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/hard_geometry_problems_with_diagrams.
Euclidean geometry is a compelling testbed for AI reasoning, as it demands the combination of intuitive diagram understanding, axiomatic deduction, and algebraic computation. Yet, existing approaches typically address only a subset of these abilities or struggle with competition-level problems. We introduce \textit{Euclid-Omni}, a unified neuro-symbolic framework that couples a formal geometry system with Large Language Models (LLMs) and Vision-Language Models (VLMs) to tackle both calculation- and proving-style problems, in formal and natural languages, up to Olympiad-level difficulty. At its core, we develop \textit{Euclidea}, a versatile symbolic geometry solver that automatically generates reasoning steps through deductive inference and algebraic computation. Building on this, we develop a data-generation pipeline that synthesizes symbolic problems and solutions, renders diagrams, and translates them into natural language, producing large-scale, diverse datasets for training LLMs and VLMs across a wide range of reasoning settings. Experiments show that VLMs trained on our synthetic data achieve superior performance on calculation tasks, and that LLMs combined with \textit{Euclidea} are competitive with state-of-the-art systems on Olympiad-level proving problems, despite using orders of magnitude less compute and training data. Code and scripts are publicly available at https://github.com/20171130/Euclid-Omni