Matrix multiplication with exponent at most 9/4

What OpenAI claims

Proves ω ≤ 9/4 over ℂ, giving O_ε(n^9/4+ε) arithmetic operations for square matrix multiplication. In characteristic zero, some inner dimension na with a > 0.465 permits n^2+o(1) rectangular multiplication. Further square bounds give ω < 2.258 outside finitely many positive characteristics and ω < 2.371054886006746 over every fixed field. (Lean)

Papers (2)

1. An Upper Bound of 9/4 for the Matrix Multiplication Exponent

   2 October 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract We prove that the exponent of matrix multiplication over the complex numbers is at most 9/4.

2. Staggered extraction for exact matrix multiplication over every field

   24 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract We prove that the arithmetic exponent of square matrix multiplication over every fixed field satisfies ω < 2.371054886006746. This includes every positive characteristic.

Status

Preprint. The papers have not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.