The paper introduces a new benchmark for diagrammatic reasoning in olympiad geometry, comprising 954 self‑contained problems and a 297‑problem hard subset. Each problem is paired with a human‑authored, high‑fidelity diagram in Asymptote code and a suite of metrics for evaluating diagram construction. Experiments show that current foundation models excel at solving the problems but produce markedly less faithful diagrams, with an average compile success rate of only 36.14%.
arXiv:2608. 08964v1 Announce Type: new Abstract: The generation of mathematically precise diagrams from tex- tual prompts has emerged as a critical yet underexplored capability of Large Language Models (LLMs).
arXiv:2607. 27670v2 Announce Type: replace-cross Abstract: Jigsaw puzzle solving requires jointly reasoning about visual content and geometric constraints, yet existing benchmarks use rectangular cuts that create ambiguous ground truth in texture-repeated regions.
Euclid-Omni is a unified neuro‑symbolic framework that integrates a formal geometry system with Large Language Models and Vision‑Language Models to solve both calculation and proving problems in Euclidean geometry up to Olympiad level. Its core component, Euclidea, automatically generates deductive reasoning steps and algebraic computations, while a data‑generation pipeline creates synthetic symbolic problems, diagrams, and natural‑language translations for training. Experiments show that VLMs trained on this synthetic data outperform on calculation tasks, and LLMs paired with Euclidea match state‑of‑the‑art proving systems using far less compute and data.
ChitraMiti introduces a synthetic benchmark of 12,874 Bengali planar geometry problems with structured 15‑attribute descriptions, alongside a complementary set of 500 textbook diagrams. Using a three‑phase protocol that tests diagram‑only, diagram‑plus‑description, and description‑only inputs, the study finds that description‑only performance matches diagram‑plus‑description performance across several VLMs, yet models still struggle with cross‑modal verification. Fine‑tuning on ChitraMiti improves results on both datasets, though a gap remains compared to the best zero‑shot model.
arXiv:2608.28600v1 Announce Type: new Abstract: Large language models (LLMs) achieve strong performance on mathematical reasoning benchmarks, yet the mathematically meaningful skills underlying their...
PhysElite is a new bilingual multimodal benchmark designed to evaluate large language models on Olympiad-level physics problems. It contains 11,586 problems, each paired with visual diagrams, step-by-step bilingual Chinese‑English solution derivations, and the final answer. Benchmarking 18 models revealed that even the best reaches only 33.7% accuracy, and a step‑level analysis highlights where models falter in reasoning.
arXiv:2510.09302v2 Announce Type: replace-cross Abstract: While Multimodal Large Language Models (MLLMs) have achieved remarkable success in difficult purely textual mathematical reasoning tasks, eve...
The paper introduces InternGeometry, a large language model agent that achieves medalist-level performance on International Mathematical Olympiad geometry problems. It overcomes traditional heuristic limitations by iteratively proposing and verifying auxiliary constructions with a symbolic engine, supported by a dynamic memory mechanism that allows over 200 interactions per problem. Using Complexity-Boosting Reinforcement Learning, InternGeometry trains on only 13,000 examples—0.004% of the data used by AlphaGeometry 2—and solves 44 of 50 IMO geometry problems, surpassing the average gold medalist score.
arXiv:2608. 14741v1 Announce Type: cross Abstract: We introduce PolyComp, a procedurally generated and verified benchmark that stresses visual recognition and compositional spatial reasoning.
arXiv:2606. 14176v1 Announce Type: new Abstract: Geometry problem generation is useful for AI-assisted education and multimodal mathematical reasoning, but reliable synthesis remains difficult because the problem statement, diagram, constraints, and solution should be mutually consistent.
arXiv:2606. 09278v1 Announce Type: cross Abstract: Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints.
arXiv:2608.30156v1 Announce Type: new Abstract: Plane geometry problem (PGP) solving has become a critical benchmark for multimodal reasoning because it requires accurate visual perception and precis...