© 2018

Foundations of Mathematics and Physics One Century After Hilbert

New Perspectives

  • Joseph Kouneiher

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Joseph Kouneiher
    Pages 1-73
  3. Joseph Kouneiher, John Stachel
    Pages 97-106
  4. Colin McLarty
    Pages 107-127
  5. Michael Atiyah
    Pages 129-133
  6. Alain Connes
    Pages 159-196
  7. Ali H. Chamseddine
    Pages 211-251
  8. Sebastian De Haro, Jeremy Butterfield
    Pages 305-376
  9. J. Attard, J. François, S. Lazzarini, T. Masson
    Pages 377-415
  10. Kevin Shu, Sharjeel Aziz, Vy-Luan Huynh, David Warrick, Matilde Marcolli
    Pages 417-441

About this book


This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating.  All those who want to  benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.


Minkowski space Noncommutative geometry K-homology Relationship between physics and mathematics K-theory Heisenberg commutation relations Twistor theory Bosonization Pati-Salam symmetries Hilbert’s sixth problem quantum groups Virasoro algebra Penrose's quasi-local mass construction Thirring model massive integrable field theory string theory quantum gravity gauge theory Hilbert's foundations of physics Riemannian geometry

Editors and affiliations

  • Joseph Kouneiher
    • 1
  1. 1.Nice and Sophia Antipolis UniversityNiceFrance

Bibliographic information


“This wonderful book is full of such insights, reflections, analyses, appraisals, and even anecdotes, and should be a smash hit: we should all seek to know more about these foundations, and we have a wonderful set of essays here, based off Hilbert’s original wonderful lectures, and a lot more.” (Michael Berg, MAA Reviews, July, 2018)