Bridging Mathematics and Artificial Intelligence: Foundations, Theory, and Applications

In recent years, the rapid progress of Artificial Intelligence (AI) has been closely tied to advances in foundational and advanced mathematics. From optimization theory and linear algebra to differential equations, measure theory, and topology, mathematical tools underpin the design, analysis, and understanding of modern AI systems.

This Research Topic aims to highlight the latest developments at the intersection of mathematics and AI. We welcome contributions that either apply mathematical theory to AI problems or develop new mathematics inspired by challenges in AI. A core focus is on providing rigorous frameworks that lead to provable guarantees, greater robustness, interpretability, and performance in machine learning and AI algorithms.

Topics of interest include, but are not limited to:

- Mathematical foundations of optimization in machine learning (e.g., nonconvex analysis, stochastic approximation, trust-region and proximal methods)

- Differential equations and dynamical systems in AI (e.g., neural ODEs, continuous-time models)

- Information theory and its role in learning algorithms

- Mathematics for the AI in engineering including the signal processing and wireless communication application.

- Geometry and topology in deep learning (e.g., manifold learning, geometric deep learning)

- Theoretical aspects of neural networks: expressivity, generalization, and convergence analysis

- Reinforcement learning and control theory from a mathematical perspective

- Mathematical modeling of uncertainty in AI (e.g., probabilistic modeling, Bayesian inference, PAC learning)

- Numerical analysis and scientific computing techniques in AI applications (e.g., physics-informed neural networks, surrogate modeling)

This Research Topic invites contributions from both mathematicians working on AI-motivated problems and AI researchers seeking rigorous tools to address foundational challenges. We are especially interested in works that bridge theory and practice, and that contribute to making AI systems more transparent, efficient, and trustworthy.

By bringing together experts in mathematics, optimization, and artificial intelligence, this collection will serve as a platform for interdisciplinary exchange and foster the development of mathematically grounded AI methods. We encourage original research articles, review papers, and perspective pieces from both academia and industry.

Article types and fees

This Research Topic accepts the following article types, unless otherwise specified in the Research Topic description:

• Brief Research Report
• Curriculum, Instruction, and Pedagogy
• Data Report
• Editorial
• FAIR² Data
• General Commentary
• Hypothesis and Theory
• Methods
• Mini Review
• ... View all formats

Articles that are accepted for publication by our external editors following rigorous peer review incur a publishing fee charged to Authors, institutions, or funders.

Article types

This Research Topic accepts the following article types, unless otherwise specified in the Research Topic description:

• Brief Research Report
• Curriculum, Instruction, and Pedagogy
• Data Report
• Editorial
• FAIR² Data
• General Commentary
• Hypothesis and Theory
• Methods
• Mini Review
• Opinion
• Original Research
• Perspective
• Review
• Technology and Code

Keywords: Mathematical Foundations, Artificial Intelligence, Machine Learning Theory, Optimization, Differential Equations, Geometry and Topology, Information Theory, Robustness Interpretability, Scientific Computing, Neural Networks, Probabilistic Modeling, Reinforcement Learning, Bayesian Inference, Control Theory

Important note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.