AlphaEvolve: DeepMind's AI Breaks a 56-Year Matrix Multiplication Record

Google DeepMind unveiled AlphaEvolve on May 14, 2025 — an evolutionary coding agent powered by Gemini for algorithm discovery and optimisation: it pairs large language models' idea generation with automated evaluators, using an evolutionary framework to improve the most promising programs (DeepMind blog, 2025-05-14).

48 multiplications and a 56-year record#

The blog states AlphaEvolve's procedure multiplies two 4x4 complex-valued matrices using 48 scalar multiplications, improving on the best previously known result in this setting, Strassen's 1969 algorithm. The white paper abstract puts it more precisely: the first improvement in this setting after 56 years (arXiv:2506.13131, 2025-06-16).

What is already deployed inside Google#

The blog lists three deployed uses:

• Data-center scheduling: a simple but effective heuristic for Borg that the blog says has been in production for over a year, continuously recovering on average 0.7% of Google's worldwide compute.
• Hardware design: a Verilog rewrite removing unnecessary bits in a matrix-multiplication arithmetic circuit; the proposal had to pass verification for functional correctness and was integrated into an upcoming TPU.
• Model training and inference: a 23% speedup of a key kernel in Gemini's architecture, leading to a 1% reduction in Gemini's training time, plus up to a 32.5% speedup on the FlashAttention kernel implementation.

Math results and the limits of the claims#

The blog says AlphaEvolve was applied to over 50 open problems in mathematical analysis, geometry, combinatorics and number theory: in roughly 75% of cases it rediscovered state-of-the-art solutions (to Google's knowledge), and in 20% it improved on the previously best known solutions. One example pushed the kissing-number lower bound in 11 dimensions to 593 outer spheres.

Note where these numbers come from: 0.7%, 23%, 1%, 32.5%, 75% and 20% are Google's own internal results and self-assessed measures — the blog's wording is "to the best of our knowledge." What outsiders can verify is the maths in the white paper (48 multiplications), not every engineering figure.