mlsanityData to 14 Oct 2026

Towards Geometry Problem Solving in the Large Model Era: A Survey

arXiv 2506.02690 ↗First posted 3 Jun 2025cs.CV math.GTcited by 8

On the map: LLM reasoning → Spatial and embodied reasoning

Abstract (arXiv)

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning. Builds on 30 of its 61 references that are in the map. First posted on arXiv 3 Jun 2025.

Builds on

30 of 61 references.

Closest ancestors · 9

Same direction, newest first

  1. 2025Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integration17 Apr
  2. 2025GeoSense: Evaluating Identification and Application of Geometric Principles in Multimodal Reasoning17 Apr
  3. 2024Geo-LLaVA: A Large Multi-Modal Model for Solving Geometry Math Problems with Meta In-Context Learning12 Dec
  4. 2024GeoCoder: Solving Geometry Problems by Generating Modular Code through Vision-Language Models17 Oct
  5. 2024Diagram Formalization Enhanced Multi-Modal Geometry Problem Solver6 Sep
  6. 2024Beyond Lines and Circles: Unveiling the Geometric Reasoning Gap in Large Language Models6 Feb
  7. 2023GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoning19 Dec
  8. 2023A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram22 Feb
  9. 2022UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression6 Dec

Other references · 21

  1. 2023GPT-4 Technical Reportcited by 18,396
  2. 2024The Llama 3 Herd of Modelscited by 14,715
  3. 2023Visual Instruction Tuningcited by 7,869
  4. 2023Qwen Technical Reportcited by 3,344
  5. 2023MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contextscited by 1,614
  6. 2024MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?cited by 586
  7. 2025Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Modelscited by 384
  8. 2021Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoningcited by 383
  9. 2023Causal Reasoning and Large Language Models: Opening a New Frontier for Causalitycited by 353
  10. 2025From System 1 to System 2: A Survey of Reasoning Large Language Modelscited by 320
  11. 2021GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoningcited by 228
  12. 2023G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Modelcited by 210
9 more
  1. 2025Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2cited by 97
  2. 2025A Survey of Personalized Large Language Models: Progress and Future Directionscited by 71
  3. 2024GeoEval: Benchmark for Evaluating LLMs and Multi-Modal Models on Geometry Problem-Solvingcited by 45
  4. 2024GeoGPT4V: Towards Geometric Multi-modal Large Language Models with Geometric Image Generationcited by 32
  5. 2023FormalGeo: An Extensible Formalized Framework for Olympiad Geometric Problem Solvingcited by 27
  6. 2024GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-trainingcited by 23
  7. 2022Plane Geometry Diagram Parsingcited by 20
  8. 2022PGDP5K: A Diagram Parsing Dataset for Plane Geometry Problemscited by 14
  9. 2025GeoUni: A Unified Model for Generating Geometry Diagrams, Problems and Problem Solutionscited by 11

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 5.

8 papers.

  1. 2025ReCAD: Reinforcement Learning Enhanced Parametric CAD Model Generation with Vision-Language Modelscited by 11
  2. 2025A Survey of Deep Learning for Geometry Problem Solvingcited by 4
  3. 2026GeoTikzBridge: Advancing Multimodal Code Generation for Geometric Perception and Reasoningcited by 3
  4. 2025DynaSolidGeo: A Dynamic Benchmark for Genuine Spatial Mathematical Reasoning of VLMs in Solid Geometrycited by 1
  5. 2026Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Languagecited by 1
  6. 2026Grid Spatial Understanding: A Dataset for Textual Spatial Reasoning over Grids, Embodied Settings, and Coordinate Structurescited by 0
  7. 2026Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interactioncited by 0
  8. 2026Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometrycited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025AutoGPS: Automated Geometry Problem Solving via Multimodal Formalization and Deductive Reasoning
  2. 2024Learning to Solve Geometry Problems via Simulating Human Dual-Reasoning Process
  3. 2026Beyond Symbolic Solving: Multi Chain-of-Thought Voting for Geometric Reasoning in Large Language Models
  4. 2025Pi-GPS: Enhancing Geometry Problem Solving by Unleashing the Power of Diagrammatic Information
  5. 2025GeoBench: Rethinking Multimodal Geometric Problem-Solving via Hierarchical Evaluation
  6. 2026Solving Is Not Drawing: A Benchmark for Diagrammatic Reasoning in Olympiad Geometry
  7. 2026GeoMathCode: Understanding Interleaved Math-Code Reasoning for Geometry Problem Solving
  8. 2025GeoGramBench: Benchmarking the Geometric Program Reasoning in Modern LLMs