WHERE MATHEMATICS IS GOING
Vyacheslav Emerikovich Voitsekhovich1, Georgy Gennadievich Malinetsky2
1Tver State University, Tver, Russia
2Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia
Keywords: civilization, rationalism, science, mathematics, synergetic, complexity, movement, logic, artificial intelligence
Abstract
Modern industrial-technological civilization, along with science and mathematics, has entered a crisis period of evolution, which will end only when civilization enters a new, more spiritual stage of development. Rationalism, based upon operating with “fixed” con-cepts (in the spirit of the law of identity in logic), is outdated and unable to express the specificity of developing objects studied by the theory of self-organization. More complex thinking with moving concepts-images is being formed in science. The article describes the difficulties of the development of mathematics in the 21st century and ways to overcome them. New ideas are introduced: the future of mathematics lies in the development of scientists’ creativity, intuitive insight and the promotion of new, deeper concepts and theorems-guesses expressing their properties, rather than in the logical rigor of proofs. A large part of evidence will eventually be transferred to artificial intelligence. Modern mathematical knowledge is growing due to the applied aspect - modeling. Mathematics has already become a “branch of industry”. Science comes close to art. A new criterion of scientific character will appear, that is “truth as beauty”.
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