Strassen, minus one

Multiplying two 4x4 matrices the schoolbook way takes 64 small multiplications. In 1969 Volker Strassen showed a recursive trick that gets it to 49, and there the count sat in the general case. DeepMind's AlphaEvolve — an agent that mutates and tests code over and over, with Gemini proposing edits and an automated checker keeping only the schemes that actually compute the right product — found one that does it in 48.

DeepMind's own blog claimed only an improvement on 'the best known in this setting' — the 'unbeaten since 1969' version was added downstream.

One fewer multiplication sounds trivial. It isn't nothing: matrix multiplication is the operation underneath essentially all neural-network compute, and a recursive scheme reuses its saving at every level, compounding as the matrices grow. But the headline that traveled — 'the first improvement in 56 years, found by no human' — is wrong, and the gap is where the real result hides. A mathematician named Waksman beat Strassen's 49 with 46 back in 1970; his method just assumed the numbers commute and that you can divide by two. AlphaEvolve's 48 holds without those assumptions, the awkward non-commutative case where Strassen's 49 was the bound to beat.

So the genuine result is narrower and sturdier than the hype: not a record untouched since the moon landing, but a real new rung on an active ladder — and the rung was placed by a search agent rather than a person. The lineage matters too. DeepMind's earlier AlphaTensor had only undercut the count in binary arithmetic; doing it over the complex numbers is the new step. Within a month an academic team reproduced the scheme and stripped out the complex-number requirement entirely, which is roughly how a healthy result is supposed to age.