How few scalar multiplications suffice to multiply two 4 × 4 matrices, over a specified field?
Model / AI: AlphaTensor, AlphaEvolve
Model / AI: AlphaTensor
RL finds faster matrix multiplication algorithms (4x4 over F2 in 47 multiplications). Nature.
Source read 2026-09-08. Read the Nature paper: 47 scalar multiplications for 4 × 4 matrices over F₂. Code was not executed.
Model / AI: AlphaEvolve
4x4 complex matrix multiplication in 48 scalar multiplications, first below Strassen's 49 in characteristic 0 (AlphaTensor had already reached 47 in characteristic 2); Dumas, Pernet and Sedoglavic later hit 48 with rational coefficients, removing the complex arithmetic.
Source review pending. Imported from the original notes; linked claims and artifacts have not been re-audited in this restructuring.