Towards Autonomous Mathematics Research
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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.
Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Builds on 11 of its 48 references that are in the map. First posted on arXiv 10 Feb 2026.
Builds on
11 of 48 references.
References · 11
- 2026Learning to Discover at Test Timecited by 94
- 2025From Automation to Autonomy: A Survey on Large Language Models in Scientific Discoverycited by 86
- 2025Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipelinecited by 79
- 2025Mathematical exploration and discovery at scalecited by 66
- 2026Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the ErdHos Problemscited by 24
- 2025Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proofcited by 10
- 2025UQ: Assessing Language Models on Unsolved Questionscited by 9
- 2025G"odel Test: Can Large Language Models Solve Easy Conjectures?cited by 5
- 2025Accelerating mathematical research with language models: A case study of an interaction with GPT-5-Pro on a convex analysis problemcited by 5
- 2026Strongly Polynomial Time Complexity of Policy Iteration for L_∞ Robust MDPscited by 5
- 2025A Human-AI Collaborative Workflow for Mathematical Discovery: A Case Study in Grover-Compatible Riemannian Optimizationcited by 4
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Citing papers per year: 2026: 31.
31 papers.
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- 2026Nemotron 3 Ultra: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoningcited by 32
- 2026Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loopscited by 25
- 2026Automated Conjecture Resolution with Formal Verificationcited by 21
- 2026Scaling Test-Time Compute for Agentic Codingcited by 11
- 2026Semi-Autonomous Formalization of the Vlasov-Maxwell-Landau Equilibriumcited by 7
- 2026RMA: an Agentic System for Research-Level Mathematical Problemscited by 6
- 2026Formalizing Mathematics at Scalecited by 5
- 2026Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memorycited by 5
- 2026Matlas: A Semantic Search Engine for Mathematicscited by 3
- 2026SPIRAL: Learning to Search and Aggregatecited by 3
- 2026Verify to Amplify: Improving Reasoning via Learned Chain-of-Thought Verificationcited by 2
- 2026Deep Research of Deep Research: From Transformer to Agent, From AI to AI for Sciencecited by 1
19 more
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- 2026From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontiercited by 1
- 2026ReasFlow: Assisting Reasoning-Centric Scientific Discovery in Applied Mathematics via a Knowledge-Based Multi-Agent Systemcited by 1
- 2026VALG: An Agentic System for ML Theory Researchcited by 1
- 2026RecEvolve: A Knowledge-Driven Autonomous Agent System for Recommender Systemscited by 1
- 2026Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking)cited by 0
- 2026Efficient Reasoning on the Edgecited by 0
- 2026EDM-ARS: A Domain-Specific Multi-Agent System for Automated Educational Data Mining Researchcited by 0
- 2026R-equivalence on Cubic Surfaces I: Existing Cases with Non-Trivial Universal Equivalencecited by 0
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- 2026Entropy Centroids as Intrinsic Rewards for Test-Time Scalingcited by 0
- 2026Stable Menus of Public Goods: AI-Enabled Progresscited by 0
- 2026Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Sciencecited by 0
- 2026TCSAlgBench: Benchmarking Automated Proving for Research-Level Theoretical Computer Sciencecited by 0
- 2026Thinking Outside the Box: Can Language Models Rely on External Guidance Selectively?cited by 0
- 2026Cogentic: Multi-Agent Orchestration for Automated Proof Discoverycited by 0
- 2026From Expert-Guided Proof Search to Automated Open-Problem Solvingcited by 0
- 2026From Expert-Guided Proof Search to Automated Open-Problem Solving7 Oct 2026
- 2026Cogentic: Multi-Agent Orchestration for Automated Proof Discovery30 Sep 2026
- 2026Thinking Outside the Box: Can Language Models Rely on External Guidance Selectively?30 Sep 2026
- 2026TCSAlgBench: Benchmarking Automated Proving for Research-Level Theoretical Computer Science28 Sep 2026
- 2026Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science14 Sep 2026
- 2026VALG: An Agentic System for ML Theory Research13 Aug 2026
- 2026RecEvolve: A Knowledge-Driven Autonomous Agent System for Recommender Systems20 Jul 2026
- 2026ReasFlow: Assisting Reasoning-Centric Scientific Discovery in Applied Mathematics via a Knowledge-Based Multi-Agent System15 Jul 2026
- 2026From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier8 Jul 2026
- 2026Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops8 Jul 2026
- 2026Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory7 Jul 2026
- 2026SPIRAL: Learning to Search and Aggregate22 Jun 2026
19 more
- 2026Stable Menus of Public Goods: AI-Enabled Progress15 Jun 2026
- 2026Nemotron 3 Ultra: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning12 Jun 2026
- 2026Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discovery7 Jun 2026
- 2026Formalizing Mathematics at Scale28 May 2026
- 2026RMA: an Agentic System for Research-Level Mathematical Problems20 May 2026
- 2026TMAS: Scaling Test-Time Compute via Multi-Agent Synergy11 May 2026
- 2026Entropy Centroids as Intrinsic Rewards for Test-Time Scaling28 Apr 2026
- 2026Fine-Tuning Small Reasoning Models for Quantum Field Theory21 Apr 2026
- 2026Matlas: A Semantic Search Engine for Mathematics19 Apr 2026
- 2026Scaling Test-Time Compute for Agentic Coding16 Apr 2026
