TheoremExplainAgent: Towards Video-based Multimodal Explanations for LLM Theorem Understanding

TL;DR

This paper introduces TheoremExplainAgent, a system for generating detailed video explanations of theorems using LLMs and animations, and evaluates it with a new benchmark and metrics, revealing the importance of multimodal explanations for understanding.

Contribution

It presents TheoremExplainAgent for multimodal theorem explanations and TheoremExplainBench for systematic evaluation, advancing the generation of pedagogically meaningful visual explanations.

Findings

Agentic planning improves long-form video generation.

The o3-mini agent achieves 93.8% success rate.

Videos have minor layout issues but reveal reasoning flaws.

Abstract

Understanding domain-specific theorems often requires more than just text-based reasoning; effective communication through structured visual explanations is crucial for deeper comprehension. While large language models (LLMs) demonstrate strong performance in text-based theorem reasoning, their ability to generate coherent and pedagogically meaningful visual explanations remains an open challenge. In this work, we introduce TheoremExplainAgent, an agentic approach for generating long-form theorem explanation videos (over 5 minutes) using Manim animations. To systematically evaluate multimodal theorem explanations, we propose TheoremExplainBench, a benchmark covering 240 theorems across multiple STEM disciplines, along with 5 automated evaluation metrics. Our results reveal that agentic planning is essential for generating detailed long-form videos, and the o3-mini agent achieves a success rate of 93.8% and an overall score of 0.77. However, our quantitative and qualitative studies show that most of the videos produced exhibit minor issues with visual element layout. Furthermore, multimodal explanations expose deeper reasoning flaws that text-based explanations fail to reveal, highlighting the importance of multimodal explanations.