# Exponent of matrix multiplication

A record target in qed.bot, the register of claims of AI work in mathematics. The register grades the evidence attached to each claim; it never rules on whether a proof is correct.

- Identifier: matmul:omega
- Collection: Algorithms
- Page: https://qed.bot/t/matmul-omega
- Record: 2.371177, held by Emilien Dupont and nine co-authors, with AlphaEvolve, since 17 Aug 2026
- Machine-checked: no independent check has verified it
- Fidelity F0: Absent. No formal statement is attached to the result.
- Source: https://arxiv.org/abs/2608.16884

## Record history

- 1969: 2.8074, Volker Strassen; moved the record. https://doi.org/10.1007/bf02165411
- 1978: 2.796, Victor Pan; moved the record. https://doi.org/10.1109/sfcs.1978.34
- 1979: 2.7799, Dario Bini, Milvio Capovani, Grazia Lotti and Francesco Romani; moved the record. https://doi.org/10.1016/0020-0190(79)90113-3
- 1981: 2.522, Arnold Schönhage; moved the record. https://doi.org/10.1137/0210032
- 1982: 2.517, Francesco Romani; moved the record. https://doi.org/10.1137/0211020
- 1982: 2.496, Don Coppersmith and Shmuel Winograd; moved the record. https://doi.org/10.1137/0211038
- 1986: 2.479, Volker Strassen; moved the record. https://doi.org/10.1109/sfcs.1986.52
- 1990: 2.3755, Don Coppersmith and Shmuel Winograd; moved the record. https://doi.org/10.1016/s0747-7171(08)80013-2
- 2012: 2.3729, Virginia Vassilevska Williams; moved the record. https://doi.org/10.1145/2213977.2214056
- Jan 2014: 2.3728639, François Le Gall; moved the record. https://arxiv.org/abs/1401.7714
- Oct 2020: 2.3728596, Josh Alman and Virginia Vassilevska Williams; moved the record. https://arxiv.org/abs/2010.05846
- Nov 2022: 2.371866, Ran Duan, Hongxun Wu and Renfei Zhou; moved the record. https://arxiv.org/abs/2211.05488
- Jul 2023: 2.371552, Virginia Vassilevska Williams, Yinzhan Xu, Zixuan Xu and Renfei Zhou; moved the record. https://arxiv.org/abs/2307.07970
- Apr 2024: 2.371339, Josh Alman, Ran Duan, Virginia Vassilevska Williams, Yinzhan Xu, Zixuan Xu and Renfei Zhou; moved the record. https://arxiv.org/abs/2404.16349
- 17 Aug 2026: 2.371177, Emilien Dupont and nine co-authors, with AlphaEvolve, with AI; moved the record. https://arxiv.org/abs/2608.16884

## AI claims

### AlphaEvolve, 17 Aug 2026

An upper bound of 2.371177 on the exponent of matrix multiplication, improving 2.371339.

- Outcome: record
- Autonomy A1: Collaborative. A human and a system worked the problem together, or the system played a supporting role.
- Evidence V1: Informal. A public write-up exists and has had community scrutiny.
- Fidelity F0: Absent. No formal statement is attached to the result.
- With: Emilien Dupont, Marvin Eisenberger, Borislav Kozlovskii, Abbas Mehrabian, Francisco J. R. Ruiz, Abigail See, Renfei Zhou, Josh Alman, Virginia Vassilevska Williams, Matej Balog
- Source: Dupont et al., Improving the matrix multiplication exponent with modern optimization and AlphaEvolve, https://arxiv.org/abs/2608.16884

Cite as: qed.bot, "Exponent of matrix multiplication", https://qed.bot/t/matmul-omega, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/