AI-Generative Mathematics (AGM): A New Paradigm for AI-Driven Mathematical Modeling

J. Philippe Blankert, 22 April 2025, blankertjp@gmail.com

Introduction

This article formally introduces and coins the term AI-Generative Mathematics (AGM), a groundbreaking mathematical framework explicitly designed to integrate classical mathematical modeling with advanced artificial intelligence (AI) techniques. AGM explicitly distinguishes itself by emphasizing generative, AI-driven mathematical creation and adaptation tailored to complex, real-world systems.

Definition of AI-Generative Mathematics

AI-Generative Mathematics explicitly leverages artificial intelligence to dynamically create and refine mathematical structures, including adaptive operators, novel equations, and entirely new mathematical concepts. This innovative framework continuously adapts and improves mathematical models by learning from empirical data, thereby significantly enhancing predictive accuracy and adaptability across diverse scientific and industrial fields.

Core Components

AI-Generative Mathematics comprises three primary elements:

• Correction Operators: AI-driven mathematical adjustments designed to enhance the predictive accuracy of existing mathematical models based on real-world data.
• New Equations: Entirely novel mathematical formulations explicitly developed by AI to model complex phenomena inadequately captured by existing equations.
• Innovative Mathematical Operators: Completely new mathematical constructs explicitly created and adapted by AI for effectively addressing complex adaptive systems.

Significance

By explicitly combining AI with mathematics, AI-Generative Mathematics significantly extends modeling capabilities beyond traditional constraints. Its generative, adaptive nature uniquely positions it as a foundational methodology in scientific research, commercial applications, and educational curricula.

Conclusion

AI-Generative Mathematics represents a significant advancement in the evolution of mathematical modeling, explicitly leveraging AI to dynamically generate and refine mathematical constructs. This article formally introduces and defines this new paradigm, establishing its conceptual foundations and inviting researchers and practitioners across disciplines to explore its vast potential. Further details, updates, and a comprehensive book elaborating on AGM will follow soon.