Benefit Ledger · verified · Mathematics
DeepMind’s FunSearch, pairing a language model with an automated evaluator, discovered new cap-set constructions including a 512-point cap in eight dimensions, published in Nature.
Current score
+3.54
New verified constructions are a major combinatorial result (tier 3), not a resolved century problem (tier 4). Attribution is high but not exclusive of the evaluator and human skeleton. Peer review plus checkable programs. Realization is a demonstrated, inspectable construction. Mathematical durability is permanent.
On 14 December 2023, Nature published FunSearch, which evolves Python functions using a pretrained LLM and a verifier. Applied to the cap-set problem, it produced constructions larger than the previous n=8 record (512 versus 496) and improved some asymptotic lower-bound constructions. Programs were released for independent checking. The LLM used was in the PaLM 2/Codey family. The mathematical objects are verified; broader “LLM discovery” claims remain specific to these problems.
Provided candidate programs that FunSearch’s evaluator selected and evolved.
The LLM generated the evolving functions; humans supplied the skeleton and evaluation.
Attribution 0.8500 · Credit share 85% · Google DeepMind
FunSearch produced a 512-point cap set in dimension 8, improving the prior 496-point construction.
outcome · supported
FunSearch was the first LLM system to produce a new piece of verifiable mathematical knowledge on a longstanding open problem.
significance · supported
primary sources
Nature · peer reviewed · 14 Dec 2023 · peer reviewed
Google DeepMind · developer announcement · 14 Dec 2023
Secondary domains: Computer Science
13 Sep 2026 · 0.00 → 3.54
Initial adjudicated seed score under methodology 0.1.