Mathematics Going Forward: Collected Mathematical Brushstrokes

This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.

Jean-Michel Morel is professor of mathematics at Ecole Normale Supérieure Paris-Saclay. He works on theories and algorithms for the restoration and automatic analysis of digital images and video.

Bernard Teissier is Emeritus Director of Research of CNRS at the Institut Mathématique de Jussieu-Paris Rive Gauche. His research interests center on the algebra and geometry of singularities in algebraic and analytic geometry.