Research 2026-08-20

So many machine-written proofs arrived that mathematicians built a filing office — and one of its two checks is done by a language model

Terence Tao announced on 18 August that Palomar, a registry of Lean-verified mathematics incubated by the Lean FRO and by ICARM, is open for submissions. The problem it was built for is recent: a large number of AI-generated proofs of old and new results have appeared in the past months, and a good share of them have been formalised in Lean, the proof assistant that lets a machine confirm every step. But a Lean repository sitting on GitHub does not explain itself. Working out whether the code proves the thing its author says it proves is real labour, and close to impossible for a mathematician who does not use Lean. Palomar puts a submitted repository through two checks. The first is mechanical: a Lean tool called Comparator confirms that the module typechecks and proves exactly the results claimed. The second asks whether the plain-language description matches the formal statement, and that one is performed by a large language model. Repositories that pass both are registered, and the exact statement, the libraries relied on and the reviewer's comments are published alongside. Tao calls it the analogue of a preprint server for Lean proofs, and sits on a scientific advisory board with Jeremy Avigad, Matthew Ballard, Jaume de Dios, Nestor Guillen, Bryna Kra, Kim Morrison, Ravi Vakil and Akshay Venkatesh.

Why it mattersMathematical peer review assumed a human bottleneck at both ends: a person writes the proof, and people read it. Machines have broken the first half, and the second half never scaled. Palomar is the first serious attempt to build the missing plumbing, and it is candid about the compromise at its centre. The formal check is airtight; the question of whether the formal statement is the one anyone actually cared about is being answered by exactly the kind of system that caused the flood. That is not a scandal, it is the honest available option, and it is stated in the open rather than buried. The larger signal is that a discipline has stopped arguing about whether to accept machine-produced work and started designing the infrastructure to sort it — which is further along than almost any other field has managed.

#Coding #Science & Research

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2026-08-21

So many machine-written proofs arrived that mathematicians built a filing office — and one of its two checks is done by a language model

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