Explainable Artificial Intelligence and Mathematics: New Frontiers (and Challenges) of Research Not Only as “AppliedMath”

The increasing complexity of artificial intelligence (AI) models has led to a rising demand for explainability in AI (XAI). Explainable Arti- ficial Intelligence aims to make AI’s decision-making processes transpar- ent and understandable to humans. This paper examines the integral connection between XAI and mathematics, highlighting how mathemat- ical principles can enhance the interpretability, transparency, and trust- worthiness of AI models. We explore the mathematical foundations that underpin XAI techniques, examine case studies where mathematics has improved explainability, and propose future directions for integrating mathematics into XAI frameworks