# Large Language Models for Mathematicians

arXiv: https://arxiv.org/abs/2312.04556 · HTML: https://mlsanity.com/paper/2312.04556/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 44 references that are in the map.
- First posted on arXiv 7 Dec 2023.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [LaMDA: Language Models for Dialog Applications](https://mlsanity.com/paper/2201.08239/) (2022)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Recent Advances in Natural Language Processing via Large Pre-Trained Language Models: A Survey](https://mlsanity.com/paper/2111.01243/) (2021)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [GPTs are GPTs: An Early Look at the Labor Market Impact Potential of Large Language Models](https://mlsanity.com/paper/2303.10130/) (2023)
- [Transformer Language Models without Positional Encodings Still Learn Positional Information](https://mlsanity.com/paper/2203.16634/) (2022)
- [Baldur: Whole-Proof Generation and Repair with Large Language Models](https://mlsanity.com/paper/2303.04910/) (2023)
- [Learning to Prove Theorems via Interacting with Proof Assistants](https://mlsanity.com/paper/1905.09381/) (2019)
- [Evaluating Language Models for Mathematics through Interactions](https://mlsanity.com/paper/2306.01694/) (2023)
- [PanGu-Sigma: Towards Trillion Parameter Language Model with Sparse Heterogeneous Computing](https://mlsanity.com/paper/2303.10845/) (2023)

## Built on by (most cited first, 7 of 7)

- [A Survey on Deep Learning for Theorem Proving](https://mlsanity.com/paper/2404.09939/) (2024)
- [eCeLLM: Generalizing Large Language Models for E-commerce from Large-scale, High-quality Instruction Data](https://mlsanity.com/paper/2402.08831/) (2024)
- [Starjob: Dataset for LLM-Driven Job Shop Scheduling](https://mlsanity.com/paper/2503.01877/) (2025)
- [Grammars of Formal Uncertainty: When to Trust LLMs in Automated Reasoning Tasks](https://mlsanity.com/paper/2505.20047/) (2025)
- [Benford's Curse: Tracing Digit Bias to Numerical Hallucination in LLMs](https://mlsanity.com/paper/2506.01734/) (2025)
- [A Triumvirate of AI Driven Theoretical Discovery](https://mlsanity.com/paper/2405.19973/) (2024)
- [Reliable Use of Lemmas via Eligibility Reasoning and Section-Aware Reinforcement Learning](https://mlsanity.com/paper/2602.00998/) (2026)

## Abstract (arXiv)

Large language models (LLMs) such as ChatGPT have received immense interest for their general-purpose language understanding and, in particular, their ability to generate high-quality text or computer code. For many professions, LLMs represent an invaluable tool that can speed up and improve the quality of work. In this note, we discuss to what extent they can aid professional mathematicians. We first provide a mathematical description of the transformer model used in all modern language models. Based on recent studies, we then outline best practices and potential issues and report on the mathematical abilities of language models. Finally, we shed light on the potential of LLMs to change how mathematicians work.