- 2026k-server-bench: Automating Potential Discovery for the k-Server Conjecture8 Apr 2026
- 2026Automated Conjecture Resolution with Formal Verification4 Apr 2026
- 2026Deep Research of Deep Research: From Transformer to Agent, From AI to AI for Science30 Mar 2026
- 2026R-equivalence on Cubic Surfaces I: Existing Cases with Non-Trivial Universal Equivalence19 Mar 2026
- 2026EDM-ARS: A Domain-Specific Multi-Agent System for Automated Educational Data Mining Research18 Mar 2026
- 2026Efficient Reasoning on the Edge17 Mar 2026
- 2026Semi-Autonomous Formalization of the Vlasov-Maxwell-Landau Equilibrium16 Mar 2026
- 2026Verify to Amplify: Improving Reasoning via Learned Chain-of-Thought Verification3 Mar 2026
- 2026Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking)21 Feb 2026
- 2026Nemotron 3 Ultra: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoningcited by 32
- 2026Automated Conjecture Resolution with Formal Verificationcited by 21
- 2026Scaling Test-Time Compute for Agentic Codingcited by 11
- 2026Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memorycited by 5
- 2026SPIRAL: Learning to Search and Aggregatecited by 3
- 2026Verify to Amplify: Improving Reasoning via Learned Chain-of-Thought Verificationcited by 2
- 2026Deep Research of Deep Research: From Transformer to Agent, From AI to AI for Sciencecited by 1
- 2026Fine-Tuning Small Reasoning Models for Quantum Field Theorycited by 1
- 2026TMAS: Scaling Test-Time Compute via Multi-Agent Synergycited by 1
- 2026Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discoverycited by 1
- 2026ReasFlow: Assisting Reasoning-Centric Scientific Discovery in Applied Mathematics via a Knowledge-Based Multi-Agent Systemcited by 1
- 2026Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking)cited by 0
12 most cited of 15 All 15 (JSON)
- 2026Thinking Outside the Box: Can Language Models Rely on External Guidance Selectively?30 Sep 2026
- 2026ReasFlow: Assisting Reasoning-Centric Scientific Discovery in Applied Mathematics via a Knowledge-Based Multi-Agent System15 Jul 2026
- 2026Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory7 Jul 2026
- 2026SPIRAL: Learning to Search and Aggregate22 Jun 2026
- 2026Nemotron 3 Ultra: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning12 Jun 2026
- 2026Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discovery7 Jun 2026
- 2026TMAS: Scaling Test-Time Compute via Multi-Agent Synergy11 May 2026
- 2026Entropy Centroids as Intrinsic Rewards for Test-Time Scaling28 Apr 2026
- 2026Fine-Tuning Small Reasoning Models for Quantum Field Theory21 Apr 2026
- 2026Scaling Test-Time Compute for Agentic Coding16 Apr 2026
- 2026Automated Conjecture Resolution with Formal Verification4 Apr 2026
- 2026Deep Research of Deep Research: From Transformer to Agent, From AI to AI for Science30 Mar 2026
12 newest of 15 All 15 (JSON)
- 2026RMA: an Agentic System for Research-Level Mathematical Problemscited by 6
- 2026VALG: An Agentic System for ML Theory Researchcited by 1
- 2026RecEvolve: A Knowledge-Driven Autonomous Agent System for Recommender Systemscited by 1
- 2026EDM-ARS: A Domain-Specific Multi-Agent System for Automated Educational Data Mining Researchcited by 0
- 2026Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Sciencecited by 0
- 2026Cogentic: Multi-Agent Orchestration for Automated Proof Discoverycited by 0
- 2026Cogentic: Multi-Agent Orchestration for Automated Proof Discovery30 Sep 2026
- 2026Stellar Colosseum: A Many-Agent Harness for Long-Horizon Research in Mathematics and Theoretical Computer Science14 Sep 2026
- 2026VALG: An Agentic System for ML Theory Research13 Aug 2026
- 2026RecEvolve: A Knowledge-Driven Autonomous Agent System for Recommender Systems20 Jul 2026
- 2026RMA: an Agentic System for Research-Level Mathematical Problems20 May 2026
- 2026EDM-ARS: A Domain-Specific Multi-Agent System for Automated Educational Data Mining Research18 Mar 2026
- 2026Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loopscited by 25
- 2026Semi-Autonomous Formalization of the Vlasov-Maxwell-Landau Equilibriumcited by 7
- 2026Formalizing Mathematics at Scalecited by 5
- 2026Matlas: A Semantic Search Engine for Mathematicscited by 3
- 2026From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontiercited by 1
- 2026R-equivalence on Cubic Surfaces I: Existing Cases with Non-Trivial Universal Equivalencecited by 0
- 2026k-server-bench: Automating Potential Discovery for the k-Server Conjecturecited by 0
- 2026Stable Menus of Public Goods: AI-Enabled Progresscited by 0
- 2026TCSAlgBench: Benchmarking Automated Proving for Research-Level Theoretical Computer Sciencecited by 0
- 2026From Expert-Guided Proof Search to Automated Open-Problem Solvingcited by 0
- 2026From Expert-Guided Proof Search to Automated Open-Problem Solving7 Oct 2026
- 2026TCSAlgBench: Benchmarking Automated Proving for Research-Level Theoretical Computer Science28 Sep 2026
- 2026From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier8 Jul 2026
- 2026Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops8 Jul 2026
- 2026Stable Menus of Public Goods: AI-Enabled Progress15 Jun 2026
- 2026Formalizing Mathematics at Scale28 May 2026
- 2026Matlas: A Semantic Search Engine for Mathematics19 Apr 2026
- 2026k-server-bench: Automating Potential Discovery for the k-Server Conjecture8 Apr 2026
- 2026R-equivalence on Cubic Surfaces I: Existing Cases with Non-Trivial Universal Equivalence19 Mar 2026
- 2026Semi-Autonomous Formalization of the Vlasov-Maxwell-Landau Equilibrium16 Mar 2026
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