The theory of blowup regimes and localized non-stationary dissipative structures developed by Sergey P. Kurdyumov and his progeny received worldwide recognition. I consider the foundations of these approaches, hopes and prospects that were associated with the development of Kurdyumov’s scientific school. Time acts, on the one hand, as a creator giving birth to something new, and on the other hand as a cruel, demanding editor choosing from plans and forecasts what will become reality. If we compare a broad school of thought to a tree, this article discusses its roots, while other works in the issue the branches and leaves that have grown over the past decades.

S.P. Kurdyumov, scientific school, non-stationary dissipative structures, self-organization, synergetics, nonlinear medium eigenfunctions, symmetries, exact solutions, self-organized criticality, dynamic chaos, neural networks

Malinetskii Georgii Gennadyevich,  gmalin@Keldysh.ru,  orcid.org/0000-0001-6041-1926,  KIAM RAS