# LPML: LLM-Prompting Markup Language for Mathematical Reasoning

arXiv: https://arxiv.org/abs/2309.13078 · HTML: https://mlsanity.com/paper/2309.13078/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 13 of its 14 references that are in the map.
- First posted on arXiv 21 Sep 2023.

## Placed in

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

## Builds on (most cited first, 13 of 13)

- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [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)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)

## Built on by (most cited first, 15 of 15)

- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [ZeroSearch: Incentivize the Search Capability of LLMs without Searching](https://mlsanity.com/paper/2505.04588/) (2025)
- [GraphCLIP: Enhancing Transferability in Graph Foundation Models for Text-Attributed Graphs](https://mlsanity.com/paper/2410.10329/) (2024)
- [How Numerical Precision Affects Arithmetical Reasoning Capabilities of LLMs](https://mlsanity.com/paper/2410.13857/) (2024)
- [Graph-Augmented Reasoning: Evolving Step-by-Step Knowledge Graph Retrieval for LLM Reasoning](https://mlsanity.com/paper/2503.01642/) (2025)
- [PersonaMath: Boosting Mathematical Reasoning via Persona-Driven Data Augmentation](https://mlsanity.com/paper/2410.01504/) (2024)
- [More or Less Wrong: A Benchmark for Directional Bias in LLM Comparative Reasoning](https://mlsanity.com/paper/2506.03923/) (2025)
- [DCR: Divide-and-Conquer Reasoning for Multi-choice Question Answering with LLMs](https://mlsanity.com/paper/2401.05190/) (2024)
- [Retrieved In-Context Principles from Previous Mistakes](https://mlsanity.com/paper/2407.05682/) (2024)
- [Beyond Passive Critical Thinking: Fostering Proactive Questioning to Enhance Human-AI Collaboration](https://mlsanity.com/paper/2507.23407/) (2025)
- [MathDivide: Improved mathematical reasoning by large language models](https://mlsanity.com/paper/2405.13004/) (2024)
- [The Tyranny of Possibilities in the Design of Task-Oriented LLM Systems: A Scoping Survey](https://mlsanity.com/paper/2312.17601/) (2023)
- [Error Detection and Correction for Interpretable Mathematics in Large Language Models](https://mlsanity.com/paper/2508.03500/) (2025)
- [A Dataset for Evaluating LLM-based Evaluation Functions for Research Question Extraction Task](https://mlsanity.com/paper/2409.06883/) (2024)
- [DecoupleSearch: Decouple Planning and Search via Hierarchical Reward Modeling](https://mlsanity.com/paper/2510.21712/) (2025)

## Abstract (arXiv)

In utilizing large language models (LLMs) for mathematical reasoning, addressing the errors in the reasoning and calculation present in the generated text by LLMs is a crucial challenge. In this paper, we propose a novel framework that integrates the Chain-of-Thought (CoT) method with an external tool (Python REPL). We discovered that by prompting LLMs to generate structured text in XML-like markup language, we could seamlessly integrate CoT and the external tool and control the undesired behaviors of LLMs. With our approach, LLMs can utilize Python computation to rectify errors within CoT. We applied our method to ChatGPT (GPT-3.5) to solve challenging mathematical problems and demonstrated that combining CoT and Python REPL through the markup language enhances the reasoning capability of LLMs. Our approach enables LLMs to write the markup language and perform advanced mathematical reasoning using only zero-shot prompting.