This book presents the author’s personal historical perspective and conceptual analysis on symmetry and geometry. The author enlightens with modern views the historical process which led to the contemporary vision of space and symmetry that are used in theoretical physics and in particular in such abstract and advanced descriptions of the physical world as those provided by supergravity. The book is written intertwining storytelling and philosophical argumentation with some essential technical material.

The author argues that symmetry and geometry are inextricably entangled and their current meaning is the result of a long process of abstraction which was determined through history and can be understood within the analytic system of thought of western civilization that started with the Ancient Greeks. The evolution of geometry and symmetry theory in the last forty years has been deeply and constructively influenced by supersymmetry/supergravity and the allied constructions of strings and branes. Further advances in theoretical physics cannot be based simply on the Galilean method of interrogating nature and then formulating a testable theory to explain the observed phenomena. One ought to interrogate human thought, meaning frontier-line mathematics concerned with geometry and symmetry in order to find there the threads of so far unobserved correspondences, reinterpretations and renewed conceptions.

Table of Contents

1 The episteme

2 Symmetry and mathematics

3 How group theory came into being

4 From crystals to Plato

5 The long tale of Lie groups

6 Hermann Weyl and representation theory

7 A short history of differential geometry

8 Geometry becomes complex

9 Geometry becomes special

10 Black holes: the physics of geometry

11 Modern manifolds from ancient polyhedra

About the Author

Pietro Frè is Professor of Theoretical Physics at the University of Torino, Italy. He recently served as Scientific Counsellor of the Italian Embassy in Moscow. He has taught General Relativity for 15 years. His scientific passion lies in supergravity and all allied topics, since the inception of the field, in 1976. He was professor at SISSA, worked in the USA and at CERN. He has taught General Relativity for 15 years. He has previously published five science monographs. He is also the author of a popular science book on cosmology (“Il fascino oscuro dell’inflazione”, Springer 2009), and two novels, in Italian.