Terence Tao calls GPT-6 twin-prime breakthrough a speechless scene

Terence Tao, the Fields medalist who has always embraced AI in his own research, has gone public with a strikingly critical take on GPT-6's reported progress on the twin-prime conjecture. In a post on Mathstodon, he called the situation "a genuinely speechless scene" and warned that AI jumping in to answer hard open problems may end up holding mathematics back, as reported by Chinese tech outlet QbitAI on September 5.

The trigger is a wave of results around the launch of GPT-6 Astra. OpenAI announced that the new model used a Lean formal proof to push the upper bound on gaps between consecutive primes from 246 down to 186. Around the same time, Anthropic and Axiom said their own AI systems had narrowed the gap to 188 and 212 respectively.

The twin-prime conjecture is one of the most famous open problems in number theory. Zhang Yitang made his name by proving that infinitely many pairs of consecutive primes are separated by no more than 70 million; 2022 Fields medalist James Maynard later cut the bound to 600, and a follow-up team pushed it to 246 with conjectures that it could go lower. Just before the AI announcements, Oxford mathematician Julia Stadlmann published a new estimate for smooth moduli on August 31 that brought the bound to 240, and Tao was relieved her analysis made it out before the problem became polluted.

Tao's concern is not whether AI can do mathematics. It is that AI answers too quickly and too opaquely, and that this capability may obscure the valuable failures that are part of mathematical research. If the person or system driving the iteration already knows the final correct ansatz, he argues, exploration of other routes is suppressed, yet the reasons those apparent dead ends fail are often deeply instructive.

He develops the argument around the Navier-Stokes global regularity problem. Historically, attempts on the problem generated foundational ideas and theorems in fluid mechanics, analysis and PDE theory, from Leray-Hopf weak solutions to the Beale-Kato-Majda blowup criterion. The truly important thing is the process by which research advances, and heavy AI involvement may kill off that kind of divergent, field-building development.

His bleakest scenario: an autonomous AI harness, running on massive compute, iterates, fails, adjusts and eventually finds the correct ansatz, while the company running it keeps the entire process hidden from public view. Technically, one of the most famous open problems in mathematics would then be solved; mathematically, almost nothing would have been gained. In severe cases, Tao warns, AI's net effect on the development of mathematics could turn negative.

The episode matters on two levels. It is a concrete demonstration that frontier models can now use verifiable formal proofs to move a public mathematical bound, and it puts process transparency at the center of the AI-for-science debate: when answers are produced at black-box speed, the wider community may lose the very journey that generates new ideas.

Watch next: whether OpenAI, Anthropic and Axiom publish the full reasoning and proof artifacts behind 186, 188 and 212; whether mathematicians can understand and verify the new bound; and whether Tao's pollution concern becomes the defining question as AI turns to problems like Navier-Stokes.