---
title: "Towards a Mathematics Formalisation Assistant using Large"
description: "The authors test whether OpenAI's Codex (code-davinci-002) can serve as a… 75% accuracy. 31 references, cited by 17 papers here."
authors: ["Ayush Agrawal", "Siddhartha Gadgil", "Navin Goyal", "Ashvni Narayanan", "Anand Tadipatri"]
year: 2022
venue: "arXiv:2211.07524"
source: "https://arxiv.org/abs/2211.07524"
doi: "10.48550/arxiv.2211.07524"
arxiv: "2211.07524"
licence: "CC BY-SA 4.0 (arXiv)"
licence_url: "https://creativecommons.org/licenses/by-sa/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/agrawal-2022-mathematics-formalisation-assistant-large-language/"
---
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# Towards a Mathematics Formalisation Assistant using Large Language Models

**Authors:** Ayush Agrawal, Siddhartha Gadgil, [Navin Goyal](https://md.research.elamur.ai/free/en/authors/navin-goyal/), Ashvni Narayanan and Anand Tadipatri · **Year:** 2022 · **Venue:** arXiv:2211.07524 · **Licence:** [CC BY-SA 4.0 (arXiv)](https://creativecommons.org/licenses/by-sa/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2211.07524) · [PDF](https://arxiv.org/pdf/2211.07524v1) · [DOI 10.48550/arxiv.2211.07524](https://doi.org/10.48550/arxiv.2211.07524) · [arXiv 2211.07524](https://arxiv.org/abs/2211.07524) · [OpenAlex](https://openalex.org/W4309137047)

**Citations:** 2 citations (OpenAlex, 2026-10-14) · [17](https://md.research.elamur.ai/free/en/papers/agrawal-2022-mathematics-formalisation-assistant-large-language/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Turning textbook mathematics into machine-checkable code is slow and demands expertise with proof assistants. Very little paired informal–formal data exists, especially for proofs. The authors test whether OpenAI's Codex (code-davinci-002) can serve as a formalisation assistant for the Lean prover and its library mathlib.

**Theorem statements.** They built a set of 120 undergraduate-level statements and formalised them in Lean 4. For each input, they assembled few-shot examples by retrieving mathlib theorem–docstring pairs whose docstrings are semantically close to it. They then sampled many outputs at higher temperatures and kept those that Lean 4 could elaborate. Combining these two steps brought accuracy to nearly 75%.

**Proofs.** They studied 13 diverse theorems in Lean 3 through manual analysis. No fully correct proof appeared. However, for every theorem, at least one completion was easy for a human to repair. The most useful outputs came from a format that interleaves natural-language comments with formal steps.

The work suggests LLMs can meaningfully reduce formalisation effort despite the scarcity of aligned data.

## Key points
- The model used is Codex (code-davinci-002). Statements were targeted in Lean 4 and proofs in Lean 3, because at the time mathlib was only partly ported to Lean 4. mathlib was then about 226MB.
- The authors present input-dependent prompting (retrieving similar mathlib docstrings) and elaboration-based output filtering as new contributions for autoformalisation. Together they yield roughly 75% accuracy on 120 statements.
- The 13 theorems in the proof benchmark are drawn from a range of areas, namely algebraic number theory, the representation theory of groups, group theory itself, linear algebra, analysis and topology. The theorems use varied techniques such as contradiction and induction.
- Proofs with interleaved comments performed best, an approach the authors relate to chain-of-thought prompting. About half of the generated proofs would save substantial effort, and the rest would save some.
- The datasets were checked for overlap with Codex training data and are provided as supplementary material.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

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- [Microsoft Research](https://md.research.elamur.ai/free/en/companies/microsoft-research/) — Company, Bengaluru, India · 19 works · 4,213 citations
- [Indian Institute of Science Bangalore](https://md.research.elamur.ai/free/en/universities/indian-institute-of-science-bangalore/) — University, Bengaluru, India · 16 works · 1,462 citations
- [Indian Institute of Science Education and Research Pune](https://md.research.elamur.ai/free/en/universities/indian-institute-of-science-education-and-research-pune/) — University, Pune, India · 2 works · 19 citations

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## Cite

Cite as: Ayush Agrawal, Siddhartha Gadgil, Navin Goyal, Ashvni Narayanan and Anand Tadipatri. 2022. Towards a Mathematics Formalisation Assistant using Large Language Models. arXiv:2211.07524.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{agrawal2022mathematics,
  title = {{Towards a Mathematics Formalisation Assistant using Large Language Models}},
  author = {Ayush Agrawal, Siddhartha Gadgil, Navin Goyal, Ashvni Narayanan and Anand Tadipatri},
  year = {2022},
  doi = {10.48550/arxiv.2211.07524},
  eprint = {2211.07524},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2211.07524}
}
```

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*Updated 3 November 2026*