Open Problems in Mathematics

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.