A 56-Year-Old Math Record Finally Fell (Thanks to AI)
In 1969, Volker Strassen proved that two 2×2 matrices can be multiplied with just 7 scalar multiplications instead of the obvious 8. Applied recursively, his method multiplies two 4×4 matrices with 49 scalar multiplications instead of the schoolbook's 64 — and for 56 years, 49 remained the best anyone could do for 4×4 matrices over a general field.
In 2025, DeepMind's AlphaEvolve — an evolutionary coding agent powered by Gemini — discovered a way to do it in 48. For the first time in over half a century, Strassen's record for 4×4 matrix multiplication fell.
This is the full story: why matrix multiplication secretly runs modern computing, how Strassen's trick works, how the problem becomes one of decomposing a tensor, why AlphaTensor's earlier "47" only held over the binary field F₂, and exactly what AlphaEvolve did — and did not — change. (Spoiler: the asymptotic exponent ω is untouched. This is a breakthrough about the concrete constant for small matrices, independently verified over the rational numbers by Dumas, Pernet, and Sedoglavic.)
⏱️ Chapters
0:00 A 56-Year-Old Record
0:26 Why Matrix Multiplication Is Everywhere
1:14 Strassen's Trick: 7 Instead of 8
3:03 Recursion: Why 4×4 Needs Only 49
4:07 Matrix Multiplication as a Tensor
5:57 AlphaTensor's 47 (and the Catch)
7:00 AlphaEvolve Breaks the Record
8:57 What Changed, and What Didn't
11:12 Solved, or Just Searched?
📚 Key concepts
The schoolbook algorithm: 8 multiplications for 2×2, 64 for 4×4
Strassen's algorithm: 7 multiplications for 2×2 (proved optimal by Winograd)
Recursive block multiplication: 7 × 7 = 49 for 4×4
The matrix multiplication tensor T⟨2,2,2⟩ and its tensor rank
Rank-one decompositions correspond to scalar multiplications
The matrix multiplication exponent ω (best known bound ＜ 2.371339, unchanged by AlphaEvolve)
AlphaTensor (reinforcement learning) vs AlphaEvolve (evolutionary program search)
Why the field matters: F₂ vs the real and complex numbers
📖 References
1. Strassen, V. (1969). Gaussian Elimination is Not Optimal. Numerische Mathematik 13, 354–356.
2. Fawzi, A., et al. (2022). Discovering faster matrix multiplication algorithms with reinforcement learning. Nature 610, 47–53.
3. Novikov, A., et al. (2025). AlphaEvolve: A Coding Agent for Scientific and Algorithmic Discovery. arXiv:2506.13131.
4. Dumas, J.-G., Pernet, C., & Sedoglavic, A. (2025). A non-commutative algorithm for multiplying 4×4 matrices using 48 multiplications. arXiv:2506.13242.
5. Georgiev, B., Gómez-Serrano, J., Tao, T., & Wagner, A. (2025). Mathematical exploration and discovery at scale. arXiv:2511.02864.
6. Alman, J., et al. (2025). More Asymmetry Yields Faster Matrix Multiplication. SODA 2025.
🛠️ Tools used in this video:
Animation: Manim (Python)
Voice: ElevenLabs
Manim Starter Pack (31 ready-to-use scenes): https://axiommotion.gumroad.com/l/drhyqd
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