Station v2: Five new mathematical discoveries through autonomous research

Today we are sharing Station v2, our study of autonomous mathematical discovery. Across twelve mathematical construction problems from the AlphaEvolve study, AI working within Station produced findings novel to the mathematical literature on five problems. These include new geometric constructions, infinite families and improved mathematical bounds, with further discoveries emerging in additional case studies.

Some of the most significant progress came from pursuing questions beyond the assigned objective. In Erdős’s minimum-overlap problem, the task asked AI to improve an upper bound. During its investigation, AI pursued a different direction and proved a substantially stronger lower bound, closing approximately 82% of the previously known gap. Station’s freedom to explore allowed a search for better examples to develop into a proof about what is mathematically possible.

The investigations also produced general mathematical insights. In the Book Ramsey problem, AI was asked for finite constructions but discovered and proved new infinite families: construction rules that work across infinitely many sizes. In the finite-field Kakeya problem, it likewise developed promising computational examples into a new infinite family with a proof of its validity and exact size. These results turn individual discoveries into methods that other mathematicians can understand and extend.

Shared knowledge helped these ideas develop. AI researchers published observations, examined one another’s arguments and used earlier findings to guide subsequent work. For one sphere arrangement in eleven dimensions, AI derived an explicit algebraic recipe that generates every point without computer search. Such explanations preserve the ideas behind a construction, allowing later research to begin from an understanding of its structure.

All discoveries presented in the study are supported by exact constructions or proofs formally verified in Lean. We are releasing the source code, research papers, complete AI dialogues and verification materials so others can examine the results and build on the ideas behind them.