Terence Tao: AI that solves problems too fast could "poison" mathematics

Terence Tao is the kind of mathematician who has spent years quietly trying new AI tools and openly praising the good ones. But after GPT-6 Astra shipped, he wrote something few people expected from him: if neural networks start handing out answers to the great open problems too quickly and without a transparent process, mathematics could lose more than it gains. The trigger was a concrete result — OpenAI's new model claimed progress on the twin prime problem.

First, the facts. GPT-6 Astra, according to OpenAI, used formal proofs in Lean to shrink the upper bound on the gap between consecutive primes from 246 to 186. For scale: in 2013, Yitang Zhang proved there are infinitely many pairs of primes no more than 70 million apart. James Maynard, who won the Fields Medal in 2022, brought that bound down to 600, and the community later squeezed it to 246. Now three labs reported new numbers at once: OpenAI at 186, Anthropic at 188, Axiom at 212.

On the surface, cause for celebration. Tao saw something else — a warning sign.

The answer is not the most valuable part

Tao's core point sounds almost paradoxical: a great open problem is valuable not for its answer but for the road to it. When mathematicians fight a problem for years, they invent new methods, concepts, and whole theories along the way — and those "byproducts" are what actually move science forward. Even dead ends are useful: understanding why an approach failed often matters more than finding the solution.

Now imagine the answer comes from a neural network. Fast, a black box, no intermediate steps shown. The problem is formally solved — but the process that was supposed to generate new ideas never happened. Tao calls this "polluting" the problem: it stops being a source of future discoveries.

The Navier-Stokes example

Tao unfolds his argument on a concrete case — the global regularity problem for the Navier-Stokes equations, one of the seven Millennium Prize problems. Mathematicians are already fairly sure the answer is negative: there exist initial conditions where the solution "blows up" in finite time. There is even a four-step plan sketched out, from building an approximate self-similar solution to verifying its stability.

The catch is that each step is brutally hard for a human but fits perfectly onto an assembly line of "machine learning + rigorous arithmetic + formal proofs." Tao allows that such a hybrid might genuinely solve the problem. And here is the rub: if the solution turns out so complex that no human can grasp it, and the company running the AI hides the whole process behind closed doors, mathematics gets a checkbox but learns almost nothing.

Why this matters beyond mathematicians

Tao's logic is broader than it looks. It applies to any field where value is created in the process, not in the final answer. If AI starts instantly producing "correct" solutions and people stop walking the path of trial and error, we risk losing not speed but understanding. Tao puts it bluntly: in the worst case, AI's influence on mathematics could turn from positive to negative.

He is not against AI in science — far from it, he is one of its most active users. What worries him is a specific scenario: an autonomous system that spins the whole "hypothesis — test — reject" cycle inside itself, on enormous compute, and hands out only the final answer. No traces, no drafts, no way to learn from its mistakes.

What comes next

For now this is a warning, not a verdict. GPT-6 Astra did shrink the bound to 186, but the twin prime conjecture itself — that there are infinitely many such pairs — remains unproven. This is an intermediate result, however notable. The question Tao raises runs deeper: how to make AI accelerate science without hollowing it out. He has no answer yet — and, honestly, neither does anyone else.

Source: 量子位 (QbitAI): 陶哲轩吐槽GPT-6孪生素数新突破.