The Matrix Multiplication Exponent

Lineage and corrections

Corrects The Matrix Multiplication Exponent →

Supersedes The Matrix Multiplication Exponent →

This event attributed to Renfei Zhou

This event attributed to Josh Alman

This event attributed to Virginia Vassilevska Williams

This event attributed to Matej Balog

The Matrix Multiplication Exponent parent of this event

A record, not a resolution, and a small one by design. The bound moves from $2.371339$ to $2.371177$, about $1.6 \times 10^{-4}$, and the authors describe it as a small step. Whether $\omega = 2$ is untouched, and nothing here suggests the laser method can reach it. The interesting claim is methodological rather than numerical. The bottleneck in this line of work is a hard optimization problem, and the paper reports progress by reformulating that problem and then improving the optimizer, with AlphaEvolve doing the final refinement. That is a different kind of contribution from a new mathematical identity, and it is why the entry is filed as computation. Superseded as the best claimed bound by the OpenAI math release (October 2026), which claims omega <= 9/4 over C (Lean-checked, not independently reviewed) and omega < 2.371054886006746 over every field; see matrix-multiplication-exponent-9-4. parent of this event

VibeMathed record: The Matrix Multiplication Exponent evidence for this event

The Matrix Multiplication Exponent evidence for this event

Balog's announcement thread evidence for this event

Stronger result in the OpenAI math release evidence for this event

This event attributed to AlphaEvolve

This event attributed to Emilien Dupont

This event attributed to Marvin Eisenberger

This event attributed to Borislav Kozlovskii

This event attributed to Abbas Mehrabian

This event attributed to Francisco J. R. Ruiz

This event attributed to Abigail See