# Polymath: A Challenging Multi-modal Mathematical Reasoning Benchmark

arXiv: https://arxiv.org/abs/2410.14702 · HTML: https://mlsanity.com/paper/2410.14702/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 74 of its 137 references that are in the map.
- First posted on arXiv 6 Oct 2024.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-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 74)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [MiniGPT-4: Enhancing Vision-Language Understanding with Advanced Large Language Models](https://mlsanity.com/paper/2304.10592/) (2023)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [MMBench: Is Your Multi-modal Model an All-around Player?](https://mlsanity.com/paper/2307.06281/) (2023)
- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (2023)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [MME: A Comprehensive Evaluation Benchmark for Multimodal Large Language Models](https://mlsanity.com/paper/2306.13394/) (2023)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Video-LLaMA: An Instruction-tuned Audio-Visual Language Model for Video Understanding](https://mlsanity.com/paper/2306.02858/) (2023)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [MM-Vet: Evaluating Large Multimodal Models for Integrated Capabilities](https://mlsanity.com/paper/2308.02490/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [mPLUG-Owl: Modularization Empowers Large Language Models with Multimodality](https://mlsanity.com/paper/2304.14178/) (2023)
- [ShareGPT4V: Improving Large Multi-Modal Models with Better Captions](https://mlsanity.com/paper/2311.12793/) (2023)
- [SEED-Bench: Benchmarking Multimodal LLMs with Generative Comprehension](https://mlsanity.com/paper/2307.16125/) (2023)
- [BloombergGPT: A Large Language Model for Finance](https://mlsanity.com/paper/2303.17564/) (2023)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [LLaMA-Adapter: Efficient Fine-tuning of Language Models with Zero-init Attention](https://mlsanity.com/paper/2303.16199/) (2023)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)

## Built on by (most cited first, 22 of 22)

- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [Thinking with Images for Multimodal Reasoning: Foundations, Methods, and Future Frontiers](https://mlsanity.com/paper/2506.23918/) (2025)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [VisOnlyQA: Large Vision Language Models Still Struggle with Visual Perception of Geometric Information](https://mlsanity.com/paper/2412.00947/) (2024)
- [Probing the limitations of multimodal language models for chemistry and materials research](https://mlsanity.com/paper/2411.16955/) (2024)
- [Qwen Look Again: Guiding Vision-Language Reasoning Models to Re-attention Visual Information](https://mlsanity.com/paper/2505.23558/) (2025)
- [Observe-R1: Unlocking Reasoning Abilities of MLLMs with Dynamic Progressive Reinforcement Learning](https://mlsanity.com/paper/2505.12432/) (2025)
- [Benchmarking Multimodal Mathematical Reasoning with Explicit Visual Dependency](https://mlsanity.com/paper/2504.18589/) (2025)
- [Geoint-R1: Formalizing Multimodal Geometric Reasoning with Dynamic Auxiliary Constructions](https://mlsanity.com/paper/2508.03173/) (2025)
- [StructVRM: Aligning Multimodal Reasoning with Structured and Verifiable Reward Models](https://mlsanity.com/paper/2508.05383/) (2025)
- [GGBench: A Geometric Generative Reasoning Benchmark for Unified Multimodal Models](https://mlsanity.com/paper/2511.11134/) (2025)
- [Compose and Fuse: Revisiting the Foundational Bottlenecks in Multimodal Reasoning](https://mlsanity.com/paper/2509.23744/) (2025)
- [The Artificial Intelligence Cognitive Examination: A Survey on the Evolution of Multimodal Evaluation from Recognition to Reasoning](https://mlsanity.com/paper/2510.04141/) (2025)
- [Plane Geometry Problem Solving with Multi-modal Reasoning: A Survey](https://mlsanity.com/paper/2505.14340/) (2025)
- [How RL Unlocks the Aha Moment in Geometric Interleaved Reasoning](https://mlsanity.com/paper/2603.01070/) (2026)
- [STELAR-VISION: Self-Topology-Aware Efficient Learning for Aligned Reasoning in Vision](https://mlsanity.com/paper/2508.08688/) (2025)
- [RADAR: A Reasoning-Guided Attribution Framework for Explainable Visual Data Analysis](https://mlsanity.com/paper/2508.16850/) (2025)
- [Can you SPLICE it together? A Human Curated Benchmark for Probing Visual Reasoning in VLMs](https://mlsanity.com/paper/2509.24640/) (2025)
- [ViSurf: Visual Supervised-and-Reinforcement Fine-Tuning for Large Vision-and-Language Models](https://mlsanity.com/paper/2510.10606/) (2025)
- [MathSight: A Benchmark Exploring Have Vision-Language Models Really Seen in University-Level Mathematical Reasoning?](https://mlsanity.com/paper/2511.23112/) (2025)
- [Benchmark Health Index: A Systematic Framework for Benchmarking the Benchmarks of LLMs](https://mlsanity.com/paper/2602.11674/) (2026)
- [A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to Reasoning](https://mlsanity.com/paper/2603.08291/) (2026)

## Abstract (arXiv)

Multi-modal Large Language Models (MLLMs) exhibit impressive problem-solving abilities in various domains, but their visual comprehension and abstract reasoning skills remain under-evaluated. To this end, we present PolyMATH, a challenging benchmark aimed at evaluating the general cognitive reasoning abilities of MLLMs. PolyMATH comprises 5,000 manually collected high-quality images of cognitive textual and visual challenges across 10 distinct categories, including pattern recognition, spatial reasoning, and relative reasoning. We conducted a comprehensive, and quantitative evaluation of 15 MLLMs using four diverse prompting strategies, including Chain-of-Thought and Step-Back. The best scores achieved on PolyMATH are ~41%, ~36%, and ~27%, obtained by Claude-3.5 Sonnet, GPT-4o and Gemini-1.5 Pro respectively - highlighting the logical and visual complexity of these questions. A further fine-grained error analysis reveals that these models struggle to understand spatial relations and perform drawn-out, high-level reasoning. This is further strengthened by our ablation study estimating MLLM performance when given textual descriptions in place of diagrams. As evidenced by ~4% improvement over textual descriptions as opposed to actual images, we discover that models do not truly comprehend visual diagrams and the spatial information therein, and are thus prone to logical errors. Finally, we evaluate the OpenAI o1 models and find that their performance only matches the human baseline, highlighting the difficulty of the benchmark. The results on PolyMATH highlight the room for improvement in multi-modal reasoning and provide unique insights to guide the development of future MLLMs.