4×4 complex matrix multiplication in 48 scalar multiplications
4×4 complex matrix multiplication in 48 scalar multiplications is graded independently checked on whataifound.org, with the AI's role graded search scaffold.
AlphaEvolve found a scheme multiplying 4×4 complex matrices with 48 scalar multiplications, improving on Strassen's 49 from 1969.
- Verification
- Independently checked
- Autonomy
- Search scaffold
- Lab
- Google DeepMind
- Model
- AlphaEvolve (Gemini-based)
- Field
- Computer science
- Date
- 2025-05-14
- Problem posed
- 1969 · open 56 yrs
- Notability
- 7 Wikipedia language editions
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
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.
Sources
Community discussion
How this is graded
whataifound.org grades every entry on two axes: verification (how solid the result is, from a machine-checked proof down to refuted) and autonomy (how much the AI did versus its human collaborators). This finding is independently checked and search scaffold. Full definitions are in the methodology.
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-matmul