# Multiplications needed for 4x4 matrix multiplication over F_2

A record target in qed.bot, the register of claims of AI work in mathematics. The register grades the evidence attached to each claim; it never rules on whether a proof is correct.

- Identifier: matmul:4x4-mod2
- Collection: Algorithms
- Page: https://qed.bot/t/matmul-4x4-mod2
- Record: 47 multiplications, held by AlphaTensor, since 5 Oct 2022
- Machine-checked: yes, by qed.bot
- Source: https://github.com/google-deepmind/alphatensor

## Record history

- 1969: 49 multiplications, Strassen, applied recursively; moved the record. https://doi.org/10.1007/bf02165411
- 5 Oct 2022: 47 multiplications, AlphaTensor, with AI; moved the record. https://www.nature.com/articles/s41586-022-05172-4

## AI claims

### AlphaTensor, 5 Oct 2022

A decomposition of rank 47, improving on 49.

- Outcome: record
- Autonomy A2: Directed. The system produced the result while building on literature or framing supplied to it.
- Evidence V3: Machine-checked. The artifact was rebuilt at a pinned commit by someone other than its authors — qed.bot, or a registry that publishes the check — and it holds: a proof that elaborates on the standard axioms alone, or an object that meets the problem's own constraints. Checked by qed.bot.
- Source: Nature, Discovering faster matrix multiplication algorithms, https://www.nature.com/articles/s41586-022-05172-4

## Checks

- verified, by qed.bot: 4x4x4 in 47 multiplications, exact identity mod 2 (https://github.com/google-deepmind/alphatensor/blob/main/algorithms/factorizations_f2.npz)

Cite as: qed.bot, "Multiplications needed for 4x4 matrix multiplication over F_2", https://qed.bot/t/matmul-4x4-mod2, as of 30 Sep 2026. The register's data is published under CC BY 4.0: https://creativecommons.org/licenses/by/4.0/