Primary evidence
- Mathematical discoveries from program search with large language modelsS1 · Primary research · Paper · 2023-12-14
FunSearch reports new cap-set constructions with LLM-guided program search
Google DeepMind paired a pretrained language model with an evaluator and evolutionary program search. The resulting system searched over executable programs rather than directly emitting final mathematical answers.
What happened?
FunSearch found cap-set constructions exceeding previously known constructions in finite-dimensional and asymptotic settings, and also found improved heuristics for online bin packing.
Why it matters
The result supplied a concrete, checkable example of LLM-generated code participating in a search process that improved the known solution landscape of an established mathematical problem.
Significance rationale: The Nature paper demonstrated an LLM-based search loop producing improved constructions for an established extremal-combinatorics problem, making it a useful early reference point for AI-assisted mathematical discovery.
Historical context
Earlier developments
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Later developments
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Related milestones
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Evidence & status at a glance
- Significance
- H1 · Historical milestone
- Verification
- Paper released
- Evidence level
- E2 · Research record
- AI role
- AI primary, human verified
- Formal assurance
- No formal assurance
Contribution & verification
- Mathematical novelty
- New result
- Interface
- Informal, Numeric
- AI contribution
- The language model generated candidate programs inside an automated evolutionary loop, while deterministic evaluators selected and scored candidates.
- Human contribution
- Researchers designed the search procedure and evaluators, chose the mathematical tasks and representations, interpreted the discovered programs, and authored the scientific analysis.
- Verification
- Paper released · E2 · Research record · No formal assurance
- Last reviewed
- 2026-09-11
Technical details
- Systems
- funsearch
- Organizations
- google-deepmind
- Problems
- cap-set-problem, online-bin-packing
- Methods
- large-language-models, evolutionary-search, program-search
Sources & artifacts
- Mathematical discoveries from program search with large language modelsS1 · Primary research · Paper · accessed 2026-09-10
- FunSearch — Making new discoveries in mathematical sciences using Large Language ModelsS2 · Official institutional · Official announcement · accessed 2026-09-10
Verification history
- 2023-12-14 · Paper released · E2 · Research record
Peer-reviewed Nature article and official institutional announcement were public.
Corrections
No corrections recorded.