Beyond Lines and Circles: Unveiling the Geometric Reasoning Gap in Large Language Models

Abstract

Large Language Models (LLMs) demonstrate ever-increasing abilities in mathematical and algorithmic tasks, yet their geometric reasoning skills are underexplored. We investigate LLMs' abilities in constructive geometric problem-solving one of the most fundamental steps in the development of human mathematical reasoning. Our work reveals notable challenges that the state-of-the-art LLMs face in this domain despite many successes in similar areas. LLMs exhibit biases in target variable selection and struggle with 2D spatial relationships, often misrepresenting and hallucinating objects and their placements. To this end, we introduce a framework that formulates an LLMs-based multi-agents system that enhances their existing reasoning potential by conducting an internal dialogue. This work underscores LLMs' current limitations in geometric reasoning and improves geometric reasoning capabilities through self-correction, collaboration, and diverse role specializations.