First screen, captured 4 days ago.

The recently proposed o(n log n) integer multiplication algorithm [pdf]

What HN thinks

A multiplication algorithm got faster and the thread spent its savings arguing about what 'understand' means.

Outsourced understanding is unhealthy
Relying on an LLM to explain a paper no human can read erodes what math is for, risks undetected errors, and concentrates intelligence in a few corporations.
Validity doesn't need human comprehension
Formal verification in Lean and expert follow-up make the result checkable; AI-assisted explanation is just a new way to digest hard math, and the author is the world expert anyway.
Notation clarification: little-o vs big-O
Many commenters explained that o(n log n) is a strict improvement over the known O(n log n) FFT bound, with some nitpicking of each other's definitions.

Consensus: No consensus on whether AI-mediated understanding is acceptable, though most agree formal proof checking like Lean is a crucial safeguard and that the o vs O distinction is what makes the result notable.

Recommended in the comments

Lean ↗ (tool): Commenters pointed to an existing Lean formalization of the result and multiple independent proof checkers as a way to trust proofs without full human reading.
integer-mult-bounds-lean ↗ (library): Its authors offered it as a full formal proof of the o(n log n) result and invited contributions.

Summarised by Claude from the comment thread 3 days ago.