# A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges

arXiv: https://arxiv.org/abs/2412.11936 · HTML: https://mlsanity.com/paper/2412.11936/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 139 of its 210 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 30 of 139)

- [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)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (2023)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [BloombergGPT: A Large Language Model for Finance](https://mlsanity.com/paper/2303.17564/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [ViperGPT: Visual Inference via Python Execution for Reasoning](https://mlsanity.com/paper/2303.08128/) (2023)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [Visual Programming: Compositional visual reasoning without training](https://mlsanity.com/paper/2211.11559/) (2022)
- [MMMU-Pro: A More Robust Multi-discipline Multimodal Understanding Benchmark](https://mlsanity.com/paper/2409.02813/) (2024)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [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)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [Visual Sketchpad: Sketching as a Visual Chain of Thought for Multimodal Language Models](https://mlsanity.com/paper/2406.09403/) (2024)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)

## Built on by (most cited first, 30 of 55)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Thinking with Images for Multimodal Reasoning: Foundations, Methods, and Future Frontiers](https://mlsanity.com/paper/2506.23918/) (2025)
- [A Comprehensive Survey in LLM(-Agent) Full Stack Safety: Data, Training and Deployment](https://mlsanity.com/paper/2504.15585/) (2025)
- [LLM Agents for Education: Advances and Applications](https://mlsanity.com/paper/2503.11733/) (2025)
- [A Survey on Large Language Models for Mathematical Reasoning](https://mlsanity.com/paper/2506.08446/) (2025)
- [Reasoning Language Models: A Blueprint](https://mlsanity.com/paper/2501.11223/) (2025)
- [Position: Multimodal Large Language Models Can Significantly Advance Scientific Reasoning](https://mlsanity.com/paper/2502.02871/) (2025)
- [Multimodal Spatial Reasoning in the Large Model Era: A Survey and Benchmarks](https://mlsanity.com/paper/2510.25760/) (2025)
- [SafeEraser: Enhancing Safety in Multimodal Large Language Models through Multimodal Machine Unlearning](https://mlsanity.com/paper/2502.12520/) (2025)
- [MMUnlearner: Reformulating Multimodal Machine Unlearning in the Era of Multimodal Large Language Models](https://mlsanity.com/paper/2502.11051/) (2025)
- [MathAgent: Leveraging a Mixture-of-Math-Agent Framework for Real-World Multimodal Mathematical Error Detection](https://mlsanity.com/paper/2503.18132/) (2025)
- [Are Multimodal Large Language Models Ready for Omnidirectional Spatial Reasoning?](https://mlsanity.com/paper/2505.11907/) (2025)
- [DocPruner: A Storage-Efficient Framework for Multi-Vector Visual Document Retrieval via Adaptive Patch-Level Embedding Pruning](https://mlsanity.com/paper/2509.23883/) (2025)
- [Mark Your LLM: Detecting the Misuse of Open-Source Large Language Models via Watermarking](https://mlsanity.com/paper/2503.04636/) (2025)
- [GM-PRM: A Generative Multimodal Process Reward Model for Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2508.04088/) (2025)
- [Towards Omnidirectional Reasoning with 360-R1: A Dataset, Benchmark, and GRPO-based Method](https://mlsanity.com/paper/2505.14197/) (2025)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [MMSciBench: Benchmarking Language Models on Chinese Multimodal Scientific Problems](https://mlsanity.com/paper/2503.01891/) (2025)
- [MathFlow: Enhancing the Perceptual Flow of MLLMs for Visual Mathematical Problems](https://mlsanity.com/paper/2503.16549/) (2025)
- [NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation](https://mlsanity.com/paper/2505.17121/) (2025)
- [Sculpting the Vector Space: Towards Efficient Multi-Vector Visual Document Retrieval via Prune-then-Merge Framework](https://mlsanity.com/paper/2602.19549/) (2026)
- [PhysicsArena: The First Multimodal Physics Reasoning Benchmark Exploring Variable, Process, and Solution Dimensions](https://mlsanity.com/paper/2505.15472/) (2025)
- [QCBench: Evaluating Large Language Models on Domain-Specific Quantitative Chemistry](https://mlsanity.com/paper/2508.01670/) (2025)
- [Unlocking Multimodal Document Intelligence: From Current Triumphs to Future Frontiers of Visual Document Retrieval](https://mlsanity.com/paper/2602.19961/) (2026)
- [EssayJudge: A Multi-Granular Benchmark for Assessing Automated Essay Scoring Capabilities of Multimodal Large Language Models](https://mlsanity.com/paper/2502.11916/) (2025)
- [CAFES: A Collaborative Multi-Agent Framework for Multi-Granular Multimodal Essay Scoring](https://mlsanity.com/paper/2505.13965/) (2025)
- [GeoLaux: A Benchmark for Evaluating MLLMs' Geometry Performance on Long-Step Problems Requiring Auxiliary Lines](https://mlsanity.com/paper/2508.06226/) (2025)
- [GeoSketch: A Neural-Symbolic Approach to Geometric Multimodal Reasoning with Auxiliary Line Construction and Affine Transformation](https://mlsanity.com/paper/2509.22460/) (2025)
- [OpenRCA 2.0: From Outcome Labels to Causal Process Supervision](https://mlsanity.com/paper/2606.27154/) (2026)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)

## Abstract (arXiv)

Mathematical reasoning, a core aspect of human cognition, is vital across many domains, from educational problem-solving to scientific advancements. As artificial general intelligence (AGI) progresses, integrating large language models (LLMs) with mathematical reasoning tasks is becoming increasingly significant. This survey provides the first comprehensive analysis of mathematical reasoning in the era of multimodal large language models (MLLMs). We review over 200 studies published since 2021, and examine the state-of-the-art developments in Math-LLMs, with a focus on multimodal settings. We categorize the field into three dimensions: benchmarks, methodologies, and challenges. In particular, we explore multimodal mathematical reasoning pipeline, as well as the role of (M)LLMs and the associated methodologies. Finally, we identify five major challenges hindering the realization of AGI in this domain, offering insights into the future direction for enhancing multimodal reasoning capabilities. This survey serves as a critical resource for the research community in advancing the capabilities of LLMs to tackle complex multimodal reasoning tasks.