FunSearch made the biggest cap-set gain in 20 years

The cap set problem, a long-standing question in extremal combinatorics about the largest set of points containing no three in a line, had seen little movement for years. In December 2023, DeepMind reported that FunSearch - a large language model paired with an automated evaluator that searches over computer programs - found new cap-set constructions larger than any previously known, the largest improvement to the problem in twenty years. Because every candidate was a verifiable program checked by the evaluator, the discovery was provably correct rather than a plausible-sounding guess from the model.