Introduction to the Subject

Abstract

Extremal problems play an extraordinarily large role in the application of mathematics to practical problems, for example:

• (α) in mathematical physics (mechanics and celestial mechanics, geometrical optics, elasticity theory, hydrodynamics, rheology, relativity theory, etc.);

• (β) in geometry (geodesics, minimal surfaces, etc.);

• (γ) in mathematical economics (transport problems, optimal warehouse maintenance);

• (δ) in regulation technology (optimal control of general regulation systems, e.g., industrial installations, spaceships, etc.);

• (ε) in chemistry, geophysics, technology, etc. (optimal determination of unknown data from measurements);

• (ζ) in numerical mathematics (optimal structuring of approximation processes, etc.);

• (η) in the theory of probability (optimal control of stochastic processes, optimal estimation of unknown parameters, optimal construction of airplanes, water-power networks, etc.).

I love mathematics not only because it is applicable to technology but also because it is beautiful.

Rósza Péter

Science is a first class piece of furniture for the bei etage—as long as common sense reigns on the ground floor.

Oliver Wendell Holmes