Towards Autonomous Mathematics Research

摘要

Recent advances in foundational models have yielded reasoning systems capable of achieving a gold-medal standard at the International Mathematical Olympiad. We undertake the transition from competition-level problem solving to professional research, which presents significant new challenges. To this end we introduce Aletheia, a math research agent that iteratively generates, verifies, and revises solutions end-to-end in natural language, leveraging a novel inference-time scaling law based upon Gemini Deep Think. We demonstrate the capability of Aletheia through several milestones in autonomous mathematics research: multiple publication-grade papers, including one with no human intervention (17); an extensive semi-autonomous evaluation Feng et al. (2026b) on 700 open problems from Bloom’s Erdős Conjectures database, including autonomous solutions to four open questions; and a leading performance on FirstProof, a collection of research-level problems proposed by mathematicians to assess AI capabilities for mathematical research. Full transcripts of prompts and model outputs are shared at https://github.com/google-deepmind/superhuman/tree/main/aletheia. In order to help the public better understand the developments pertaining to AI and mathematics, we suggest quantifying standard levels of autonomy and novelty of AI-assisted results, and propose the concept of “human-AI interaction cards” for transparent documentation. We conclude with reflections on human-AI collaboration in mathematics.