Open Problems in Mathematics

Open Problems in Mathematics

<p>The goal in putting together this unique compilation was to present<br />the current status of the solutions to some of the most essential open problems<br />in pure and applied mathematics. Emphasis is also given to problems in<br />interdisciplinary research for which mathematics plays a key role.  This volume comprises highly selected contributions by some of the most<br />eminent mathematicians in the international mathematical community on<br />longstanding problems in very active domains of mathematical research. A joint<br />preface by the two volume editors is followed by a personal farewell to John F.<br />Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov<br />highlights some of Nash’s legendary mathematical achievements. </p><br /><br />The treatment in this book includes open problems in<br />the following fields: algebraic geometry, number theory, analysis, discrete<br />mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid<br />mechanics, dynamical systems and ergodic theory, cryptography, theoretical<br />computer science, and more. Extensive discussions surrounding the progress made<br />for each problem are designed to reach a wide community of readers, from<br />graduate students and established research mathematicians to physicists,<br />computer scientists, economists, and research scientists who are looking to<br />develop essential and modern new methods and theories to solve a variety of<br />open problems.