New frontiers of kinetic theory and active particle methods toward a mathematical theory of living systems

This editorial is dedicated to recent developments and perspectives of mathematical tools for the modeling and applications for collective dynamics of active particles. These scientific contributions and the critical analysis proposed in this paper aim to propose a forward look to perspectives concerning both further developments of the mathematical theory and exploring new conceivable applications, where mathematics interacts with natural sciences, social systems and economics. A key aim of the content of this issue is the perspective of understanding how mathematics can contribute to Scientific Machine Learning toward Artificial Intelligence.