A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to Reasoning

Tianyu Yang; Sihong Wu; Yilun Zhao; Zhenwen Liang; Lisen Dai; Chen Zhao; Minhao Cheng; Arman Cohan

cs.AIMar 9, 2026

A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to Reasoning

Authors: Tianyu Yang, Sihong Wu, Yilun Zhao, Zhenwen Liang, Lisen Dai, Chen Zhao, Minhao Cheng, Arman Cohan,

Organizations: University of Notre Dame · Yale University · Columbia University · New York University ·

Abstract

Multimodal Mathematical Reasoning (MMR) has recently attracted increasing attention for its capability to solve mathematical problems involving both textual and visual modalities. However, current models still face significant challenges in real-world visual math tasks, often misinterpreting diagrams, failing to align mathematical symbols with visual evidence, or producing inconsistent reasoning steps. Moreover, existing evaluations mainly focus on checking final answers rather than verifying the correctness or executability of each intermediate step. A growing body of recent research addresses these issues by integrating structured perception, explicit alignment, and verifiable reasoning within unified frameworks. To establish a clear roadmap for understanding and comparing different MMR approaches, we systematically review them around four fundamental questions: (1) What to extract from multimodal inputs, (2) How to represent and align textual and visual information, (3) How to perform the reasoning, and (4) How to evaluate the correctness of the overall reasoning process. Finally, we discuss open challenges and share our thoughts on future research directions.

Figures & tables

Benchmark	Year (Venue)	Eval Level	PAR Stage	Key Contributions
ChartQA Masry et al. (2022)	2022 (ACL Findings)	Answer	Perception + Reasoning	Real charts; logical & numeric QA.
FigureQA Kahou et al. (2017)	2018 (ICLR Workshop)	Answer	Perception	Synthetic charts; controlled reasoning.
PlotQA Methani et al. (2020b)	2020 (WACV)	Answer	Perception + Reasoning	Real plots; open‑vocab numeric answers.
IconQA Lu et al. (2021d)	2021 (NeurIPS)	Answer	Perception + Reasoning	Large icon‑based multimodal math.
CLEVR‑Math Lindström and Abraham (2022a)	2022 (NeSy Workshop)	Answer	Perception + Reasoning	Synthetic compositional arithmetic.
FinQA Chen et al. (2022c)	2021 (EMNLP)	Answer	Alignment + Reasoning	Financial table‑text; gold programs.

Table 1: Evaluation benchmarks organized by the APE hierarchy, aligned with corresponding PAR stages.

Dataset	Year (Venue)	PAR Stage	Size / Annotation	Key Contributions
Geometry Problem
GEOS Seo et al. (2015)	2015 (EMNLP)	Perception + Alignment	55 questions; text + diagram	early GPS baseline; text–diagram mapping
GEOS++ Sachan et al. (2017)	2017 (EMNLP)	Alignment	1,406 questions; partial logical forms	SAT-style benchmark with logical grounding
Geometry3K Lu et al. (2021c)	2021 (ACL)	Perception + Alignment	3,002 questions; dense formal language	formal grounding linking text and diagrams
GeoQA Chen et al. (2022b)	2021 (ACL Findings)	Alignment + Reasoning	5,010 questions; executable programs	program-supervised QA
GeoQA+ Cao and Xiao (2022a)	2022 (COLING)	Alignment + Reasoning	extended set with harder steps	challenging multi-step reasoning test

Table 2: Datasets grouped by task and annotated with the primary PAR stage they support, plus year, venue, size, and key contributions.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Survey	Venue & Year	Scope / Focus	Models	Focus
Lu et al. [2023d]	ACL’23	DL4Math	Deep Learning	Pre-LLM; model architectures and datasets;
Sun et al. [2025b]	ACM Computing’25	FM4Reason	MLLM	Broad reasoning (limited math/symbolic depth)
Ahn et al. [2024]	EACL Workshop’24	LLM4Math	LLM	Text-centered (non-MMR)
Yan et al. [2024a]	ACL Findings’25	MLLM4Math	MLLM	Benchmark- and Model-centric taxonomy
Li et al. [2025]	arXiv’25	LMRM	LLM/MLLM	Roadmap- and Stage-centric analysis
Ours	-	MLLM4Math	MLLM	First unified process-level framework revealing internal mechanisms of multimodal mathematical reasoning

Appendix

Table 1: Comparisons between representative surveys and ours. “Models” column indicates model scope discussed in each survey (e.g., deep learning models, LLM, MLLM).

