Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning

Hilbert-Geo introduces a unified formal language framework for solid geometry, addressing the limitations of existing models in 3D spatial reasoning. It employs a Parse2Reason methodology that utilizes a conditional description language (CDL) for parsing and a theorem bank for reasoning, achieving state-of-the-art performance with 77.3% accuracy on the SolidFGeo2k dataset and 84.1% on a subset of MathVerse dedicated to solid geometry, outperforming leading MLLMs like Gemini-2.5-pro and GPT-5. This framework is significant for practitioners as it enhances geometric problem-solving capabilities in both solid and plane geometry, supported by curated datasets for training and evaluation.