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Foundations of Mathematics and Physics One Century After Hilbert

New Perspectives

  • Book
  • © 2018

Overview

Editors:
  1. Joseph Kouneiher

    1. Nice and Sophia Antipolis University, Nice, France

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  • With contributions from Michael Atiyah, Roger Penrose, Edward Witten, Misha Gromov, Alain Connes, Lee Smolin, John Stachel and many others
  • Accessible to a broad audience with a background in mathematics or physics
  • Contains historical chapters such as the one on the relationship between Hilbert and Einstein

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xxi
    Download chapter PDF

  2. Where We Stand Today

    • Joseph Kouneiher
    Pages 1-73

  3. Mie’s Electromagnetic Theory of Matter and the Background to Hilbert’s Unified Foundations of Physics

    • Leo Corry
    Pages 75-96

  4. Hilbert and Einstein

    • Joseph Kouneiher, John Stachel
    Pages 97-106

  5. Grothendieck’s Unifying Vision of Geometry

    • Colin McLarty
    Pages 107-127

  6. Understanding the 6-Dimensional Sphere

    • Michael Atiyah
    Pages 129-133

  7. A Dozen Problems, Questions and Conjectures About Positive Scalar Curvature

    • Misha Gromov
    Pages 135-158

  8. Geometry and the Quantum

    • Alain Connes
    Pages 159-196

  9. What Every Physicist Should Know About String Theory

    • Edward Witten
    Pages 197-210

  10. Quanta of Space-Time and Axiomatization of Physics

    • Ali H. Chamseddine
    Pages 211-251

  11. Twistor Theory as an Approach to Fundamental Physics

    • Roger Penrose
    Pages 253-285

  12. What Are We Missing in Our Search for Quantum Gravity?

    • Lee Smolin
    Pages 287-304

  13. A Schema for Duality, Illustrated by Bosonization

    • Sebastian De Haro, Jeremy Butterfield
    Pages 305-376

  14. The Dressing Field Method of Gauge Symmetry Reduction, a Review with Examples

    • J. Attard, J. François, S. Lazzarini, T. Masson
    Pages 377-415

  15. Syntactic Phylogenetic Trees

    • Kevin Shu, Sharjeel Aziz, Vy-Luan Huynh, David Warrick, Matilde Marcolli
    Pages 417-441
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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, butsheds 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.

Reviews

“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)

Editors and Affiliations

  • Nice and Sophia Antipolis University, Nice, France

    Joseph Kouneiher

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