GeoMathCode: Understanding Interleaved Math-Code Reasoning for Geometry Problem Solving

2026-05-24

AI Summary

This work addresses the challenge of simulating human-like multi-step logical reasoning with auxiliary constructions in geometric problem solving by proposing a novel framework that integrates mathematical reasoning with procedural representations. The approach employs program code as an intermediate visual representation, decoupling discovery reasoning from code generation in a latent space and structuring the reasoning manifold through supervised fine-tuning. The study demonstrates that hierarchical syntactic code structures effectively encode rich mathematical semantics, offering greater expressiveness than purely visual representations. Experimental results show that the proposed method significantly enhances geometric reasoning performance while yielding clearer and more interpretable multi-step derivations.

Abstract

Mathematical reasoning is a hallmark of human intelligence, requiring logical deduction, symbolic manipulation, and abstract thinking. Recent multimodal large language models (MLLMs) have demonstrated strong performance on geometry problems through multi-step reasoning. To better emulate human problem-solving, intermediate steps can incorporate auxiliary visual constructions, such as additional lines or points, which improve geometric interpretation and educational clarity. In this work, we introduce the GeoMathCode, where programmatic representations serve as intermediate visual outputs. We further conduct an in-depth analysis of the underlying reasoning geometry. Experimental results show that reasoning and code generation steps can be disentangled in the latent space, while supervised fine-tuning (SFT) makes the reasoning manifold more structured and informative. Moreover, hierarchical syntactic code structures emerge as disentangled latent subspaces, and contain more mathematical symbolic information than visual representations.

Problem

• mathematical reasoning
• geometry problem solving
• interleaved reasoning
• visual construction
• programmatic representation

Innovation

• programmatic representation
• disentangled latent space
• supervised fine-tuning
• hierarchical syntactic code
• geometric reasoning