AlphaEvolve at scale on 67 math problems
Georgiev, Gomez-Serrano, Tao, Wagner
Mathematicians used AlphaEvolve on 67 research problems and report where its evolved search programs rediscovered, improved or failed to beat known results.
The loop
- Proposes
Search heuristics (programs) that look for a mathematical construction, or programs that give a formula for any n
- Judged by
User-written deterministic evaluators that score the best object found, sometimes checked afterwards by proof tools
- Steers
Best heuristics are reused in later rounds; Kakeya's program went to proof tools
Headline result
The paper reports 67 problems across analysis, combinatorics, geometry and number theory. AlphaEvolve rediscovered the best known solutions in most cases and found improved ones in several, for example an autocorrelation upper bound reduced from 1.5708 to 1.5032 and a finite field Kakeya construction of size 1/4 p^3 + 7/8 p^2 - 1/8 for primes p = 1 mod 4.
What this does not prove
The authors state it did not match previous results in all cases, struggles without a smooth score, and some gains could have been matched by traditional methods. It exploited weak verifiers in some problems (for example numerical integration in Problem 6.6), and results depended on expert prompt advice.
How it generalizes the harness
The evolutionary search and evaluators do the solving, and the outputs are mathematical constructions or formulas that stand without the model.
Classification
| What it proposes | Mathematical construction |
|---|---|
| Generative model | Gemini-based AlphaEvolve (frozen), with Deep Think and AlphaProof for proof steps |
| Algorithmic authority | Deterministic evaluator scoring the construction; some results later proven by hand or in Lean (one simple Kakeya case) |
| Feedback | Score |
| What gets updated | Prompt context and population of candidates |
| When it runs | At inference time |
| Validity | Empirical (measured) |
| Evidence | Experiments reported |
| Lineage | Application |