The modern crisis of scientific knowledge is manifested in the overdifferentiation of knowledge, the loss of a unified picture of the world, dead ends in the development of various sciences. A way out of the crisis is possible when scientists master the synergetic style of thinking, i.e. thinking in “moving thought forms”. The paradigm of Parmenides, accepted in scientific thinking, is gradually being replaced by the paradigm of Heraclitus. The thesis “The One is essentially motionless” is replaced by the thesis “Everything is movement”. The new rationalism will require a revision of many outdated traditions of scientific knowledge. We consider these problems in the context of the development of logic and applied mathematics. Applied mathematics and its transformation into an industry of strategic importance are playing a key role in changing the paradigm of science.

scientific thinking, rest, movement, moving form, generalized law of identity, mathematical metaphor, self-organization, synergetics, Parmenides, Heraclitus, from existing to emerging, philosophy of mathematics, Hilbert problems, Penrose tiles, revolution in the field of artificial intelligence

Mathematical problems and theory of numerical methods

Voytsekhovich Vyacheslav Emerikovich,  ,  orcid.org/0000-0002-8093-7121,  Tver State University

Malinetskii Georgii Gennadyevich,  ,  orcid.org/0000-0001-6041-1926,  KIAM RAS