Aleksandr Khinchin

Alexander Yakovlevich Khinchin ( alternate spelling: Aleksandr Jakovlevich Khintchine, Russian Александр Яковлевич Хинчин, scientific transliteration: .. Aleksandr Jakovlevic Chinčin; * 7 Julijul / July 19 1894greg in Kondyrjowo in today's Kaluga oblast, † November 18, 1959 in Moscow) was a Russian mathematician. His main area of ​​work was the stochastics. Such a sentence to the weak law of large numbers is named after him. He is referred to in the literature ( among others) as one of the founders of probability theory in the Soviet Union. He also wrote several important works on the history of mathematics.

Stations of the teaching and research

In Kaluga, he completed a secondary school, only to deepen 1906-1907 in Zurich at a private school his schooling. After that he went to Moscow on a real high school. At Moscow University he began his mathematical studies in 1911. In the research group led by the mathematician Nikolai Nikolaevich Luzin, he began his first independent investigations into the function theory. After his studies, which he finished in 1916, he worked at a polytechnic institute in Moscow and was subsequently appointed professor at the Faculty of mathematics and physics in Ivanovo- Vosnessensk.

When he was offered in 1922 a chair of mathematics, he went back to Moscow. Previously, he had worked at a research institute of the State University in Moscow. In 1939 the Academy of Sciences of the USSR, he was named a corresponding member. In the thirties he became head of the section for the methodology of teaching in the People's Commissariat for Education of the RSFSR. From the mid- forties, he also belonged to the Presidium of the Russian Academy of pedagogical sciences for years to come.

Research

Building on the work of Arnaud Denjoy respect to a generalized integration method, he began to formulate the conditions that at a defined interval of a measurable function on almost all points an asymptotic derivation can be formed. After that Khinchin focused on research in the field of number theory, such as the properties of irrational numbers.

He dealt with the application of the metric theory of functions in the field of probability theory. In particular, he looked at the context of sums of independent random variables and infinitely divisible distributions. He was able to show, for example, that with a suitable choice of the constants, the sum of normalized, independent and identically distributed distributions always converges to a normal distribution ( central limit theorem ).

At the same time as Andrei Nikolaevich Kolmogorov he showed some basics for the description of random processes, which are needed for the construction and function of technical, automatic systems and their workflows. This work led him to the field of classical quantum physics, where he was able to prove by analytical means some contexts. With the same developed by George David Birkhoff conditions for the ergodic theorem succeeded Khinchin, to show that it is sufficient in experimental procedures to consider only a stationary process if the mean and associated scatter of experimental variables have to be estimated. Furthermore, he turned to the field of information theory, the basics of Claude Elwood Shannon were created. The Wiener- Khinchin theorem is named after him and after Norbert Wiener.