Three papers. Two weeks. None of them read. That is where David Harvey stands on an AI-written claim to beat his own record for multiplying large integers. Harvey and Joris van der Hoeven's 2021 algorithm runs in O(n log n) bit operations, a bound the field widely took to be optimal. A model belonging to an unnamed American technology company, in a pile of manuscripts dumped on GitHub, says the true cost is lower. Harvey's verdict, in a note dated Tuesday, is that the claim is plausible.
How he got there is the story. He tried the papers and gave up; the dump, he writes, is not strong on exposition. So he asked Claude Fable 5.1 to explain the main one, then asked again, and kept drilling until pieces of the argument came into focus. Then he wrote this:
Fable seems to understand the argument and thinks that it is correct. I expect that thousands of frontier LLM instances around the world have come to the same conclusion over the last two weeks. If not, surely we would have heard by now.David Harvey, UNSW Sydney
That last sentence is doing work it can't do. A thousand instances of a model agreeing is not a thousand referees. It is one referee with a lot of copies, and the confidence a proof earns has always been counted in independent checks, not in readers.
A thousand instances of a model agreeing is not a thousand referees. It is one referee with a lot of copies.
Refereeing works because the second reader fails differently from the first: different training, different advisers, different habits of skimming the step that looks routine. Two readers who would stumble on the same lemma are worth one. Instances of a single model share every blind spot by construction. Models from rival labs are less correlated than that, but nobody has measured how much less, and in refereeing independence is something you show, not something you assume. The silence is weaker still. Silence counts as evidence only when the people able to object are many and looking. Harvey reckons few humans anywhere understand every detail of the 2021 algorithm the new work builds on. Most of what we haven't heard is from people who couldn't check.
The strongest objection is Harvey's own, and it's a fair one. He defends calling what the model does understanding: it answers fiddly technical questions about the paper correctly and lucidly, which is exactly how he'd decide a colleague had understood something. He also records the gap that should unsettle anyone in his field. Two weeks of hard work got him through a small fraction of the main paper; the model reads the whole thing in minutes from a fresh context. Grant all of it. Understanding still isn't independence. A model that grasps the argument and finds it sound is what you'd see if the proof is right, and also what you'd see if the error sits in a step every model of this generation finds persuasive. Only a checker that fails in a different way can tell those apart.
That's what makes the note worth reading beyond the mathematics. Harvey's slow, partial, human understanding is the one check in his loop that could fail differently, and he prices it honestly: the main result is possibly correct, he writes, and he flags that he chose those words carefully. He asks for the other kind of check too, a formal proof in Lean, which would fail in a way neither he nor Fable does. That proof doesn't exist yet, and his own reading covers a fraction of one paper.
The models will keep agreeing with the dump. Agreement is cheap now, and it will get cheaper. What it can't buy is a second way of being wrong. Harvey spent two weeks earning one, on a fraction of one paper.