Problem · problem

The exponent of matrix multiplication

Strassen broke the $n^3$ barrier, and the bound has crept down since, to about 2.371 by 2024. Each step now wins in the third decimal place. AlphaTensor in 2022 found new small-case algorithms by search, showing that machine search can contribute. A faster algorithm is a checkable object; a lower bound would need a proof.

Posed 1969, after Volker Strassen's $O(n^{2.81})$ algorithm.

Sources

Wikipedia: Matrix multiplication algorithm

Algorithms · Computation

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