# Towards Autonomous Mathematics Research

arXiv: https://arxiv.org/abs/2602.10177 · HTML: https://mlsanity.com/paper/2602.10177/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 48 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Builds on (most cited first, 11 of 11)

- [Learning to Discover at Test Time](https://mlsanity.com/paper/2601.16175/) (2026)
- [From Automation to Autonomy: A Survey on Large Language Models in Scientific Discovery](https://mlsanity.com/paper/2505.13259/) (2025)
- [Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipeline](https://mlsanity.com/paper/2507.15855/) (2025)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the ErdHos Problems](https://mlsanity.com/paper/2601.22401/) (2026)
- [Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof](https://mlsanity.com/paper/2510.23513/) (2025)
- [UQ: Assessing Language Models on Unsolved Questions](https://mlsanity.com/paper/2508.17580/) (2025)
- [G"odel Test: Can Large Language Models Solve Easy Conjectures?](https://mlsanity.com/paper/2509.18383/) (2025)
- [Accelerating mathematical research with language models: A case study of an interaction with GPT-5-Pro on a convex analysis problem](https://mlsanity.com/paper/2510.26647/) (2025)
- [Strongly Polynomial Time Complexity of Policy Iteration for L_∞ Robust MDPs](https://mlsanity.com/paper/2601.23229/) (2026)
- [A Human-AI Collaborative Workflow for Mathematical Discovery: A Case Study in Grover-Compatible Riemannian Optimization](https://mlsanity.com/paper/2512.09443/) (2025)

## Built on by (most cited first, 30 of 40)

- [Nemotron 3 Ultra: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning](https://mlsanity.com/paper/2606.15007/) (2026)
- [Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops](https://mlsanity.com/paper/2607.07663/) (2026)
- [Automated Conjecture Resolution with Formal Verification](https://mlsanity.com/paper/2604.03789/) (2026)
- [Scaling Test-Time Compute for Agentic Coding](https://mlsanity.com/paper/2604.16529/) (2026)
- [Formalizing Mathematics at Scale](https://mlsanity.com/paper/2605.29955/) (2026)
- [Semi-Autonomous Formalization of the Vlasov-Maxwell-Landau Equilibrium](https://mlsanity.com/paper/2603.15929/) (2026)
- [Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory](https://mlsanity.com/paper/2607.06447/) (2026)
- [RMA: an Agentic System for Research-Level Mathematical Problems](https://mlsanity.com/paper/2605.22875/) (2026)
- [Verify to Amplify: Improving Reasoning via Learned Chain-of-Thought Verification](https://mlsanity.com/paper/2603.03538/) (2026)
- [CREBench: Evaluating Large Language Models in Cryptographic Binary Reverse Engineering](https://mlsanity.com/paper/2604.03750/) (2026)
- [Matlas: A Semantic Search Engine for Mathematics](https://mlsanity.com/paper/2604.17484/) (2026)
- [SPIRAL: Learning to Search and Aggregate](https://mlsanity.com/paper/2606.23595/) (2026)
- [VALG: An Agentic System for ML Theory Research](https://mlsanity.com/paper/2608.13060/) (2026)
- [The Problem Is the Problem: Towards Scalable Mathematical Discovery](https://mlsanity.com/paper/2608.16977/) (2026)
- [Accelerating Scientific Research with Gemini in the Real-World](https://mlsanity.com/paper/2608.26701/) (2026)
- [Deep Research of Deep Research: From Transformer to Agent, From AI to AI for Science](https://mlsanity.com/paper/2603.28361/) (2026)
- [Fine-Tuning Small Reasoning Models for Quantum Field Theory](https://mlsanity.com/paper/2604.18936/) (2026)
- [TMAS: Scaling Test-Time Compute via Multi-Agent Synergy](https://mlsanity.com/paper/2605.10344/) (2026)
- [Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discovery](https://mlsanity.com/paper/2606.08728/) (2026)
- [From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier](https://mlsanity.com/paper/2607.07779/) (2026)
- [ReasFlow: Assisting Reasoning-Centric Scientific Discovery in Applied Mathematics via a Knowledge-Based Multi-Agent System](https://mlsanity.com/paper/2607.14178/) (2026)
- [MECA: A Mechanism-Centered Agent for Constructing Well-Specified and Valuable Mathematical Conjectures](https://mlsanity.com/paper/2607.27709/) (2026)
- [RecEvolve: A Knowledge-Driven Autonomous Agent System for Recommender Systems](https://mlsanity.com/paper/2609.01622/) (2026)
- [Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science](https://mlsanity.com/paper/2609.15983/) (2026)
- [Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking)](https://mlsanity.com/paper/2602.18918/) (2026)
- [Efficient Reasoning on the Edge](https://mlsanity.com/paper/2603.16867/) (2026)
- [EDM-ARS: A Domain-Specific Multi-Agent System for Automated Educational Data Mining Research](https://mlsanity.com/paper/2603.18273/) (2026)
- [R-equivalence on Cubic Surfaces I: Existing Cases with Non-Trivial Universal Equivalence](https://mlsanity.com/paper/2603.19215/) (2026)
- [k-server-bench: Automating Potential Discovery for the k-Server Conjecture](https://mlsanity.com/paper/2604.07240/) (2026)
- [Lectures on AI for Mathematics](https://mlsanity.com/paper/2604.11504/) (2026)

## Abstract (arXiv)

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.