The work outlines the key ideas of Kurdyumov S.P., an outstanding specialist in applied mathematics, self-organization theory, transdisciplinary research. It considers the development of his scientific ideas in the last decade and formulates a set of open problems in synergetics which will probably stimulate the development of this approach. The article is an engaged version of the report made at Xth Kurdyumov readings held in Tver State University in 2015.

S.P. Kurdyumov, Keldysh Institute of Applied Mathematics, scientific school, theory of blow-up regimes, self-organization, synergetics, problem of time, dynamic chaos, self-organized criticality, paradigm, risk management

Mathematical modelling in actual problems of science and technics