# Do MLLMs Really Understand Space? A Mathematical Reasoning Evaluation

arXiv: https://arxiv.org/abs/2602.11635 · HTML: https://mlsanity.com/paper/2602.11635/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 37 of its 50 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)

## Builds on (most cited first, 30 of 37)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [InternVL3: Exploring Advanced Training and Test-Time Recipes for Open-Source Multimodal Models](https://mlsanity.com/paper/2504.10479/) (2025)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities](https://mlsanity.com/paper/2401.12168/) (2024)
- [Thinking in Space: How Multimodal Large Language Models See, Remember, and Recall Spaces](https://mlsanity.com/paper/2412.14171/) (2024)
- [DeepSeek-VL2: Mixture-of-Experts Vision-Language Models for Advanced Multimodal Understanding](https://mlsanity.com/paper/2412.10302/) (2024)
- [BLINK: Multimodal Large Language Models Can See but Not Perceive](https://mlsanity.com/paper/2404.12390/) (2024)
- [Kimi-VL Technical Report](https://mlsanity.com/paper/2504.07491/) (2025)
- [SpatialRGPT: Grounded Spatial Reasoning in Vision Language Models](https://mlsanity.com/paper/2406.01584/) (2024)
- [Spatial-MLLM: Boosting MLLM Capabilities in Visual-based Spatial Intelligence](https://mlsanity.com/paper/2505.23747/) (2025)
- [MMSI-Bench: A Benchmark for Multi-Image Spatial Intelligence](https://mlsanity.com/paper/2505.23764/) (2025)
- [Building and better understanding vision-language models: insights and future directions](https://mlsanity.com/paper/2408.12637/) (2024)
- [SpatialBot: Precise Spatial Understanding with Vision Language Models](https://mlsanity.com/paper/2406.13642/) (2024)
- [3DSRBench: A Comprehensive 3D Spatial Reasoning Benchmark](https://mlsanity.com/paper/2412.07825/) (2024)
- [SAT: Dynamic Spatial Aptitude Training for Multimodal Language Models](https://mlsanity.com/paper/2412.07755/) (2024)
- [OmniSpatial: Towards Comprehensive Spatial Reasoning Benchmark for Vision Language Models](https://mlsanity.com/paper/2506.03135/) (2025)
- [Is A Picture Worth A Thousand Words? Delving Into Spatial Reasoning for Vision Language Models](https://mlsanity.com/paper/2406.14852/) (2024)
- [EmbSpatial-Bench: Benchmarking Spatial Understanding for Embodied Tasks with Large Vision-Language Models](https://mlsanity.com/paper/2406.05756/) (2024)
- [Natural Language Understanding and Inference with MLLM in Visual Question Answering: A Survey](https://mlsanity.com/paper/2411.17558/) (2024)
- [MM-Spatial: Exploring 3D Spatial Understanding in Multimodal LLMs](https://mlsanity.com/paper/2503.13111/) (2025)
- [LEGO-Puzzles: How Good Are MLLMs at Multi-Step Spatial Reasoning?](https://mlsanity.com/paper/2503.19990/) (2025)
- [GeoEval: Benchmark for Evaluating LLMs and Multi-Modal Models on Geometry Problem-Solving](https://mlsanity.com/paper/2402.10104/) (2024)
- [Visual Agentic AI for Spatial Reasoning with a Dynamic API](https://mlsanity.com/paper/2502.06787/) (2025)
- [How to Enable LLM with 3D Capacity? A Survey of Spatial Reasoning in LLM](https://mlsanity.com/paper/2504.05786/) (2025)
- [NuScenes-SpatialQA: A Spatial Understanding and Reasoning Benchmark for Vision-Language Models in Autonomous Driving](https://mlsanity.com/paper/2504.03164/) (2025)
- [From Seeing to Doing: Bridging Reasoning and Decision for Robotic Manipulation](https://mlsanity.com/paper/2505.08548/) (2025)
- [Personalizing Multimodal Large Language Models for Image Captioning: An Experimental Analysis](https://mlsanity.com/paper/2412.03665/) (2024)

## Built on by (most cited first, 6 of 6)

- [WorldCoder-Bench: Benchmarking Physically Grounded 3D World Synthesis](https://mlsanity.com/paper/2606.01869/) (2026)
- [TRACE: A Self-Evolving Skill Bank for Consistent, Limit-Aware LLM Agents](https://mlsanity.com/paper/2608.22793/) (2026)
- [Modality Disentangled Learning for Incomplete Multimodal Emotion Recognition: A Primitive Memory Distillation Perspective](https://mlsanity.com/paper/2608.30563/) (2026)
- [PACMI: Provenance-Aware Cascading Memory Invalidation for Long-Term LLM Agents](https://mlsanity.com/paper/2610.05732/) (2026)
- [Can Language Models Learn to Reject Their Own Bad Reasoning Steps?](https://mlsanity.com/paper/2610.05976/) (2026)
- [Facts Don't Speak Louder than Words: The Behavioral Essence of Long-CoT Distillation](https://mlsanity.com/paper/2610.17607/) (2026)

## Abstract (arXiv)

Multimodal large language models (MLLMs) have achieved strong performance on perception-oriented tasks, yet their ability to perform mathematical spatial reasoning, defined as the capacity to parse and manipulate two- and three-dimensional relations, remains unclear. Humans easily solve textbook-style spatial reasoning problems with over 95% accuracy, but we find that most leading MLLMs fail to reach even 60% on the same tasks. This striking gap highlights spatial reasoning as a fundamental weakness of current models. To investigate this gap, we present MathSpatial, the first large-scale and systematic dataset resource dedicated to mathematical spatial reasoning in MLLMs. MathSpatial provides two complementary subsets: (i)~MathSpatial-Bench, a rigorously curated evaluation set of 2,000 problems spanning 3 categories and 11 subtypes, designed to isolate spatial reasoning from perceptual noise; and (ii)~MathSpatial-Corpus, a training set of 8,000 problems equipped with verified solutions and structured reasoning traces. All problems are sourced from authentic educational materials and undergo multi-stage quality control including deduplication, geometric consistency checking, and cross-validated solution verification. Benchmarking 16 leading MLLMs on MathSpatial-Bench reveals that spatial reasoning remains a fundamental bottleneck: even GPT-5 lags behind human performance by over 35 percentage points, with particularly poor results on abstract deduction tasks. We further show that training on MathSpatial-Corpus yields consistent improvements across model families, demonstrating the dataset's practical value for advancing spatial reasoning capabilities. MathSpatial is publicly available at https://shuolucs.github.io/MathSpatial.