Task	Representative System	PAR	Highest APE	Primary Benchmarks	Executable Interface	Representative Performance
Geometry	GEOS	Perception + Alignment	Executable	GEOS (official & practice SAT geometry)	Equation solver over parsed text + diagram	49% accuracy on official SAT geometry questions and 61% on practice questions; on the $\sim$ 51% of questions the system chooses to answer, accuracy exceeds 96%.
Geometry	NGS / GeoQA program-supervised	Alignment + Reasoning	Executable	GeoQA, GeoQA+	Program executor over symbolic programs	60.0% accuracy on GeoQA; the improved DPE-NGS reaches 62.65% on GeoQA and 66.09% on GeoQA+.
Geometry	Inter-GPS	Alignment + Reasoning	Executable	Geometry3K, GeoQA, GEOS	Geometry DSL / theorem rules	78.3% accuracy on Geometry3K and 68.0% on GeoQA, clearly improving over earlier NGS (60% on GeoQA); also outperforms GEOS on the GEOS dataset.
Geometry	PGPSNet	Alignment + Reasoning	Executable	Geometry3K, GeoQA	Program-supervised geometry DSL	77.9% accuracy on Geometry3K and 70.4% on GeoQA.
Geometry	LANS	Alignment + Reasoning	Executable	Geometry3K, GeoQA	Geometry DSL with learned abstraction	82.3% accuracy on Geometry3K and 74.0% on GeoQA, ranking among the strongest traditional GPS systems.
Geometry	FormalGeo-style provers / FGeo-HyperGNet	Alignment + Reasoning	Executable	FormalGeo7K	FormalGeo DSL + symbolic engine	Around 85.5% overall accuracy and 87.7% step-wise accuracy on FormalGeo7K, significantly outperforming previous geometry solvers.

Appendix

Table 2: Representative systems and reported performance on shared benchmarks.

Multimodal Reasoning

Multimodal reasoning studies how AI systems combine text with images, audio, video, and other signals to solve evidence-dependent tasks.

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Mathematical reasoning is a fundamental capability for educational applications of Large Language Models (LLMs), where reliable problem solving requires not only correct answers but also coherent and verifiable reasoning processes. Multi-agent systems (MASs) have shown growing potential in this domain by leveraging collaboration and verification among multiple LLM agents. However, existing evaluations primarily focus on the correctness of final answers in text-only settings, offering limited insight into multimodal reasoning capabilities, the reliability of intermediate reasoning steps, and robustness against reasoning errors. To address these limitations, we introduce MAMath-Bench, a process-aware benchmark designed to evaluate the multimodal mathematical reasoning capabilities of MASs. MAMath-Bench comprises 1,003 problems spanning 11 mathematical categories, multiple difficulty levels, and several modalities, including text, images, and audio. It features fine-grained milestone annotations to evaluate systems across three dimensions: problem-solving correctness, reasoning-process reliability, and robustness to adversarial reasoning-chain perturbations. Our evaluation yields three key findings. First, multi-agent collaboration does not consistently improve final-answer accuracy over strong single LLMs. Second, collaboration can substantially enhance the coverage of intermediate reasoning, but such gains may come at the cost of increased reasoning redundancy. Third, current systems remain vulnerable to adversarial reasoning errors, particularly those involving subtle structural perturbations. The dataset is available at https://github.com/mira-ai-lab/AgentMath.

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