# Do Large Language Models Truly Grasp Mathematics? An Empirical Exploration From Cognitive Psychology

arXiv: https://arxiv.org/abs/2410.14979 · HTML: https://mlsanity.com/paper/2410.14979/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 19 Oct 2024.

## Builds on (most cited first, 14 of 14)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Reasoning or Reciting? Exploring the Capabilities and Limitations of Language Models Through Counterfactual Tasks](https://mlsanity.com/paper/2307.02477/) (2023)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [Thinking Fast and Slow in Large Language Models](https://mlsanity.com/paper/2212.05206/) (2022)
- [WaveCoder: Widespread And Versatile Enhancement For Code Large Language Models By Instruction Tuning](https://mlsanity.com/paper/2312.14187/) (2023)
- [STOC-TOT: Stochastic Tree-of-Thought with Constrained Decoding for Complex Reasoning in Multi-Hop Question Answering](https://mlsanity.com/paper/2407.03687/) (2024)

## Built on by (most cited first, 1 of 1)

- [League of LLMs: A Benchmark-Free Paradigm for Mutual Evaluation of Large Language Models](https://mlsanity.com/paper/2507.22359/) (2025)

## Abstract (arXiv)

The cognitive mechanism by which Large Language Models (LLMs) solve mathematical problems remains a widely debated and unresolved issue. Currently, there is little interpretable experimental evidence that connects LLMs' problem-solving with human cognitive psychology.To determine if LLMs possess human-like mathematical reasoning, we modified the problems used in the human Cognitive Reflection Test (CRT). Our results show that, even with the use of Chains of Thought (CoT) prompts, mainstream LLMs, including the latest o1 model (noted for its reasoning capabilities), have a high error rate when solving these modified CRT problems. Specifically, the average accuracy rate dropped by up to 50% compared to the original questions.Further analysis of LLMs' incorrect answers suggests that they primarily rely on pattern matching from their training data, which aligns more with human intuition (System 1 thinking) rather than with human-like reasoning (System 2 thinking). This finding challenges the belief that LLMs have genuine mathematical reasoning abilities comparable to humans. As a result, this work may adjust overly optimistic views on LLMs' progress towards artificial general intelligence.