...Preface During the past century, the impact of mathematics on humanity has been more tremendous than ever since Galileo's agonizing fight against the old establishment and the revolution which physics experienced after Newton's subsequent synthesis. At the beginning of the last century, mathematical ideas and techniques were spread to theoretical and applied physics by the influence of two of the greatest mathematicians of all times, D. Hilbert and H. Poincar6, being then at the zenith of their careers. Their ability to establish very deep at first glance often hidden connections between a priori separated branches of science convinced physicists to adopt and work with the most powerful existing mathematical tools. Whereas the 20th century really was the century of physics, mathematics enjoyed a well deserved reputation from its very beginning, so facilitating the huge impact it had subsequently on humanity. This reputation has been crucial for the tremendous development of science and technology. Although mathematics supported the development of weapons of mass destruction, it simultaneously promoted the advancement of computers and high technology, without which the substantial improvement of the living conditions humanity as a whole has experienced, could not have been realized. In no previous time the world has seen such a spectacular growth of scientific knowledge as during the last century, with mathematics playing a central role in most scientific and...
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