# Solving Math Word Problems by Combining Language Models With Symbolic Solvers

arXiv: https://arxiv.org/abs/2304.09102 · HTML: https://mlsanity.com/paper/2304.09102/

## Key facts

- Cited by 124 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 16 Apr 2023.

## Builds on (most cited first, 9 of 9)

- [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)
- [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)
- [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)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)

## Built on by (most cited first, 30 of 124)

- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Can Language Models Solve Graph Problems in Natural Language?](https://mlsanity.com/paper/2305.10037/) (2023)
- [ToolkenGPT: Augmenting Frozen Language Models with Massive Tools via Tool Embeddings](https://mlsanity.com/paper/2305.11554/) (2023)
- [Tool Learning with Large Language Models: A Survey](https://mlsanity.com/paper/2405.17935/) (2024)
- [Large Language Model Cascades with Mixture of Thoughts Representations for Cost-efficient Reasoning](https://mlsanity.com/paper/2310.03094/) (2023)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [SatLM: Satisfiability-Aided Language Models Using Declarative Prompting](https://mlsanity.com/paper/2305.09656/) (2023)
- [Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solving](https://mlsanity.com/paper/2405.12205/) (2024)
- [Demystifying Chains, Trees, and Graphs of Thoughts](https://mlsanity.com/paper/2401.14295/) (2024)
- [Unifying the Perspectives of NLP and Software Engineering: A Survey on Language Models for Code](https://mlsanity.com/paper/2311.07989/) (2023)
- [Grammar Prompting for Domain-Specific Language Generation with Large Language Models](https://mlsanity.com/paper/2305.19234/) (2023)
- [Unlocking the Capabilities of Thought: A Reasoning Boundary Framework to Quantify and Optimize Chain-of-Thought](https://mlsanity.com/paper/2410.05695/) (2024)
- [Autonomous LLM-driven research from data to human-verifiable research papers](https://mlsanity.com/paper/2404.17605/) (2024)
- [Granite-Function Calling Model: Introducing Function Calling Abilities via Multi-task Learning of Granular Tasks](https://mlsanity.com/paper/2407.00121/) (2024)
- [Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning](https://mlsanity.com/paper/2306.02408/) (2023)
- [LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages](https://mlsanity.com/paper/2405.13144/) (2024)
- [Dualformer: Controllable Fast and Slow Thinking by Learning with Randomized Reasoning Traces](https://mlsanity.com/paper/2410.09918/) (2024)
- [OptiMUS: Optimization Modeling Using MIP Solvers and large language models](https://mlsanity.com/paper/2310.06116/) (2023)
- [API-BLEND: A Comprehensive Corpora for Training and Benchmarking API LLMs](https://mlsanity.com/paper/2402.15491/) (2024)
- [Preference Optimization for Reasoning with Pseudo Feedback](https://mlsanity.com/paper/2411.16345/) (2024)
- [MechGPT, a language-based strategy for mechanics and materials modeling that connects knowledge across scales, disciplines and modalities](https://mlsanity.com/paper/2310.10445/) (2023)
- [Explainable Claim Verification via Knowledge-Grounded Reasoning with Large Language Models](https://mlsanity.com/paper/2310.05253/) (2023)
- [Capabilities of Large Language Models in Control Engineering: A Benchmark Study on GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra](https://mlsanity.com/paper/2404.03647/) (2024)
- [Planning Anything with Rigor: General-Purpose Zero-Shot Planning with LLM-based Formalized Programming](https://mlsanity.com/paper/2410.12112/) (2024)
- [MCIP: Protecting MCP Safety via Model Contextual Integrity Protocol](https://mlsanity.com/paper/2505.14590/) (2025)
- [Efficient Tool Use with Chain-of-Abstraction Reasoning](https://mlsanity.com/paper/2401.17464/) (2024)
- [INMS: Memory Sharing for Large Language Model based Agents](https://mlsanity.com/paper/2404.09982/) (2024)
- [Adaptive Tool Use in Large Language Models with Meta-Cognition Trigger](https://mlsanity.com/paper/2502.12961/) (2025)
- [MeLM, a generative pretrained language modeling framework that solves forward and inverse mechanics problems](https://mlsanity.com/paper/2306.17525/) (2023)

## Abstract (arXiv)

Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has emerged as a promising direction for solving math word problems, but prior approaches such as Program-Aided Language model (PAL) are biased towards simple procedural problems and less effective for problems that require declarative reasoning. We propose an approach that combines an LLM that can incrementally formalize word problems as a set of variables and equations with an external symbolic solver that can solve the equations. Our approach achieves comparable accuracy to the original PAL on the GSM8K benchmark of math word problems and outperforms PAL by an absolute 20% on ALGEBRA, a new dataset of more challenging word problems extracted from Algebra textbooks. Our work highlights the benefits of using declarative and incremental representations when interfacing with an external tool for solving complex math word problems. Our data and prompts are publicly available at https://github.com/joyheyueya/declarative-math-word-problem.