. Their accounts of private conversations differ.

The dispute widened on Friday when 25 Fields medallists signed a declaration warning that competition among AI companies could damage mathematics. The signatories included Manjul Bhargava, Terence Tao and Maryna Viazovska.

What did OpenAI claim?

OpenAI said on September 8 that an internal system had solved the Navier Stokes existence and smoothness problem. The equations describe how fluids move.

The problem asks whether smooth three dimensional fluid motion can develop a singularity, where velocity grows without bound in finite time. It is one of seven Millennium Prize Problems.

OpenAI said its system established that such a breakdown can occur when a smooth external force is applied. The company released a written proof and a formal version in Lean.

The company said roughly 10,000 concurrent agents exchanged 2.7 million messages and produced about 130 billion output tokens. It said they reached the result in 88 hours.

OpenAI said it began the effort on September 1 after hearing rumours that two Millennium Prize problems had been resolved. It tested several problems using a new internal model.

OpenAI said its proof has not completed the established process of independent mathematical review. The company also said it does not intend to claim the one million dollar prize.

How did the dispute begin?

Buckmaster said he and Alpöge had worked privately for about a year, using Claude, Codex and other models. Their collaboration was not officially backed by either employer.

They built on research by Diego Córdoba and Luis Martínez Zoroa into fluid breakdown caused by external forcing. Buckmaster said they obtained key Euler and Boussinesq results on August 15.

He said the first AI generated proof was formally verified in Lean on August 22. The pair then tried to turn difficult machine generated arguments into readable papers.

On September 3, Buckmaster contacted an OpenAI mathematician after hearing that information about their progress had reached the company. OpenAI asked for details and offered computing resources.

OpenAI says its agents had already started work on September 1 and reached their Navier Stokes result on September 5. Buckmaster spoke with OpenAI researchers the following day.

Buckmaster alleges Bubeck twice proposed excluding Alpöge from authorship of a possible paper because he worked at Anthropic. He also says Bubeck asked why he would ruin his career by going public.

Bubeck denies trying to remove Alpöge’s credit for his own work. He says Alpöge’s employment complicated any authorship on OpenAI’s separate proof.

Bubeck apologised for the career remark, calling it an extremely poor choice of words. Sam Altman said Bubeck and the OpenAI team had acted with integrity and generosity.

These statements provide competing accounts of private calls and messages. No independent inquiry cited by the parties has publicly resolved that disagreement.

Did OpenAI use the academics’ work?

Buckmaster said the pair had placed drafts and arguments into Codex throughout their project. He questioned whether that material could have influenced OpenAI’s model, but stopped short of making an accusation.

OpenAI says its researchers and agents did not see the pair’s work before publication. It also says an investigation found their previous two months of Codex prompts could not have influenced the system.

The materials behind that investigation and the full agent logs have not been made public. The question therefore depends partly on OpenAI’s account.

There is also a technical distinction. Buckmaster and Alpöge announced a forced Euler result, while OpenAI says its system separately proved unforced Euler and forced Navier Stokes results.

Why are mathematicians worried?

The new Math and AI declaration says AI may accelerate genuine mathematical understanding. Its complaint is that corporate races reward fast announcements rather than readable arguments, attribution and careful review.

A formally checked proof is significant, but it does not settle every scientific question. Mathematicians must assess whether the encoded statement matches the intended theorem and understand the ideas behind it.

The dispute also shows a sharp resource imbalance. OpenAI could deploy thousands of agents after hearing a rumour, while academics were still converting machine output into a paper humans could read.

Researchers may become less willing to share early ideas or use proprietary tools if they fear being overtaken. That could weaken the open exchange on which mathematical research depends.

The declaration follows the Leiden Declaration, published in June and endorsed by the International Mathematical Union. It called for disclosure, human responsibility, proper attribution, open science and independent review.

OpenAI withdrew sponsorship from a Caltech mathematics event on Thursday after researchers criticised the company, TechCrunch reported. The withdrawal showed that the conflict had moved beyond one proof and three researchers.

The central issue is now larger than who reached one result first. It concerns who controls research tools, who receives credit, and whether machine checked answers produce knowledge people can understand.

(With inputs from PTI)