Lectures of probability on Polish territory at the end of the nineteenth and early twentieth centuries

Dorota Dudek ; Wiesław Zięba

Antiquitates Mathematicae, Tome 4 (2010).

Résumé

Probability theory at the turn of the nineteenth and twentieth centuries was not treated as a branch of  mathematics, but as a part of physics. Therefore, the grounds of tasks and truthfulness rights probability often took place through experiments (which led to many erroneous statements). Following the formation and development of the theory of probability we observe some groundbreaking achievements that have enabled this area to stand on a new qualitative level. Such an achievement was undoubtedly the discovery by Jacob Bernoulli's law of large numbers. But before that happened it appeared a number of problems and doubts related to the concept of certainty or with the notion of a random event. The development of this theory resulted in the need to clarify its basis. It required the development of statistical physics, economics, commerce, insurance and other areas  based on probabilistic methods, as well as the development of probability theory itself. In order to determine the logical structure and consistency of mathematical arguments it has been necessary to separate the basic concepts and assumptions, and check their consistency. These problems could only be axiomatization of probability theory. In 1900, at the Second Congress of Mathematicians in Paris, David Hilbert in his seminal lecture  formulated  23 issues. In them appeared VI important issue, concerning the axiomatic among other things probability. The axioms of probability theory are given in 1923 by A. Łomnicki (based on set theory and the theory of measurement), and then in 1933 by the Russian mathematician A.~N.~Kołmogorowa

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