AlphaEvolve × Strassen
AI broke Strassen's 56-year record for 4×4 matrix multiplication: 48 vs 49 scalar ops.
Matrix multiplication is the most fundamental operation in computing. Strassen (1969) showed 7 multiplications suffice for 2×2 (not 8), giving O(n^2.807). Applied recursively to 4×4, this gives 49. AlphaEvolve found a scheme using only 48 — the first improvement in 56 years.
Formula
Strassen (1969) showed 2×2 matrix multiplication needs only 7 scalar multiplications, launching fast matrix multiplication.
DeepMind's AlphaEvolve found an algorithm for 4×4 complex matrix multiplication using 48 multiplications, beating 49.
The exponent ω is the infimum such that n×n matrices can be multiplied in O(nω) operations; ω = 2 is conjectured.
Summary
Matrix multiplication is the most fundamental operation in computing. Strassen (1969) showed 7 multiplications suffice for 2×2 (not 8), giving O(n^2.807). Applied recursively to 4×4, this gives 49. AlphaEvolve found a scheme using only 48 — the first improvement in 56 years.
