The Mathematical and Philosophical Legacy of Alexander Grothendieck

Alexander Grothendieck is often considered one of the greatest mathematicians of the twentieth century (if not all time), and his unique vision continues to impact and inspire many fields and researchers today. Utilizing a multidisciplinary approach, this edited volume explores the profound influence his work and ideas have had not only on mathematics, but also on logic and philosophy. Chapters are written by international scholars, and many were inspired by talks given at the conference “Grothendieck, A Multifarious Giant” at Chapman University (May 24-28, 2022). Some chapters are written from a historical perspective and discuss the development of the main themes that characterized Grothendieck's work. Others are more mathematical in nature, analyzing and extending some of his more relevant and obscure results that are still not well understood. Philosophical implications and applications in logic are the subjects of other chapters. This volume will be of interest not only to mathematicians working in algebraic geometry, category theory, and other areas to which Grothendieck contributed, but also to philosophers, logicians, and historians of science.

Preface.- Grothendieck's 40 Main Years (1949-1991).- Grothendieck and Differential Equations.- The Birkho-Grothendieck Theorem.- In nite Products, Congruent Numbers.- The Enduring Legacy of Grothenedieck's Duality Theorem.- Conjectures and Counterexamples in Grothendieck's Work in Functional Analysis.- Tohoku 60 years after.- About Grothendieck Fibrations.-Grothendieck did not Believe in Universes, He believed in Topos and Schemes.- Motivating Motives.- My View on and Experience with Grothendieck's Anabelian Geometry.- Grothendieck's Use of Equality.- Towards a Geometry for Syntax.- Boolean Valued Models, Sheafifications, and Boolean Ultrapowers of Tychono Spaces.- Investigating De nability in Propositional Logic.- Grothendieck and Model Theory.- Context-Dependence and Descent Theory.- Grothendieck and Teichmüller Modular Spaces.

Marco Panza, Philosopher and Historian of Mathematics and Logic. After his studies in Italy and France, he has worked in Geneva, Nantes, Mexico, Barcelona, Paris and South California. He is presently Research Director at the CNRS (IHPST) and Kennedy Professor of Philosophy at Chapman University. His main research interests and major publications concern the history of Greek, Earl-Modern and 18th-century Mathematics, the foundational program of G. Frege, including his recent legacy, the present discussion about the nature of Mathematical Objects in the light of a Philosophy of Mathematical Practice.

Daniele C. Struppa is the President of Chapman University, where he also holds the Donald Bren Presidential Chair in Mathematics. After his studies at the University of Milano and his doctorate at the University of Maryland, College Park, he held positions at the University of Milano, at the Scuola Normale Superiore in Pisa, at the University of Calabria, at George Mason University, and finally at Chapman University. His main current interests are in hypercomplex analysis, and in the applications of Fourier Analysis to Quantum Physics, with particular emphasis on the theory of superoscillations.

Jean-Jacques Szczeciniarz is Professor emeritus at the University Paris Diderot. After his studies at Paris Sorbonne, and Paris Jussieu, as a student of Ecole Normale Supérieure, he was Lecturer at Paris 7, Paris 10 Nanterre, and professor at Bordeaux and Paris Diderot. He was President of the Philosophy jury of ENS and of the Philosophy Commission of the National Committee of Universities. He received the Great Prize of the Academy of science and Prize of the City of Paris. He is currently working on extensions of schema theory (F1) and the transformations this implies for philosophy.