Autoformalization in the Era of Large Language Models: A Survey
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Abstract (arXiv)
Autoformalization, the process of transforming informal mathematical propositions into verifiable formal representations, is a foundational task in automated theorem proving, offering a new perspective on the use of mathematics in both theoretical and applied domains. Driven by the rapid progress in artificial intelligence, particularly large language models (LLMs), this field has witnessed substantial growth, bringing both new opportunities and unique challenges. In this survey, we provide a comprehensive overview of recent advances in autoformalization from both mathematical and LLM-centric perspectives. We examine how autoformalization is applied across various mathematical domains and levels of difficulty, and analyze the end-to-end workflow from data preprocessing to model design and evaluation. We further explore the emerging role of autoformalization in enhancing the verifiability of LLM-generated outputs, highlighting its potential to improve both the trustworthiness and reasoning capabilities of LLMs. Finally, we summarize key open-source models and datasets supporting current research, and discuss open challenges and promising future directions for the field.
Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 37 of its 64 references that are in the map. First posted on arXiv 29 May 2025.
Builds on
37 of 64 references.
References · 37
- 2021MiniF2F: a cross-system benchmark for formal Olympiad-level mathematicscited by 380
- 2023Can AI-Generated Text be Reliably Detected?cited by 372
- 2022Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofscited by 278
- 2025DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decompositioncited by 270
- 2022Autoformalization with Large Language Modelscited by 252
- 2024DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Datacited by 225
- 2024DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Searchcited by 189
- 2025Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learningcited by 173
- 2025Goedel-Prover: A Frontier Model for Open-Source Automated Theorem Provingcited by 126
- 2025BFS-Prover: Scalable Best-First Tree Search for LLM-based Automatic Theorem Provingcited by 82
- 2024Formal Mathematical Reasoning: A New Frontier in AIcited by 80
- 2024A Survey on Deep Learning for Theorem Provingcited by 55
25 more
- 2024SpecGen: Automated Generation of Formal Program Specifications via Large Language Modelscited by 51
- 2025FormalMATH: Benchmarking Formal Mathematical Reasoning of Large Language Modelscited by 45
- 2015A formal proof of the Kepler conjecturecited by 42
- 2024Autoformalize Mathematical Statements by Symbolic Equivalence and Semantic Consistencycited by 39
- 2023Finding Inductive Loop Invariants using Large Language Modelscited by 35
- 2024AlphaVerus: Bootstrapping Formally Verified Code Generation through Self-Improving Translation and Treefinementcited by 33
- 2023Towards Autoformalization of Mathematics and Code Correctness: Experiments with Elementary Proofscited by 27
- 2024Divide and Translate: Compositional First-Order Logic Translation and Verification for Complex Logical Reasoningcited by 27
- 2024Reliable Evaluation and Benchmarks for Statement Autoformalizationcited by 25
- 2023Lyra: Orchestrating Dual Correction in Automated Theorem Provingcited by 24
- 2025PDE-Controller: LLMs for Autoformalization and Reasoning of PDEscited by 23
- 2022Towards a Mathematics Formalisation Assistant using Large Language Modelscited by 22
- 2023Towards Verifiable Text Generation with Symbolic Referencescited by 13
- 2023A New Approach Towards Autoformalizationcited by 10
- 2024GFLean: An Autoformalisation Framework for Lean via GFcited by 9
- 2023SoTaNa: The Open-Source Software Development Assistantcited by 8
- 2024Learning Guided Automated Reasoning: A Brief Surveycited by 7
- 2025Instantiation-based Formalization of Logical Reasoning Tasks using Language Models and Logical Solverscited by 7
- 2025APE-Bench: Evaluating Automated Proof Engineering for Formal Math Librariescited by 6
- 2025Knowledge Augmented Complex Problem Solving with Large Language Models: A Surveycited by 6
- 2025Step-Wise Formal Verification for LLM-Based Mathematical Problem Solvingcited by 5
- 2025From Knowledge Generation to Knowledge Verification: Examining the BioMedical Generative Capabilities of ChatGPTcited by 4
- 2025Lean-ing on Quality: How High-Quality Data Beats Diverse Multilingual Data in AutoFormalizationcited by 4
- 2025A Combinatorial Identities Benchmark for Theorem Proving via Automated Theorem Generationcited by 4
- 2025Augmenting Smart Contract Decompiler Output through Fine-grained Dependency Analysis and LLM-facilitated Semantic Recoverycited by 2
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Citing papers per year: 2025: 6; 2026: 13.
