Open Problems in Mathematics

  • John Forbes Nash, Jr.
  • Michael Th. Rassias

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Scott Aaronson
    Pages 1-122
  3. Owen Barrett, Frank W. K. Firk, Steven J. Miller, Caroline Turnage-Butterbaugh
    Pages 123-171
  4. Michael Bennett, Preda Mihăilescu, Samir Siksek
    Pages 173-205
  5. Alain Connes
    Pages 225-257
  6. Jenny Harrison, Harrison Pugh
    Pages 273-302
  7. Louis H. Kauffman
    Pages 303-345
  8. Walter Morris, Valeriu Soltan
    Pages 351-375
  9. Jonathan Rosenberg
    Pages 377-402
  10. René Schoof
    Pages 403-416
  11. Paul Seymour
    Pages 417-437
  12. Alexander Soifer
    Pages 439-457
  13. Endre Szemerédi
    Pages 459-477
  14. Robert C. Vaughan
    Pages 479-520
  15. Claire Voisin
    Pages 521-543

About this book


The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role.  This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements.

The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.


John Nash Jr. publication open problems mathematics generalized Fermat equation quantum systems Riemann hypothesis Navier Stokes equations Novikov's conjecture Hadwiger's conjecture

Editors and affiliations

  • John Forbes Nash, Jr.
    • 1
  • Michael Th. Rassias
    • 2
  1. 1.Department of MathematicsSenior Research Mathematician, Princeton UniversityPrincetonUSA
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA

Bibliographic information