Towards Autonomous Mathematics Research

Recent advances in foundational models have yielded reasoning systems capable of achieving a gold-medal standard at the International Mathematical Olympiad. The transition from competition-level problem-solving to professional research, however, requires navigating vast literature and constructing long-horizon proofs. In this work, we introduce Aletheia, a math research agent that iteratively generates, verifies, and revises solutions end-to-end in natural language. Specifically, Aletheia is powered by an advanced version of Gemini Deep Think for challenging reasoning problems, a novel inference-time scaling law that extends beyond Olympiad-level problems, and intensive tool use to navigate the complexities of mathematical research. We demonstrate the capability of Aletheia from Olympiad problems to PhD-level exercises and most notably, through several distinct milestones in AI-assisted mathematics research: (a) a research paper (Feng26) generated by AI without any human intervention in calculating certain structure constants in arithmetic geometry called eigenweights; (b) a research paper (LeeSeo26) demonstrating human-AI collaboration in proving bounds on systems of interacting particles called independent sets; and (c) an extensive semi-autonomous evaluation (Feng et al., 2026a) of 700 open problems on Bloom's Erdos Conjectures database, including autonomous solutions to four open questions. 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, as well as propose a novel concept of human-AI interaction cards for transparency. We conclude with reflections on human-AI collaboration in mathematics and share all prompts as well as model outputs at https://github.com/google-deepmind/superhuman/tree/main/aletheia.

Gemini: A Family of Highly Capable Multimodal Models

This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultra model advances the state of the art in 30 of 32 of these benchmarks - notably being the first model to achieve human-expert performance on the well-studied exam benchmark MMLU, and improving the state of the art in every one of the 20 multimodal benchmarks we examined. We believe that the new capabilities of Gemini models in cross-modal reasoning and language understanding will enable a wide variety of use cases and we discuss our approach toward deploying them responsibly to users.