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- 2025Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physicscited by 27
- 2025StepFun-Formalizer: Unlocking the Autoformalization Potential of LLMs through Knowledge-Reasoning Fusioncited by 15
- 2025ASSESS: A Semantic and Structural Evaluation Framework for Statement Similaritycited by 8
- 2025Towards a Common Framework for Autoformalizationcited by 7
- 2026OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inferencecited by 4
- 2026DreamProver: Evolving Transferable Lemma Libraries via a Wake-Sleep Theorem-Proving Agentcited by 4
- 2026Formalizing Numerical Analysis: An Agent Pipeline and Quality Audit Beyond Kernel Acceptancecited by 3
- 2026Theory-Scale Auto-Formalization of Logics for Computer Sciencecited by 3
- 2026FormalRx: Rectify and eXamine Semantic Failures in Autoformalizationcited by 2
- 2026TheoremBench: Evaluating LLMs on Theorem Proving in Formal Mathematicscited by 1
- 2026Autoformalization of Agent Instructions into Policy-as-Codecited by 1
- 2026VALG: An Agentic System for ML Theory Researchcited by 1
7 more
- 2025Mathematics with large language models as provers and verifierscited by 0
- 2025Towards Autoformalization of LLM-generated Outputs for Requirement Verificationcited by 0
- 2026SFT-GRPO Data Overlap as a Post-Training Hyperparameter for Autoformalizationcited by 0
- 2026Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discoverycited by 0
- 2026Visored: A Controlled-Natural-Language Prover for LLM-Generated Mathematicscited by 0
- 2026MioFFAn: an Annotation Software for Formula Formalization with LLM Automation Capabilitiescited by 0
- 2026ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimizationcited by 0
- 2026ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimization28 Sep 2026
- 2026VALG: An Agentic System for ML Theory Research13 Aug 2026
- 2026FormalRx: Rectify and eXamine Semantic Failures in Autoformalization6 Jul 2026
- 2026Autoformalization of Agent Instructions into Policy-as-Code25 Jun 2026
- 2026Theory-Scale Auto-Formalization of Logics for Computer Science25 Jun 2026
- 2026Visored: A Controlled-Natural-Language Prover for LLM-Generated Mathematics16 Jun 2026
- 2026Formalizing Numerical Analysis: An Agent Pipeline and Quality Audit Beyond Kernel Acceptance12 Jun 2026
- 2026TheoremBench: Evaluating LLMs on Theorem Proving in Formal Mathematics8 Jun 2026
- 2026MioFFAn: an Annotation Software for Formula Formalization with LLM Automation Capabilities15 May 2026
- 2026DreamProver: Evolving Transferable Lemma Libraries via a Wake-Sleep Theorem-Proving Agent29 Apr 2026
- 2026Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discovery23 Apr 2026
- 2026SFT-GRPO Data Overlap as a Post-Training Hyperparameter for Autoformalization15 Apr 2026
7 more
- 2026OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inference2 Feb 2026
- 2025Towards Autoformalization of LLM-generated Outputs for Requirement Verification14 Nov 2025
- 2025Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics14 Oct 2025
- 2025Mathematics with large language models as provers and verifiers11 Oct 2025
- 2025ASSESS: A Semantic and Structural Evaluation Framework for Statement Similarity26 Sep 2025
- 2025Towards a Common Framework for Autoformalization11 Sep 2025
- 2025StepFun-Formalizer: Unlocking the Autoformalization Potential of LLMs through Knowledge-Reasoning Fusion6 Aug 2025
