4×4 complex matrix multiplication in 48 scalar multiplications
AlphaEvolve found a scheme multiplying 4×4 complex matrices with 48 scalar multiplications, improving on Strassen's 49 from 1969.
- Model
- AlphaEvolve (Gemini-based)
- Field
- Computer science
- Date
- 2025-05-14
- Problem posed
- 1969 · open 56 yrs
Sources
Original work
Announcement
Media coverage
Independent commentary
What was found
Strassen's 1969 algorithm had stood at 49 multiplications for 56 years in this setting. AlphaEvolve was not purpose-built for matrix multiplication; it is a general evolutionary coding agent. The scheme is exactly checkable.
Novelty check
Strassen (1969) and subsequent literature exhaustively catalogued; 49 was the standing record for complex-valued 4×4. Confirmed new.
Caveats and known objections
Applies to complex-valued matrices specifically. Practical speedup is limited; the significance is theoretical. Related follow-up work by others has explored rank-23 schemes for 3×3.
Nobody outside the lab has checked this yet.
Reading the primary source closely enough to say whether it supports the claim counts as a check, and you are credited on the entry.
Or on GitHub: submit a check challenge the grade send a correction or send a pull request
Flag this for triage
Signals order the review queue and nothing else. They are never published, and they never move a grade: that takes a citation.
Entry history (1 event)
- AddedEntered the registry graded Independently checked and Search scaffold.
Entries are never deleted. A grade that does not hold up is downgraded on the record, with the reason beside it.
Community discussion
Graded independently checked for verification and search scaffold for autonomy. What these mean.
Cite this entry
whataifound.org. (2025). 4×4 complex matrix multiplication in 48 scalar multiplications. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2025-05-alphaevolve-matmulBibTeX
@misc{whataifound-googledeepmind-2025-matmul,
title = {4×4 complex matrix multiplication in 48 scalar multiplications},
author = {{whataifound.org}},
year = {2025},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Google DeepMind. Verification: Independently checked. Autonomy: Search scaffold.},
url = {https://whataifound.org/finding/2025-05-alphaevolve-matmul}
}