TheoremExplainAgent: Towards Multimodal Explanations for LLM Theorem Understanding

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.

Towards Goal-oriented Large Language Model Prompting: A Survey

Large Language Models (LLMs) have shown prominent performance in various downstream tasks in which prompt engineering plays a pivotal role in optimizing LLMs' performance. This paper, not as an overview of current prompt engineering methods, aims to highlight the limitation of designing prompts while holding an anthropomorphic assumption that expects LLMs to think like humans. From our review of 35 representative studies, we demonstrate that a goal-oriented prompt formulation, which guides LLMs to follow established human logical thinking, significantly improves the performance of LLMs. Furthermore, We introduce a novel taxonomy that categorizes goal-oriented prompting methods into five interconnected stages and we demonstrate the broad applicability of our framework by summarizing ten applicable tasks. With four future directions proposed, we hope to further emphasize and promote goal-oriented prompt engineering.