Towards Geometry Problem Solving in the Large Model Era: A Survey

TL;DR

This survey reviews recent progress in AI-driven geometry problem solving, highlighting advances enabled by large models, and discusses future directions for achieving human-level geometric reasoning.

Contribution

It systematically synthesizes GPS advancements across benchmarks, parsing, and reasoning, proposing a unified analytical framework and identifying key future research opportunities.

Findings

Large models have improved SAT-level GPS performance.

Current methodologies are fragmented across benchmarks and frameworks.

Emerging opportunities include automated benchmark generation and neuro-symbolic integration.

Abstract

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.