Open Problems in Mathematics

By: Jr. and John Forbes Forbes Nash and Michael Th. Th. Rassias

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Synopsis: The goal in putting together this unique compilation was to presentthe current status of the solutions to some of the most essential open problemsin pure and applied mathematics. Emphasis is also given to problems ininterdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the mosteminent mathematicians in the international mathematical community onlongstanding problems in very active domains of mathematical research. A jointpreface 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 Gromovhighlights some of Nash's legendary mathematical achievements. The treatment in this book includes open problems inthe following fields: algebraic geometry, number theory, analysis, discretemathematics, PDEs, differential geometry, topology, K-theory, game theory, fluidmechanics, dynamical systems and ergodic theory, cryptography, theoreticalcomputer science, and more. Extensive discussions surrounding the progress madefor each problem are designed to reach a wide community of readers, fromgraduate students and established research mathematicians to physicists,computer scientists, economists, and research scientists who are looking todevelop essential and modern new methods and theories to solve a variety ofopen problems.