# Large Language Models' Understanding of Math: Source Criticism and Extrapolation

arXiv: https://arxiv.org/abs/2311.07618 · HTML: https://mlsanity.com/paper/2311.07618/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 12 Nov 2023.

## Builds on (most cited first, 10 of 10)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [How is ChatGPT's behavior changing over time?](https://mlsanity.com/paper/2307.09009/) (2023)
- [Reasoning or Reciting? Exploring the Capabilities and Limitations of Language Models Through Counterfactual Tasks](https://mlsanity.com/paper/2307.02477/) (2023)
- [Formal Mathematics Statement Curriculum Learning](https://mlsanity.com/paper/2202.01344/) (2022)
- [Thor: Wielding Hammers to Integrate Language Models and Automated Theorem Provers](https://mlsanity.com/paper/2205.10893/) (2022)
- [Skill-Mix: a Flexible and Expandable Family of Evaluations for AI models](https://mlsanity.com/paper/2310.17567/) (2023)
- [On the Principles of Parsimony and Self-Consistency for the Emergence of Intelligence](https://mlsanity.com/paper/2207.04630/) (2022)
- [Novice Learner and Expert Tutor: Evaluating Math Reasoning Abilities of Large Language Models with Misconceptions](https://mlsanity.com/paper/2310.02439/) (2023)

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

- [A Survey on Deep Learning for Theorem Proving](https://mlsanity.com/paper/2404.09939/) (2024)
- [Grammars of Formal Uncertainty: When to Trust LLMs in Automated Reasoning Tasks](https://mlsanity.com/paper/2505.20047/) (2025)
- [QUITE: Quantifying Uncertainty in Natural Language Text in Bayesian Reasoning Scenarios](https://mlsanity.com/paper/2410.10449/) (2024)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)

## Abstract (arXiv)

It has been suggested that large language models such as GPT-4 have acquired some form of understanding beyond the correlations among the words in text including some understanding of mathematics as well. Here, we perform a critical inquiry into this claim by evaluating the mathematical understanding of the GPT-4 model. Considering that GPT-4's training set is a secret, it is not straightforward to evaluate whether the model's correct answers are based on a mathematical understanding or based on replication of proofs that the model has seen before. We specifically craft mathematical questions which their formal proofs are not readily available on the web, proofs that are more likely not seen by the GPT-4. We see that GPT-4 is unable to solve those problems despite their simplicity. It is hard to find scientific evidence suggesting that GPT-4 has acquired an understanding of even basic mathematical concepts. A straightforward way to find failure modes of GPT-4 in theorem proving is to craft questions where their formal proofs are not available on the web. Our finding suggests that GPT-4's ability is to reproduce, rephrase, and polish the mathematical proofs that it has seen before, and not in grasping mathematical concepts. We also see that GPT-4's ability to prove mathematical theorems is continuously expanding over time despite the claim that it is a fixed model. We suggest that the task of proving mathematical theorems in formal language is comparable to the methods used in search engines such as Google while predicting the next word in a sentence may be a misguided approach, a recipe that often leads to excessive extrapolation and eventual failures. Prompting the GPT-4 over and over may benefit the GPT-4 and the OpenAI, but we question whether it is valuable for machine learning or for theorem proving.