A 56-Year-Old Math Record Finally Fell (Thanks to AI)

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In 1969, Volker Strassen proved that two 2×2 matrices can be multiplied with just 7 scalar multiplications instead of the obvious 8. Applied recursively, his method multiplies two 4×4 matrices with 49 scalar multiplications instead of the schoolbook's 64 — and for 56 years, 49 remained the best anyone could do for 4×4 matrices over a general field.

In 2025, DeepMind's AlphaEvolve — an evolutionary coding agent powered by Gemini — discovered a way to do it in 48. For the first time in over half a century, Strassen's record for 4×4 matrix multiplication fell.

This is the full story: why matrix multiplication secretly runs modern computing, how Strassen's trick works, how the problem becomes one of decomposing a tensor, why AlphaTensor's earlier "47" only held over the binary field F₂, and exactly what AlphaEvolve did — and did not — change. (Spoiler: the asymptotic exponent ω is untouched. This is a breakthrough about the concrete constant for small matrices, independently verified over the rational numbers by Dumas, Pernet, and Sedoglavic.)

⏱️ Chapters
0:00 A 56-Year-Old Record
0:26 Why Matrix Multiplication Is Everywhere
1:14 Strassen's Trick: 7 Instead of 8
3:03 Recursion: Why 4×4 Needs Only 49
4:07 Matrix Multiplication as a Tensor
5:57 AlphaTensor's 47 (and the Catch)
7:00 AlphaEvolve Breaks the Record
8:57 What Changed, and What Didn't
11:12 Solved, or Just Searched?

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