# MathDivide: Improved mathematical reasoning by large language models

arXiv: https://arxiv.org/abs/2405.13004 · HTML: https://mlsanity.com/paper/2405.13004/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 34 references that are in the map.
- First posted on arXiv 12 May 2024.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only](https://mlsanity.com/paper/2306.01116/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Distilling Reasoning Capabilities into Smaller Language Models](https://mlsanity.com/paper/2212.00193/) (2022)
- [PREFER: Prompt Ensemble Learning via Feedback-Reflect-Refine](https://mlsanity.com/paper/2308.12033/) (2023)
- [Pretrained Language Models are Symbolic Mathematics Solvers too!](https://mlsanity.com/paper/2110.03501/) (2021)
- [Improving Large Language Models in Event Relation Logical Prediction](https://mlsanity.com/paper/2310.09158/) (2023)
- [LPML: LLM-Prompting Markup Language for Mathematical Reasoning](https://mlsanity.com/paper/2309.13078/) (2023)
- [Novice Learner and Expert Tutor: Evaluating Math Reasoning Abilities of Large Language Models with Misconceptions](https://mlsanity.com/paper/2310.02439/) (2023)
- [Supervisory Prompt Training](https://mlsanity.com/paper/2403.18051/) (2024)

## Built on by (most cited first, 3 of 3)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [A Technical Survey of Reinforcement Learning Techniques for Large Language Models](https://mlsanity.com/paper/2507.04136/) (2025)
- [A Survey on Feedback-based Multi-step Reasoning for Large Language Models on Mathematics](https://mlsanity.com/paper/2502.14333/) (2025)

## Abstract (arXiv)

Large language models have been proven to be capable of handling complex linguistic and cognitive tasks. Therefore their usage has been extended to tasks requiring logical reasoning ability such as Mathematics. In this paper, we propose a prompting technique called MathDivide that breaks down the mathematical problem into simpler subproblems. Each of the subproblems is formulated as an algebraic expression whose value is evaluated by the Python code generated by the LLM for the corresponding algebraic expression. The values fed to the Python code are the numerical values provided in the problem statement. The solutions for the subproblems are composed together to obtain the final answer for the problem statement. Finally, the final answer is compared to the correct answer. If the final answer matches the correct answer, it is produced as output else a refinement prompt is fed to the LLM. We experiment with this prompting technique on both closed-source LLM models and open-source LLM models using GSM8K dataset. The results obtained demonstrate that MathDivide was able to significantly outperform the leading prompting technique called Math-prompter.