Integer multiplication below n log n

Author: OpenAI

Date: September 23, 2026

OpenAI published a preprint in its open math repository claiming an algorithm for integer multiplication with complexity below n log n—the theoretical lower bound established by Schönhage and Strassen’s work and long considered a fundamental barrier in computational number theory.

The preprint is available at:
https://github.com/openai/math/blob/main/preprints/Integer-multiplication-below-n-log-n-September-23-2026/paper.pdf

Citation

@misc{OAI:Integer-multiplication-below-n-log-n-September-23-2026,
  author = {{OpenAI}},
  title = {{Integer multiplication below $n\log n$}},
  howpublished = {OpenAI Math Release preprint},
  year = {2026}
}

This release is part of OpenAI’s broader mathematics research program, which has previously produced formal proofs and algorithmic advances shared via the openai/math GitHub repository. The result, if verified by the mathematical community, would represent a landmark breakthrough in fundamental algorithms.

Related context: OpenAI also published “Sharing AI progress in mathematics” on October 6, 2026, discussing ongoing AI-assisted mathematical research (https://openai.com/index/sharing-ai-progress-in-mathematics/).