The OpenAI CEO struck a reflective note a day after the company released 722 manuscripts, with thanks to “the machines” and to generations of mathematicians.
OpenAI CEO Sam Altman has offered a rare reflective post in the wake of his company’s release of more than 300 mathematical results, saying he is “looking up at the stars with extra awe tonight.”
“Thy sea is so great and my boat is so small,” Altman wrote, in a line often attributed to an old Breton fishermen’s prayer. He then thanked “the machines, and the structure of reality, for letting us understand a little more.” He also thanked “the untold number of people who put in the technical work, brick by brick over the generations,” to get to a point where “such a wonder is possible.”
What prompted it
The post follows OpenAI’s release of a catalog of 722 manuscripts grouped into 372 result families, which the company says were produced by an unreleased internal model. Altman had earlier picked out four of them as the biggest: a proof of the quasi-Riemann hypothesis, a proof of the Unique Games Conjecture, a proof of the Hodge conjecture for CM abelian varieties, and a resolution of the free group factors problem.
The Riemann zeta function, which governs much of what we know about the distribution of prime numbers, has no zeros with real part above 7/8. That is not the Riemann hypothesis itself, which would need 1/2, and it wouldn’t win the Millennium Prize. But no one had previously shown that zeros stay out of any fixed strip near the edge, which makes it a long-standing goal in its own right. Altman said in his earlier post that it has a Lean proof, meaning a computer has checked the logical steps.
The caveats still apply
The tone of Altman’s post is different from the one that has followed OpenAI’s recent math announcements. The results are claims that outside mathematicians haven’t yet confirmed, and OpenAI’s own readme says not all of them have Lean formalizations and that some of the unformalized ones “could have issues.”
The context for the gratitude in the post is also worth noting. OpenAI’s earlier claim that an internal model had produced a proof of the Navier–Stokes problem came with a dispute over credit involving mathematician Tristan Buckmaster. On September 11, 25 Fields Medal winners, including Terence Tao, signed a declaration saying rapid AI proofs are harming mathematics and that results are being announced in a rush, without proper verification or documentation of earlier work. Tao has also warned that AI proofs can be a net negative for mathematics if they arrive as opaque black boxes.
A fast-moving race
The release is the latest in a rapid run of claims. OpenAI has said its models have resolved more than 100 long-standing mathematical problems beyond Navier–Stokes, and an informal tracker counted 234 problems solved with OpenAI’s models as of early August, ahead of Anthropic’s 57. Fields Medalist Cédric Villani called the Navier–Stokes claim “a cataclysm unlike anything math has known.” OpenAI president Greg Brockman had said that AI could solve a Millennium Prize problem in two to five years, and the company has been recruiting from the field: Fields Medalist Jacob Tsimerman is taking leave from Toronto to join OpenAI.
Whether the awe turns out to be warranted depends on what mathematicians find when they read the manuscripts. The Lean-checked results can be tested relatively quickly, while the rest will need expert readers and time. Altman’s post acknowledges the people behind the field’s long history. The mathematical community will now decide how much of this new chapter is theirs to accept.