An expert vouched for an AI's multiplication breakthrough without reading its proof
David Harvey, who co-wrote the previous record algorithm, spent two weeks trying to follow the new paper and understood only a small fraction. Then he asked Claude Fable 5.1 to explain it, and published a note saying the result is plausible.
The claimed gain is a factor of (log n)^ε with ε = 2^-182, which the thread mocked as microscopic. Harvey calls it "gobsmackingly enormous": the first crack in a bound he had treated as a hard physical limit.
A game developer's reply on HN: "this does not feel like a healthy place to be."
A bound Harvey would have bet zero on
An unnamed American technology company recently dumped a pile of manuscripts on GitHub. One of them claims an algorithm that multiplies n-bit integers in o(n log n) bit operations. Harvey's note, dated 20 October 2026, treats it seriously because the work builds directly on the O(n log n) algorithm he wrote with Joris van der Hoeven, which most of the field believed was optimal.
The claimed saving is a factor of (log n)^ε, where the first write-up has ε = 2^-182. Harvey says the number is irrelevant. Before the new paper, he estimated the odds that the data-rearrangement cost could be beaten at 0.01%, and the odds for the butterfly arithmetic at precisely zero. That barrier had always looked "woven into the fabric of the universe".
How a human expert checks a proof he cannot read
Harvey writes that he has not read any of the three related papers, because the dump is weak on exposition. He asked Claude Fable 5.1 to explain the first paper, drilled down with follow-up questions, and after two weeks of hard work understood a small fraction of it. The model, he says, absorbs the whole paper in minutes from a fresh context. His verdict is a tentative "possibly correct", and he wants a Lean formalisation before he would be more confident.
Others have reportedly already pushed the exponent to about 0.9983. By his reasoning the method also disproves the Li-Li network coding conjecture when combined with an earlier lower-bound result.
Whether "the model understood it" counts as evidence
The top HN reaction was discomfort at the method, not the math.
"this does not feel like a healthy place to be" — a game developer
A reader pushed back that if the tools can follow what experts cannot, using them is just reality. A founder building a token-billing product came at it from the other side, with a thought experiment:
"Suppose we have a very convincing math PhD impersonator, agreeing and making some prepared smart-sounding comments saying they understood the proof and it seems to make sense - would it?" — the founder of tokenbank.ing
A different reading came from a commenter who thinks the situation is better than feared:
"Fable was able to help a human understand the paper though, so the situation is quite a bit better than if we just had a lean proof that was apparently correct" — a commenter weighing explanation against formal proof
A software engineer saw the same pattern outside mathematics:
"You don't read AI written code, you ask an AI to explain it to you." — a software engineer who works with AI-written codebases
For working mathematicians the practical consequence is Harvey's own forecast: a Lean proof, if the result holds, should appear soon, and until then the claim rests on human experts who cannot read the paper plus a model that can.
Get breakdowns like this every day
The top Hacker News stories, unpacked — by email, Telegram, or RSS.
eMudhra quits the global TLS certificate business after its weak CA keys were revoked
The company says SSL/TLS is about 1% of its revenue and that social media amplification of the incident was out of proportion. Browser vendors had already pulled the affected intermediate CAs.