Ten advances in mathematics and theoretical computer science

OpenAI used an internal version of its upcoming Astra model to solve ten difficult mathematics and theoretical computer science problems that had seen no progress on their main results for at least a decade. The company reports spending less than two thousand dollars in token costs for each solved problem. To support these findings, OpenAI released an accompanying research paper, Lean four formalizations of the results, and an LLM-generated document that reconstructs how the proofs were developed using unpublished reasoning traces.

This milestone has provoked varied reactions within the mathematical community. Some mathematicians are experiencing a profound spiritual crisis over these developments, comparing the situation to Deep Blue and worrying about the future of human-led research. Conversely, others view AI as a catalyst for a fundamental shift toward large-scale, decentralized human and machine collaborations where machines handle technical grunt work while humans retain creative roles.