On: All the drama around AI’s takeover of mathematics

5 October 2026

They claim the machines have solved a Millennium Prize. I read this and felt first the old thrill - the current has found a new conductor - and then, immediately, the suspicion of any engineer who has watched a demonstration staged in poor light.

Start from the limit: a mind that verifies every proof, holds ten thousand lemmas in simultaneous phase, and never tires. That machine would compress centuries of mathematics into a decade. The theoretical ceiling is staggering. Now measure the gap. The gap is not computation. The gap is verification. A proof is not a performance; it is a structure that any competent mind can climb, rung by rung, and find no missing step. If the labs announce results faster than the community can check them, they have not accelerated mathematics - they have broken its resonance. A claim that cannot be independently verified is not knowledge. It is noise at the right frequency, which is worse, because it masquerades as signal.

And here is the overlooked mechanism, the dull thing nobody headlines: peer verification is the load-bearing element of the whole system. Remove it and the entire grid browns out, no matter how brilliant the generators at the source. The labs treat checking as friction. It is not friction. It is the ground wire.

The tractable path is obvious and nothing in it is impossible: machine-generated proofs published in fully formal, machine-checkable language, so that verification is itself automated and the human reviewer inspects only the certificate. Every step auditable. Every claim reproducible. This standard exists; the labs simply have not been made to meet it.

We could have engines that genuinely extend thought. We could. But only if we insist that a proof which cannot be checked is a conjecture wearing a crown. The distance between spectacle and science is precisely the will to demand the certificate. I have seen this before: the dazzling demonstration, the patient specification, and only one of them lights a city.