OpenAI Claims 'Internal AI Model' Just Cracked A $1 Million Math Mystery That Was Unresolved For 90 Years: Mathematicians Raise Fears

OpenAI said that an internal model 'significantly more capable than GPT-6 Astra' had produced a proof showing that the three-dimensional Navier-Stokes equations can develop a singularity in finite time, tackling one of mathematics' seven unsolved Millennium Prize Problems. This problem has allegedly remained unresolved for 90 years.

How the breakthrough came together

The company said its effort began on September 1, after researchers heard rumours that two of the Millennium Prize problems had already been solved and turned its newest internal model toward the remaining ones. OpenAI executives told reporters the project consumed enormous computing resources, costing in the millions of dollars and involving roughly 10,000 agents working in parallel. The company later clarified that the effort began after hearing a rumour that it eventually traced back to Levent Alpoge, an Anthropic employee, and Tristan Buckmaster, a mathematics professor at NYU. OpenAI says the proof has been verified using the programming language Lean, which effectively guarantees its correctness.

A rival claim surfaces first

The night before OpenAI's announcement, Buckmaster had posted that he and Alpoge had proved a related result, that the frictionless Euler equations can 'blow up', building on an approach pioneered by mathematicians Diego Cordoba and Luis Martinez-Zoroa. Buckmaster later said he and Alpoge had spent close to a year making slow progress on the problem before accelerating rapidly from mid-August using several AI models from both companies.

Allegations of data access and pressure tactics

Buckmaster publicly questioned whether OpenAI had pursued a research direction it learned about from his and Alpoge's work, and raised concerns about whether private material from OpenAI's Codex tool could have played a role. According to his account, he asked OpenAI directly whether its model had been trained on or had accessed the Codex sessions where he and Alpoge had stored their drafts, and says he did not receive a clear answer on the training question.

He further alleged that OpenAI researcher Sebastien Bubeck pushed to have Alpoge removed from authorship of any joint paper because of his employment at Anthropic, OpenAI's biggest competitor. Buckmaster said that when he threatened to make the exchange public, Bubeck responded by asking why he would want to 'ruin your career'.

OpenAI's response

OpenAI said it did not access Buckmaster or Alpoge's specific user data while pursuing the proof. Bubeck denied the allegations in a post on social media, calling them false and inflammatory, and said in a press briefing that he had approached the discussion following standard academic norms while emphasising that OpenAI recognised the priority of Buckmaster and Alpoge's earlier work. OpenAI has said it reached out to the pair after completing its own proof and Lean verification, offering a concurrent release and recognition of their priority in a joint announcement.

Tao warns of a chilling effect on mathematics

Fields Medalist Terence Tao, widely regarded as one of the world's leading mathematicians, raised broader concerns about AI labs using long-standing open problems as demonstrations of their models' capabilities. He said he had hoped AI would serve mathematicians the way a microscope serves biologists, but worried it was increasingly being used to produce answers without the accompanying insight into why a particular approach worked - insight he says often matters more to the field's progress than the answer itself. He also argued that AI companies rarely disclose the failed approaches their models tried, even though such dead ends often seed future breakthroughs, and warned that treating open problems purely as targets to be 'solved' could erode incentives for mathematicians to share unfinished work.

Published on: Wednesday, September 09, 2026, 09:36 AM IST