OpenAI hints at second Millennium Prize math breakthrough

Less than two weeks after claiming to have solved the Navier-Stokes existence and smoothness problem, OpenAI has suggested it may be close to cracking another of mathematics' seven Millennium Prize Problems, with speculation centering on the Hodge Conjecture. The move comes as the company faces an organized backlash from the mathematics community, including a letter signed by 25 Fields Medal recipients warning of a "severe misalignment" between AI companies and the discipline they are reshaping.

The Navier-Stokes Fallout

On September 8, OpenAI announced that roughly 10,000 coordinated AI agents, powered by an unreleased internal model, had produced a 166-page proof and a Lean formalization showing that the Navier-Stokes equations can "blow up" — yielding infinite fluid velocities from smooth initial conditions — during an 88-hour computation that began on September 1. The announcement immediately drew accusations from NYU mathematician Tristan Buckmaster, who alleged that OpenAI had rushed to tackle the problem after learning that he and Anthropic researcher Levent Alpöge were making progress using a similar approach. OpenAI denied the claims, saying it was "categorically" impossible for Buckmaster's work to have influenced its internal model.nytimes+3

The controversy escalated rapidly. On September 11, Terence Tao and 24 other Fields medalists published a declaration titled "A Severe Misalignment of AI in Mathematics," arguing that AI companies are treating famous problems as benchmarks to brute-force rather than as vehicles for genuine understanding. "Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others," the letter stated. Nearly 6,000 additional mathematicians have since endorsed it.science+2

Separately, more than 1,000 mathematicians signed an open letter opposing a planned "mathathon" at Caltech that would have paired researchers with AI computing credits from OpenAI and Anthropic, calling it corporate exploitation of early-career scholars. OpenAI subsequently withdrew from the event.science

A Second Millennium Problem

Even as mathematicians work through the dense Navier-Stokes proof, OpenAI has signaled it may be nearing a solution to a second Millennium Prize Problem, according to reporting by The Information and Science. The company has not confirmed which problem it is targeting, but speculation has converged on the Hodge Conjecture, a problem in algebraic geometry so abstract that even its formulation requires graduate-level expertise. Rumors have also pointed to the Birch and Swinnerton-Dyer conjecture as a possible target for OpenAI or Anthropic.theinformation+4

The timing has drawn sharp criticism. Javier Gómez-Serrano of Brown University, who lectured on the Navier-Stokes proof at Harvard on September 11, described the 166-page document as "incomprehensible" and said the mathematical community is experiencing an "existential crisis". Sergei Gukov of Caltech compared the moment to "an earthquake".science

Whether OpenAI's next claim, if it materializes, will deepen the rift with mathematicians or mark a turning point toward collaboration remains an open question. As the Fields medalists wrote: the challenge facing mathematics now "indicates issues that all of humanity might face: how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place".terrytao.wordpress