# MultiMath: Bridging Visual and Mathematical Reasoning for Large Language Models

arXiv: https://arxiv.org/abs/2409.00147 · HTML: https://mlsanity.com/paper/2409.00147/

## Key facts

- Cited by 70 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)

## Builds on (most cited first, 21 of 21)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [mPLUG-Owl: Modularization Empowers Large Language Models with Multimodality](https://mlsanity.com/paper/2304.14178/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [SPHINX: The Joint Mixing of Weights, Tasks, and Visual Embeddings for Multi-modal Large Language Models](https://mlsanity.com/paper/2311.07575/) (2023)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [Math-LLaVA: Bootstrapping Mathematical Reasoning for Multimodal Large Language Models](https://mlsanity.com/paper/2406.17294/) (2024)
- [CMATH: Can Your Language Model Pass Chinese Elementary School Math Test?](https://mlsanity.com/paper/2306.16636/) (2023)

## Built on by (most cited first, 30 of 70)

- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [Unlocking Multimodal Mathematical Reasoning via Process Reward Model](https://mlsanity.com/paper/2501.04686/) (2025)
- [Advancing Multimodal Reasoning: From Optimized Cold Start to Staged Reinforcement Learning](https://mlsanity.com/paper/2506.04207/) (2025)
- [MINT-CoT: Enabling Interleaved Visual Tokens in Mathematical Chain-of-Thought Reasoning](https://mlsanity.com/paper/2506.05331/) (2025)
- [MathCoder-VL: Bridging Vision and Code for Enhanced Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2505.10557/) (2025)
- [SophiaVL-R1: Reinforcing MLLMs Reasoning with Thinking Reward](https://mlsanity.com/paper/2505.17018/) (2025)
- [Perception-R1: Advancing Multimodal Reasoning Capabilities of MLLMs via Visual Perception Reward](https://mlsanity.com/paper/2506.07218/) (2025)
- [Advancing Multimodal Reasoning via Reinforcement Learning with Cold Start](https://mlsanity.com/paper/2505.22334/) (2025)
- [MMR1: Enhancing Multimodal Reasoning with Variance-Aware Sampling and Open Resources](https://mlsanity.com/paper/2509.21268/) (2025)
- [ErrorRadar: Benchmarking Complex Mathematical Reasoning of Multimodal Large Language Models Via Error Detection](https://mlsanity.com/paper/2410.04509/) (2024)
- [VisualToolAgent (VisTA): A Reinforcement Learning Framework for Visual Tool Selection](https://mlsanity.com/paper/2505.20289/) (2025)
- [First SFT, Second RL, Third UPT: Continual Improving Multi-Modal LLM Reasoning via Unsupervised Post-Training](https://mlsanity.com/paper/2505.22453/) (2025)
- [Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning](https://mlsanity.com/paper/2410.17885/) (2024)
- [MV-MATH: Evaluating Multimodal Math Reasoning in Multi-Visual Contexts](https://mlsanity.com/paper/2502.20808/) (2025)
- [Game-RL: Synthesizing Multimodal Verifiable Game Data to Boost VLMs' General Reasoning](https://mlsanity.com/paper/2505.13886/) (2025)
- [We-Math 2.0: A Versatile MathBook System for Incentivizing Visual Mathematical Reasoning](https://mlsanity.com/paper/2508.10433/) (2025)
- [MM-PRM: Enhancing Multimodal Mathematical Reasoning with Scalable Step-Level Supervision](https://mlsanity.com/paper/2505.13427/) (2025)
- [VL-Cogito: Progressive Curriculum Reinforcement Learning for Advanced Multimodal Reasoning](https://mlsanity.com/paper/2507.22607/) (2025)
- [BlueLM-V-3B: Algorithm and System Co-Design for Multimodal Large Language Models on Mobile Devices](https://mlsanity.com/paper/2411.10640/) (2024)
- [AStar: Boosting Multimodal Reasoning with Automated Structured Thinking](https://mlsanity.com/paper/2502.02339/) (2025)
- [Scaling Agentic Reinforcement Learning for Tool-Integrated Reasoning in VLMs](https://mlsanity.com/paper/2511.19773/) (2025)
- [Math Blind: Failures in Diagram Understanding Undermine Reasoning in MLLMs](https://mlsanity.com/paper/2503.20745/) (2025)
- [MDK12-Bench: A Multi-Discipline Benchmark for Evaluating Reasoning in Multimodal Large Language Models](https://mlsanity.com/paper/2504.05782/) (2025)
- [VisBias: Measuring Explicit and Implicit Social Biases in Vision Language Models](https://mlsanity.com/paper/2503.07575/) (2025)
- [Revisiting Visual Understanding in Multimodal Reasoning through a Lens of Image Perturbation](https://mlsanity.com/paper/2506.09736/) (2025)
- [Euclid: Supercharging Multimodal LLMs with Synthetic High-Fidelity Visual Descriptions](https://mlsanity.com/paper/2412.08737/) (2024)
- [Human Cognitive Benchmarks Reveal Foundational Visual Gaps in MLLMs](https://mlsanity.com/paper/2502.16435/) (2025)
- [MathFlow: Enhancing the Perceptual Flow of MLLMs for Visual Mathematical Problems](https://mlsanity.com/paper/2503.16549/) (2025)
- [Distributed LLMs and Multimodal Large Language Models: A Survey on Advances, Challenges, and Future Directions](https://mlsanity.com/paper/2503.16585/) (2025)
- [Accurate and Diverse LLM Mathematical Reasoning via Automated PRM-Guided GFlowNets](https://mlsanity.com/paper/2504.19981/) (2025)

## Abstract (arXiv)

The rapid development of large language models (LLMs) has spurred extensive research into their domain-specific capabilities, particularly mathematical reasoning. However, most open-source LLMs focus solely on mathematical reasoning, neglecting the integration with visual injection, despite the fact that many mathematical tasks rely on visual inputs such as geometric diagrams, charts, and function plots. To fill this gap, we introduce MultiMath-7B, a multimodal large language model that bridges the gap between math and vision. MultiMath-7B is trained through a four-stage process, focusing on vision-language alignment, visual and math instruction-tuning, and process-supervised reinforcement learning. We also construct a novel, diverse and comprehensive multimodal mathematical dataset, MultiMath-300K, which spans K-12 levels with image captions and step-wise solutions. MultiMath-7B achieves state-of-the-art (SOTA) performance among open-source models on existing multimodal mathematical benchmarks and also excels on text-only mathematical benchmarks. Our model and dataset are available at textcolorblueurlhttps://github.com/pengshuai-rin/MultiMath.