Open Problems in Mathematics explained

Open Problems in Mathematics is a book, edited by John Forbes Nash Jr. and Michael Th. Rassias, published in 2016 by Springer . The book consists of seventeen expository articles, written by outstanding researchers, on some of the central open problems in the field of mathematics. The book also features an Introduction on John Nash: Theorems and Ideas, by Mikhail Leonidovich Gromov. According to the editors’ Preface, each article is devoted to one open problem or a “constellation of related problems”.^{[1] [2] [3] [4] [5]}

Choice of problems

Nash and Rassias write in the preface of the book that the open problems presented “were chosen for a variety of reasons. Some were chosen for their undoubtable importance and applicability, others because they constitute intriguing curiosities which remain unexplained mysteries on the basis of current knowledge and techniques, and some for more emotional reasons. Additionally, the attribute of a problem having a somewhat vintage flavor was also influential” in their decision process.^[6]

Table of contents

• Preface, by John F. Nash Jr. and Michael Th. Rassias
• A Farewell to “A Beautiful Mind and a Beautiful Person”, by Michael Th. Rassias
• Introduction, John Nash: Theorems and Ideas, by Mikhail Leonidovich Gromov
• P =? NP, by Scott Aaronson
• From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond, by Owen Barrett, Frank W. K. Firk, Steven J. Miller, and Caroline Turnage-Butterbaugh
• The Generalized Fermat Equation, by Michael Bennett, Preda Mihăilescu, and Samir Siksek
  • • • The Conjecture of Birch and Swinnerton-Dyer, by John H. Coates An Essay on the Riemann Hypothesis, by Alain Connes Navier–Stokes Equations: A Quick Reminder and a Few Remarks, by Peter Constantin Plateau’s Problem, by Jenny Harrison and Harrison Pugh
    • The Unknotting Problem, by Louis Kauffman How Can Cooperative Game Theory Be Made More Relevant to Economics?: An Open Problem, by Eric Maskin The Erdős–Szekeres Problem, by Walter Morris and Valeriu Soltan
  • Novikov’s Conjecture, by Jonathan Rosenberg The Discrete Logarithm Problem, by René Schoof
    • • Hadwiger’s Conjecture, by Paul Seymour The Hadwiger–Nelson Problem, by Alexander Soifer Erdős’s Unit Distance Problem, by Endre Szemerédi Goldbach’s Conjectures: A Historical Perspective, by Robert Charles Vaughan
• The Hodge Conjecture, by Claire Voisin

Notes and References

1. https://www.ams.org/journals/notices/201605/201605FULLISSUE.pdf Open Problems in Mathematics, Notices of the AMS, v.63 No. 5 p. 506, May 2016.
2. https://www.ias.edu/2016/rassias-nash Open Problems in Mathematics with John Nash
3. Book: John Forbes Nash Jr.

   . Nash . J. F. . John Forbes Nash Jr. . Rassias . M. Th. . Open Problems in Mathematics . Springer, New York . 2016 .

4. News: Open Problems in Mathematics (review). Zaldiva. Felipe. November 7, 2016. Mathematical Association of America. 23 January 2017.
5. Web site: Review: Open Problems in Mathematics. Bultheel. Adhemar. Adhemar Bultheel . August 8, 2016. European Mathematical Society. 23 January 2017.
6. Book: John Forbes Nash Jr.

   . Nash . J. F. . John Forbes Nash Jr. . Rassias . M. Th. . Preface: Open Problems in Mathematics . Springer, New York . 2016 . v-vi .