- 2026DreamProver: Evolving Transferable Lemma Libraries via a Wake-Sleep Theorem-Proving Agentcited by 4
- 2026Formalizing Numerical Analysis: An Agent Pipeline and Quality Audit Beyond Kernel Acceptancecited by 3
- 2026Autoformalization of Agent Instructions into Policy-as-Codecited by 1
- 2026VALG: An Agentic System for ML Theory Researchcited by 1
- 2026VALG: An Agentic System for ML Theory Research13 Aug 2026
- 2026Autoformalization of Agent Instructions into Policy-as-Code25 Jun 2026
- 2026Formalizing Numerical Analysis: An Agent Pipeline and Quality Audit Beyond Kernel Acceptance12 Jun 2026
- 2026DreamProver: Evolving Transferable Lemma Libraries via a Wake-Sleep Theorem-Proving Agent29 Apr 2026
- 2025Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physicscited by 27
- 2025StepFun-Formalizer: Unlocking the Autoformalization Potential of LLMs through Knowledge-Reasoning Fusioncited by 15
- 2026FormalRx: Rectify and eXamine Semantic Failures in Autoformalizationcited by 2
- 2026SFT-GRPO Data Overlap as a Post-Training Hyperparameter for Autoformalizationcited by 0
- 2026FormalRx: Rectify and eXamine Semantic Failures in Autoformalization6 Jul 2026
- 2026SFT-GRPO Data Overlap as a Post-Training Hyperparameter for Autoformalization15 Apr 2026
- 2025Ax-Prover: A Deep Reasoning Agentic Framework for Theorem Proving in Mathematics and Quantum Physics14 Oct 2025
- 2025StepFun-Formalizer: Unlocking the Autoformalization Potential of LLMs through Knowledge-Reasoning Fusion6 Aug 2025
- 2025ASSESS: A Semantic and Structural Evaluation Framework for Statement Similaritycited by 8
- 2025Towards a Common Framework for Autoformalizationcited by 7
- 2026OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inferencecited by 4
- 2026Theory-Scale Auto-Formalization of Logics for Computer Sciencecited by 3
- 2026TheoremBench: Evaluating LLMs on Theorem Proving in Formal Mathematicscited by 1
- 2025Mathematics with large language models as provers and verifierscited by 0
- 2025Towards Autoformalization of LLM-generated Outputs for Requirement Verificationcited by 0
- 2026Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discoverycited by 0
- 2026Visored: A Controlled-Natural-Language Prover for LLM-Generated Mathematicscited by 0
- 2026MioFFAn: an Annotation Software for Formula Formalization with LLM Automation Capabilitiescited by 0
- 2026ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimizationcited by 0
- 2026ProofLoom: Proof-Obligation-Driven Theory Construction for Autoformalizing Research-Level Stochastic Optimization28 Sep 2026
- 2026Theory-Scale Auto-Formalization of Logics for Computer Science25 Jun 2026
- 2026Visored: A Controlled-Natural-Language Prover for LLM-Generated Mathematics16 Jun 2026
- 2026TheoremBench: Evaluating LLMs on Theorem Proving in Formal Mathematics8 Jun 2026
- 2026MioFFAn: an Annotation Software for Formula Formalization with LLM Automation Capabilities15 May 2026
- 2026Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discovery23 Apr 2026
- 2026OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inference2 Feb 2026
- 2025Towards Autoformalization of LLM-generated Outputs for Requirement Verification14 Nov 2025
- 2025Mathematics with large language models as provers and verifiers11 Oct 2025
- 2025ASSESS: A Semantic and Structural Evaluation Framework for Statement Similarity26 Sep 2025
- 2025Towards a Common Framework for Autoformalization11 Sep 2025
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