# Can Language Models Rival Mathematics Students? Evaluating Mathematical Reasoning through Textual Manipulation and Human Experiments

arXiv: https://arxiv.org/abs/2412.11908 · HTML: https://mlsanity.com/paper/2412.11908/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 17 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 16 of 16)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [Time Travel in LLMs: Tracing Data Contamination in Large Language Models](https://mlsanity.com/paper/2308.08493/) (2023)
- [Evaluating Language Models for Mathematics through Interactions](https://mlsanity.com/paper/2306.01694/) (2023)
- [FCoReBench: Can Large Language Models Solve Challenging First-Order Combinatorial Reasoning Problems?](https://mlsanity.com/paper/2402.02611/) (2024)

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

- [Token-by-Token Regeneration and Domain Biases: A Benchmark of LLMs on Advanced Mathematical Problem-Solving](https://mlsanity.com/paper/2501.17084/) (2025)

## Abstract (arXiv)

In this paper we look at the ability of recent large language models (LLMs) at solving mathematical problems in combinatorics. We compare models LLaMA-2, LLaMA-3.1, GPT-4, and Mixtral against each other and against human pupils and undergraduates with prior experience in mathematical olympiads. To facilitate these comparisons we introduce the Combi-Puzzles dataset, which contains 125 problem variants based on 25 combinatorial reasoning problems. Each problem is presented in one of five distinct forms, created by systematically manipulating the problem statements through adversarial additions, numeric parameter changes, and linguistic obfuscation. Our variations preserve the mathematical core and are designed to measure the generalisability of LLM problem-solving abilities, while also increasing confidence that problems are submitted to LLMs in forms that have not been seen as training instances. We found that a model based on GPT-4 outperformed all other models in producing correct responses, and performed significantly better in the mathematical variation of the problems than humans. We also found that modifications to problem statements significantly impact the LLM's performance, while human performance remains unaffected.