First screen, captured 4 days ago.

Κ = 0.003 for integer multiplication crossed

What HN thinks

Integer multiplication is apparently a speedrun category now, complete with a crime-scene log-scale chart.

Lean verification confirms the result
Commenters formally verified the surprising sub-n-log-n bound in Lean on Mathlib's Turing machine model and are pushing kappa improvements, inviting contributions.
How does the speedup work?
Readers asked for intuition; replies point to splitting one FFT into many smaller FFTs and sharing a small amount of work, plus explanatory papers.
The tracking chart is badly made
The bigospeedrun graph was mocked for a misleading log scale and buggy controls, sparking a tangent on LLMs writing bespoke code instead of using mature libraries.

Consensus: Most agree the bounds are moving surprisingly fast and that the result holds up under formal verification, even if the jargon is impenetrable.

Recommended in the comments

integer-mult-bounds-lean ↗ (library): It provides machine-checked proofs of the new kappa bounds and welcomes contributions.
Big O Speedrun ↗ (service): Shared as a way to follow how the bounds are progressing.

Summarised by Claude from the comment thread 3 days ago.

Points: 31
Comments: 22
Best rank: #17
Posted: 2026-10-21 by aleph_minus_one
Category: Science

integer-multiplication computational-complexity algorithms github openai-codex mathematics

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