# Solving Is Not Drawing: A Benchmark for Diagrammatic Reasoning in Olympiad Geometry

arXiv: https://arxiv.org/abs/2608.18111 · HTML: https://mlsanity.com/paper/2608.18111/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 16 of 16)

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- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [CodeBLEU: a Method for Automatic Evaluation of Code Synthesis](https://mlsanity.com/paper/2009.10297/) (2020)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [MLLM-as-a-Judge: Assessing Multimodal LLM-as-a-Judge with Vision-Language Benchmark](https://mlsanity.com/paper/2402.04788/) (2024)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [AutomaTikZ: Text-Guided Synthesis of Scientific Vector Graphics with TikZ](https://mlsanity.com/paper/2310.00367/) (2023)
- [GeoUni: A Unified Model for Generating Geometry Diagrams, Problems and Problem Solutions](https://mlsanity.com/paper/2504.10146/) (2025)
- [LLM Code Customization with Visual Results: A Benchmark on TikZ](https://mlsanity.com/paper/2505.04670/) (2025)
- [GeoSDF: Plane Geometry Diagram Synthesis via Signed Distance Field](https://mlsanity.com/paper/2506.13492/) (2025)
- [Text2Arch: A Dataset for Generating Scientific Architecture Diagrams from Natural Language Descriptions](https://mlsanity.com/paper/2604.14941/) (2026)

## Abstract (arXiv)

Foundation models such as GPT and Claude now solve olympiad-level mathematics with remarkable proficiency, so much so that geometry problem solving has become a standard proxy for their mathematical reasoning. Yet solving a geometry problem and drawing the figure it depends on are not the same skill: progress often hinges on a faithful diagram with the right auxiliary constructions and incidences, and it is unclear that a model which reasons its way to the answer can also produce one. A growing collection of benchmarks, including MathVista, and MathVerse, measures whether models reach the correct answer, but to our knowledge, none isolate the distinct ability to construct the diagram itself, leaving this capability unmeasured. We introduce an open-source benchmark that targets this gap: 954 self-contained olympiad geometry problems, with a 297-problem hard subset, each paired with its solution and a human-authored, high-fidelity diagram in renderable Asymptote code, together with a suite of text-, code-, image-, VLM-, and constraint-based metrics for what we term diagrammatic reasoning. Evaluating current foundation models reveals a pronounced gap between solving and drawing: their diagrams are markedly less faithful, with an average compile success rate of only 36.14%. Strong mathematical reasoning, we find, does not imply the ability to construct accurate geometric diagrams. Our benchmark and dataset can be accessed at https://huggingface.co/datasets/max98765/hardgeometryproblemswithdiagrams.