# Reasoning, Code, or Both? How Large Language Models Handle Variations in Math Questions

arXiv: https://arxiv.org/abs/2605.26414 · HTML: https://mlsanity.com/paper/2605.26414/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 8 of its 8 references that are in the map.
- First posted on arXiv 26 May 2026.

## Placed in

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

## Builds on (most cited first, 8 of 8)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers](https://mlsanity.com/paper/2402.19255/) (2024)
- [Winning Gold at IMO 2025 with a Model-Agnostic Verification-and-Refinement Pipeline](https://mlsanity.com/paper/2507.15855/) (2025)
- [ASyMOB: Algebraic Symbolic Mathematical Operations Benchmark](https://mlsanity.com/paper/2505.23851/) (2025)
- [SBSC: Step-By-Step Coding for Improving Mathematical Olympiad Performance](https://mlsanity.com/paper/2502.16666/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) achieve impressive accuracy on mathematical reasoning benchmarks, yet their performance drops when problems are modified with simple changes like different names or numbers. Code execution methods, which let models generate and run Python code instead of reasoning in natural language, have been proposed as a solution, but their effect on reasoning robustness (the ability to maintain accuracy across problem variations) has not been systematically tested. This study evaluates three approaches on 1,000 problems from the GSM-Symbolic dataset: pure reasoning using chain-of-thought (CoT) prompting, single-shot code execution using Program-Aided Language models (PAL), and iterative code execution using Step-by-Step Coding (SBSC). All three were run on paired original and modified problems using Claude Haiku 4.5. CoT was the most robust method, with an accuracy drop of 1.3 percentage points and 1.8% of problems breaking under perturbation. PAL was the least robust at 1.7 percentage points and 3.1% broke, with SBSC falling in between. Although these differences were not statistically significant (p = .096), the directional trend was consistent across all measures, suggesting that code execution, whether single-shot or iterative, does not improve reasoning robustness on grade-school-level problem variations.