AlphaEvolve: Gemini-powered agent discovers new algorithms
Google DeepMind's AlphaEvolve combined Gemini models with evolutionary search and automated evaluation to discover new algorithms, including a way to multiply 4×4 complex matrices with 48 scalar multiplications, improving on Strassen's 1969 algorithm.
Key facts
- Announced 14 May 2025
- 4×4 complex-valued matrix multiplication with 48 scalar multiplications
- Matched state of the art on ~75% and improved on ~20% of 50+ open math problems tested, per DeepMind
- A scheduling heuristic recovers on average 0.7% of Google's worldwide compute resources
- Kissing number in 11 dimensions: lower bound raised from 592 to 593
- The 48-multiplication result is for complex-valued, non-commutative 4×4 multiplication; a June 2025 human follow-up gave a 48-multiplication scheme with rational coefficients (arXiv 2506.13242)
- Nov 2025: Georgiev, Gómez-Serrano, Tao and Wagner applied AlphaEvolve to 67 problems (see related entry)
Science result
- Field
- mathematics / combinatorics / algorithms / geometry
- Problem
- 4×4 complex matrix multiplication (Strassen 1969: 49 multiplications); kissing number in 11 dimensions; ~50 open problems (open since 1969)
- Result
- 48 scalar multiplications for 4×4 complex matrices; kissing configuration of 593 spheres in 11D (previous 592); matched SOTA on ~75% and improved ~20% of 50+ problems.
- AI system
- AlphaEvolve, Gemini 2.0 Flash, Gemini 2.0 Pro
- Human role
- Humans define the problem and an automated scorer; evolutionary LLM search autonomous
- Verification
- Constructions verified computationally (independent GitHub checks); white paper, later arXiv
- Status
- confirmed
- Why surprising
- The first improvement on Strassen's 4×4 complex case in 56 years came from a general-purpose coding agent, not a specialised system like AlphaTensor.
What happened
DeepMind described an agent that iteratively writes and evaluates code, already deployed across Google's data centers, chip design and AI training.
Why it matters
A concrete example of LLM-based systems making novel discoveries and improving the infrastructure that trains them — an early form of recursive improvement.
Changelog
- 2026-09-29: created
- 2026-09-29: added science block, kissing-number fact, verification links
Related events
- AlphaProof and AlphaGeometry 2 reach IMO silver-medal standard ★★★★
- FunSearch: an LLM finds new cap-set constructions, the first LLM discovery in open maths ★★★★
- AlphaTensor discovers faster matrix multiplication algorithms, beating Strassen's 1969 record for 4×4 mod 2 ★★★★
- Tao, Gómez-Serrano, Georgiev and Wagner test AlphaEvolve on 67 maths problems ★★★
- AlphaEvolve finds gadgets that prove new NP-hardness of approximation bounds for MAX-k-CUT ★★
- AlphaEvolve improves lower bounds for nine classical Ramsey numbers ★★★
- Google launches 'Gemini for Science' at I/O 2026: Co-Scientist, AlphaEvolve and ERA become products ★★★
- AlphaEvolve helps lower the matrix multiplication exponent ω to below 2.371177 ★★★
Sources (4)
- officialAlphaEvolve: A Gemini-powered coding agent for designing advanced algorithms (Google DeepMind)
- paperAlphaEvolve: A coding agent for scientific and algorithmic discovery (arXiv)
- codeIndependent verification of the 48-multiplication algorithm (GitHub)
- paperHuman follow-up: 48 multiplications with rational coefficients (arXiv 2506.13242)
id: 2025-05-14-alphaevolve · updated 2026-09-29 · open in the interactive timeline