A Conceptual History of Space and Symmetry

From Plato to the Superworld

  • Pietro Giuseppe Fré

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Pietro Giuseppe Fré
    Pages 1-7
  3. Pietro Giuseppe Fré
    Pages 9-31
  4. Pietro Giuseppe Fré
    Pages 33-59
  5. Pietro Giuseppe Fré
    Pages 61-88
  6. Pietro Giuseppe Fré
    Pages 89-127
  7. Pietro Giuseppe Fré
    Pages 129-155
  8. Pietro Giuseppe Fré
    Pages 157-206
  9. Pietro Giuseppe Fré
    Pages 207-239
  10. Pietro Giuseppe Fré
    Pages 241-267
  11. Pietro Giuseppe Fré
    Pages 269-287
  12. Pietro Giuseppe Fré
    Pages 289-306
  13. Back Matter
    Pages 307-319

About this book


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.


Geometry and symmetry theory History of theoretical physics Geometrization of physics Supersymmetric field-theories Geometrical structures in physics Group theory Superstring theory and supergravity

Authors and affiliations

  • Pietro Giuseppe Fré
    • 1
  1. 1.University of TorinoTurinItaly

Bibliographic information