Automated Theorem Proving

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Automated theorem proving studies how to turn goals and assumptions into proofs that trusted checkers can validate, supporting dependable mathematics and software verification. Approaches range from symbolic search, resolution, tableaux, SAT/SMT solving, and tactics to language models that retrieve lemmas, decompose goals, learn from proof traces, and use Lean, Rocq, Isabelle, or Dafny feedback. Evaluation spans contest benchmarks such as miniF2F and PutnamBench, large proof libraries, code-verification tasks, and research-level problems. A central challenge is moving from benchmark success to robust, economical proofs whose formal statements faithfully capture the intended mathematics or specifications; autoformalization and semantic verification remain difficult.

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160 papers29 papers in the last four weeks, up 142% on the four weeks before. 0.2% of all new papers.

Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking)
Feb 21, 2026Brecht Verbeken, Brando Vagenende, Marie-Anne Guerry +2Large Language Model-Guided Theorem Proving LLM Mathematical Reasoning
Data Analytics Lab, Vrije Universiteit Brussel, Pleinlaan 5, 1050 Brussel, Belgium · imec-SMIT, Vrije Universiteit Brussel, Pleinlaan 9, 1050 Brussels, Belgium · School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
When Agda met Vampire
Feb 21, 2026Artjoms Šinkarovs, Michael RawsonInteractive Theorem Proving Automated Theorem Proving
Electronics and Computer Science, University of Southampton, UK
Nazrin: An Atomic Neural Proof Automation Tactic in Lean 4
Feb 21, 2026Leni Aniva, Iori Oikawa, David Dill +1Automated Theorem Proving Lean Theorem Proving
Stanford University, Stanford, U.S. · Northeastern University, Massachusetts, U.S. · Stanford University
M2F: Automated Formalization of Mathematical Literature at Scale
Feb 19, 2026Zichen Wang, Wanli Ma, Zhenyu Ming +3Autoformalization Formal Verification
School of Mathematical Sciences, Peking University · Beijing International Center for Mathematical Research, Peking University · Huawei Technologies +1
GDEPO: Group Dual-dynamic and Equal-right Advantage Policy Optimization for Sample-Efficient Reinforcement Learning
Jan 11, 2026Zhengqing Yan, Fan Guo, Xinyang Liu +5Group Relative Policy Optimization Reinforcement Learning with Verifiable Rewards
State Key Laboratory of Engines, Tianjin University, 300354 Tianjin, China. · Artificial Intelligence Center, Cylingo Group, 100080 Beijing, China.
MINIF2F-DAFNY: LLM-Guided Mathematical Theorem Proving via Auto-Active Verification
Dec 11, 2025Mantas Baksys, Stefan Zetzsche, Olivier Bouissou +1Automated Theorem Proving Formal Verification
University of Cambridge, Cambridge, UK · Amazon Web Services, London, UK · Amazon Web Services, Boston, USA
TopoAlign: A Framework for Aligning Code to Math via Topological Decomposition
Oct 13, 2025Yupei Li, Philipp Borchert, Gerasimos LampourasAutomated Theorem Proving Autoformalization
1Imperial College London, UK · *Work conducted during an internship at Huawei Noah’s Ark Lab, London. · 2Huawei Noah’s Ark Lab, London, UK
Discovering New Theorems via LLMs with In-Context Proof Learning in Lean
Sep 16, 2025Kazumi Kasaura, Naoto Onda, Yuta Oriike +3Automated Theorem Proving In-Context Learning
OMRON SINIC X Corporation · RIKEN AIP · AutoRes +7
AI Mathematician: Towards Fully Automated Frontier Mathematical Research
May 28, 2025Yuanhang Liu, Yanxing Huang, Yanqiao Wang +2AI-Assisted Mathematical Discovery AI-Assisted Scientific Research
Qiuzhen College, Tsinghua University · Department of Mathematical Sciences, Tsinghua University · Institute for AI Industry Research (AIR), Tsinghua University, Beijing, China +1
Reliable Proof Generation with LLMs via Analogical Retrieval and Symbolic Verification: A Case Study in Euclidean Geometry
May 20, 2025Oren Sultan, Eitan Stern, Dafna ShahafAutomated Theorem Proving Neuro-Symbolic Reasoning
The Hebrew University of Jerusalem

Feb 21, 2026J/K move · Enter open · S save

Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking)

Brecht Verbeken, Brando Vagenende, Marie-Anne Guerry, Andres Algaba+1

Data Analytics Lab, Vrije Universiteit Brussel, Pleinlaan 5, 1050 Brussel, Belgium · imec-SMIT, Vrije Universiteit Brussel, Pleinlaan 9, 1050 Brussels, Belgium · School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

Large Language Model-Guided Theorem Proving LLM Mathematical Reasoning Automated Theorem Proving LLM Evaluation

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Large Language Models (LLMs) are increasingly used as scientific copilots, but evidence on their role in research-level mathematics remains limited, especially for workflows accessible to individual researchers. We present early evidence for vibe-proving with a consumer subscription LLM through an auditable case study that resolves Conjecture 20 of Ran and Teng (2024) on the exact nonreal spectral region of a 4-cycle row-stochastic nonnegative matrix family. We analyze seven shareable ChatGPT-5.2 (Thinking) threads and four versioned proof drafts, documenting an iterative pipeline of generate, referee, and repair. The model is most useful for high-level proof search, while human experts remain essential for correctness-critical closure. The final theorem provides necessary and sufficient region conditions and explicit boundary attainment constructions. Beyond the mathematical result, we contribute a process-level characterization of where LLM assistance materially helps and where verification bottlenecks persist, with implications for evaluation of AI-assisted research workflows and for designing human-in-the-loop theorem proving systems.