AlphaEvolve Breaks a 56-Year-Old Matrix Multiplication Record

This week, Google DeepMind shared remarkable news. For some time now, they have been working on a project called AlphaEvolve — an AI system built on LLMs and genetic algorithms, designed with one goal in mind: to discover new algorithms. And it has already delivered.

A New Matrix Multiplication Algorithm After 56 Years of Stagnation

AlphaEvolve found a new way to multiply 4×4 matrices using just 48 multiplications. The previous record was 49, set by Strassen back in 1969. The standard method taught in school requires 64.

Nearly 60 years without progress — and then, a breakthrough. Made not by a human.

How the Algorithm Discovery System Actually Works

What makes this especially remarkable is that AlphaEvolve was not specifically trained to multiply matrices. It is a general-purpose system: it takes as input a piece of code with an approximate solution and a verification program, then uses genetic algorithms to autonomously generate dozens or hundreds of new candidate solutions — entirely on its own.

Why Matrix Multiplication Matters for AI and Computing

Matrix multiplication is the engine behind nearly all modern computation:

• 3D graphics and physics simulations
• Machine learning and neural networks
• Cryptography
• Data center operations
• Even the behavior of quantum systems

A single extra operation in a fundamental routine translates to trillions of redundant calculations happening across the world every day. Now, there are fewer of them.

AlphaEvolve’s Broader Impact on Open Mathematical Problems

This result is not an isolated win. AlphaEvolve was run against 70+ open mathematical problems, and in one out of every five, it found a better solution than anything previously known to science — while in the rest, it independently arrived at already-known optimal solutions.

Among its other achievements:

• Raising the kissing number lower bound in 11 dimensions from 592 to 593 — that is, the number of spheres that can simultaneously touch a single central sphere
• Optimizing the architecture of Google’s TPU chips
• Speeding up Gemini model training by 1% through a 23% improvement in a key matrix multiplication kernel

What This Means for the Future of AI-Driven Mathematics

We are still at the very beginning of this journey. The question is no longer whether AI can make meaningful contributions to mathematics — it already has. The more interesting question now is how far it can go.