Open Problems in Mathematics

by John Forbes Nash Jr. (Editor), Michael Th. Rassias (Editor)

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.

Genres: Mathematics

556 pages, Hardcover

Published July 14, 2016

Reviews

[Riley Holmes · Rating 5 out of 5]

I picked this up because the first (and most meaty) chapter on P vs NP was written by Scott Aaronson - solicited by John "Beautiful Mind" Nash.
http://www.scottaaronson.com/blog/?p=...
A trip to the cutting edge is no walk in the park, but most of the chapters were accessible enough to spark interest in the problems before my eyes glazed over on the more technical details.
Nash's last book before his unfortunate demise is a trove of information and inspiration. Each chapter provides a thorough look at the state of knowledge, with hundreds of references at varying levels of depth and breadth.
Highly recommended for anyone working or interested in math research.