# FormalScience: Scalable Human-in-the-Loop Autoformalisation of Science with Agentic Code Generation in Lean

arXiv: https://arxiv.org/abs/2604.23002 · HTML: https://mlsanity.com/paper/2604.23002/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 51 references that are in the map.
- First posted on arXiv 24 Apr 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- LLM agents and tool use / [Educational agents and math problem solving](https://mlsanity.com/agents/educational-agents-and-math-problem-solving/)

## Builds on (most cited first, 30 of 32)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [Executable Code Actions Elicit Better LLM Agents](https://mlsanity.com/paper/2402.01030/) (2024)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [The AI Scientist-v2: Workshop-Level Automated Scientific Discovery via Agentic Tree Search](https://mlsanity.com/paper/2504.08066/) (2025)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [Lean Workbook: A large-scale Lean problem set formalized from natural language math problems](https://mlsanity.com/paper/2406.03847/) (2024)
- [Herald: A Natural Language Annotated Lean 4 Dataset](https://mlsanity.com/paper/2410.10878/) (2024)
- [Autoformalize Mathematical Statements by Symbolic Equivalence and Semantic Consistency](https://mlsanity.com/paper/2410.20936/) (2024)
- [Verification and Refinement of Natural Language Explanations through LLM-Symbolic Theorem Proving](https://mlsanity.com/paper/2405.01379/) (2024)
- [Reliable Evaluation and Benchmarks for Statement Autoformalization](https://mlsanity.com/paper/2406.07222/) (2024)
- [ATLAS: Autoformalizing Theorems through Lifting, Augmentation, and Synthesis of Data](https://mlsanity.com/paper/2502.05567/) (2025)
- [Autoformalization in the Wild: Assessing LLMs on Real-World Mathematical Definitions](https://mlsanity.com/paper/2502.12065/) (2025)
- [Consistent Autoformalization for Constructing Mathematical Libraries](https://mlsanity.com/paper/2410.04194/) (2024)
- [Enhancing Ethical Explanations of Large Language Models through Iterative Symbolic Refinement](https://mlsanity.com/paper/2402.00745/) (2024)
- [MathGAP: Out-of-Distribution Evaluation on Problems with Arbitrarily Complex Proofs](https://mlsanity.com/paper/2410.13502/) (2024)
- [Grammars of Formal Uncertainty: When to Trust LLMs in Automated Reasoning Tasks](https://mlsanity.com/paper/2505.20047/) (2025)
- [Formalizing Chemical Physics using the Lean Theorem Prover](https://mlsanity.com/paper/2210.12150/) (2022)
- [DRIFT: Decompose, Retrieve, Illustrate, then Formalize Theorems](https://mlsanity.com/paper/2510.10815/) (2025)
- [Towards a Common Framework for Autoformalization](https://mlsanity.com/paper/2509.09810/) (2025)
- [Beyond Gold Standards: Epistemic Ensemble of LLM Judges for Formal Mathematical Reasoning](https://mlsanity.com/paper/2506.10903/) (2025)
- [Similarity-Based Equational Inference in Physics](https://mlsanity.com/paper/2103.13496/) (2021)
- [Exploring the Limits of Fine-grained LLM-based Physics Inference via Premise Removal Interventions](https://mlsanity.com/paper/2404.18384/) (2024)

## Built on by (most cited first, 4 of 4)

- [Prove2Me: An Open Collaborative Platform for Scaling Math Formalization](https://mlsanity.com/paper/2608.28433/) (2026)
- [Pythagoras-Prover: Advancing Efficient Formal Proving via Augmented Lean Formalisation](https://mlsanity.com/paper/2606.12594/) (2026)
- [Hypothesis-Disciplined Multi-Agent Automated Formalization of Asymptotic Statistical Theory](https://mlsanity.com/paper/2606.20642/) (2026)
- [AxQM: A Textbook-Scale Benchmark for Formal Proof Synthesis in a Library of Finite-Dimensional Quantum Mechanics](https://mlsanity.com/paper/2609.05157/) (2026)

## Abstract (arXiv)

Formalising informal mathematical reasoning into formally verifiable code is a significant challenge for large language models. In scientific fields such as physics, domain-specific machinery (textite.g. Dirac notation, vector calculus) imposes additional formalisation challenges that modern LLMs and agentic approaches have yet to tackle. To aid autoformalisation in scientific domains, we present FormalScience; a domain-agnostic human-in-the-loop agentic pipeline that enables a single domain expert (without deep formal language experience) to produce textitsyntactically correct and textitsemantically aligned formal proofs of informal reasoning for low economic cost. Applying FormalScience to physics, we construct FormalPhysics, a dataset of 200 university-level (LaTeX) physics problems and solutions (primarily quantum mechanics and electromagnetism), along with their Lean4 formal representations. Compared to existing formal math benchmarks, FormalPhysics achieves perfect formal validity and exhibits greater statement complexity. We evaluate open-source models and proprietary systems on a statement autoformalisation task on our dataset via zero-shot prompting, self-refinement with error feedback, and a novel multi-stage agentic approach, and explore autoformalisation limitations in modern LLM-based approaches. We provide the first systematic characterisation of semantic drift in physics autoformalisation in terms of concepts such as notational collapse and abstraction elevation which reveals what formal language verifies when full semantic preservation is unattainable. We release the codebase together with an interactive UI-based FormalScience system which facilitates autoformalisation and theorem proving in scientific domains beyond physics.https://github.com/jmeadows17/formal-science