Andrey Kolmogorov
Native spelling: Андрей Николаевич Колмогоров
1903–1987, Tambov, Russian Empire (now Russia), Moscow, Soviet Union (now Russia)
Soviet mathematician whose 1933 monograph axiomatized probability theory using measure theory; he also made foundational contributions to Fourier series, topology, turbulence, dynamical systems (KAM theory), and algorithmic complexity.
Andrey Kolmogorov entered Moscow State University in 1920 and, while still an undergraduate in Nikolai Luzin's circle, stunned analysts in 1922 by constructing an integrable function whose Fourier series diverges almost everywhere. He graduated in 1925, completed his doctorate in 1929, and was appointed professor at Moscow State University in 1931.
His 1933 monograph 'Grundbegriffe der Wahrscheinlichkeitsrechnung' ('Foundations of the Theory of Probability') placed probability on a rigorous measure-theoretic axiomatic basis and provided a rigorous definition of conditional expectation. Earlier work with Aleksandr Khinchin established the three-series theorem, and his 1931 and 1938 papers laid the analytical foundations of continuous-time Markov processes and diffusion theory.
Kolmogorov's reach extended across mathematics: he co-discovered cohomology rings in topology (independently of J. W. Alexander), published fundamental 1941 papers on the statistical theory of turbulent fluid flow, initiated KAM theory in Hamiltonian mechanics in 1954, resolved Hilbert's thirteenth problem with his student Vladimir Arnold in 1957, and in the 1960s founded algorithmic information theory (Kolmogorov complexity). He received the Wolf Prize in Mathematics in 1980.
Workplaces: Moscow State University, Steklov Mathematical Institute
Russia