The recently proposed O(n log n) integer multiplication algorithm [pdf]
Summary
David Harvey and Joris van der Hoeven's paper presenting a groundbreaking O(n log n) integer multiplication algorithm, breaking the long-standing complexity barrier for multiplying large integers.
View Cached Full Text
Cached at: 10/22/26, 03:25 AM
Similar Articles
Auto Research: Integer multiplication below n log n
An automated research run exploring integer multiplication algorithms with complexity below n log n, providing reproducible contributions, a repository contribution guide, and interactive visualization of ideas and pull requests.
Integer multiplication below n log n
OpenAI released the openai/math repository containing 722 manuscripts in 372 research families — spanning results like integer multiplication below n log n, the irrationality exponent of π, and Mahler conjectures — produced by an unreleased internal model over ~4,000 problems, with many results formalized in Lean.
Mathematicians still don’t know the fastest way to multiply numbers
The article explores the unsolved problem in computer science of finding the fastest possible multiplication algorithm, tracing its history from the grade-school O(n²) method to modern breakthroughs like Karatsuba's 1960 discovery and the recent 2024 result, and explains why this matters for AI, encryption, and other digital tasks.
Κ = 0.003 for integer multiplication crossed
A community research repository reports a sharper exponent bound for integer multiplication, achieving T(n)=O(n(log n)^(1-κ)) with κ=0.0023 under the OpenAI #109 framework, conditional on unverified hypotheses and not yet a complete Lean proof.
Improving the matrix multiplication exponent with modern optimization and AlphaEvolve
The paper proposes improvements to the optimization problem in combination loss analysis using modern techniques and AlphaEvolve, yielding an improved upper bound on the matrix multiplication exponent.