Can AI Rediscover Geometry?

The evaluation pipeline assesses the fidelity of symbolic equation recovery from 3D surface data by integrating regression errors—quantified by Normalized Mean Squared Error ($NMSE$)—with strict symbolic equivalence checks and geometry-aware distance metrics such as Chamfer and Hausdorff distances, thereby providing a comprehensive measure of both numerical and structural accuracy.

A new benchmark challenges large language models to derive the equations defining 3D surfaces, revealing current limitations in their ability to perform geometric reasoning.