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Unlike some other reproductions of classic texts (1) We have not
used OCR(Optical Character Recognition), as this leads to bad
quality books with introduced typos. (2) In books where there are
images such as portraits, maps, sketches etc We have endeavoured to
keep the quality of these images, so they represent accurately the
original artefact. Although occasionally there may be certain
imperfections with these old texts, we feel they deserve to be made
available for future generations to enjoy.
Unlike some other reproductions of classic texts (1) We have not
used OCR(Optical Character Recognition), as this leads to bad
quality books with introduced typos. (2) In books where there are
images such as portraits, maps, sketches etc We have endeavoured to
keep the quality of these images, so they represent accurately the
original artefact. Although occasionally there may be certain
imperfections with these old texts, we feel they deserve to be made
available for future generations to enjoy.
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.
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