7. Probability and Statistics Soviet Essays - Sheynin, Oscar

2. The history of probability theory may be tentatively separated into four portions of time.The first period, when the elements of our science were created, is connected with the namesof Pascal (1623 – 1662), Fermat (1601 – 1665) and especially Jakob Bernoulli (1654 – 1705).The second one lasted throughout the 18 th , and the beginning of the 19 th century: De Moivre(1667 – 1754), Laplace (1749 – 1827), Gauss (1777 – 1855) and Poisson (1781 – 1840). Thethird period, i.e., the second half of the 19 th century, is largely connected with the names ofRussian scientists, Chebyshev (1821 – 1894), Markov (1856 – 1922) and Liapunov (1857 –1918). In Western Europe, general theoretical research in probability theory during this timeremained somewhat in the background. With regard to its theoretical stochastic methods, theemerging mathematical statistics (Quetelet, Cournot, Galton, K. Pearson, Bruns,Bortkiewicz) mainly managed with the results of the previous period, whereas the newrequirements made by statistical physics were not yet sufficiently expressed in generalcontributions on the theory of probability. In Russia, meanwhile, almost exclusively by theefforts of the three abovementioned celebrated mathematicians, the entire system of thetheory was reconstructed, broadened and essentially deepened. Their work formed a solidbasis for the development of probability theory during the fourth period, the beginning of the20 th century. This was the time of a general strengthening of interest in the theory asmanifested in all countries, and of an extraordinary broadening of its field of application invarious special branches of natural sciences, technology and social sciences. Although theSoviet {school of} probability does not possess such an exclusive place in this intensiveinternational scientific work as the one that fell to the lot of the classical Russian research ofthe previous period, it seems to me that its rank is also very significant, and that, with regardto the general problems of the probability theory itself, it even occupies the first place.3. Russian scientists did not participate in the work of the first period, when the mainelementary concepts of our science, the elementary propositions such as the addition and themultiplication theorems, and the elementary arithmetical and combinatorial methods wereestablished. The concrete material studied mostly amounted to problems in games of chance(dice, playing cards, etc). Paradoxically, however, this was mainly a philosophical period inthe development of the theory of probability.It was the time when mathematical natural science was created. The goal of the epoch wasto comprehend the unusual broadness and flexibility (and, as it appeared then, omnipotence)of the mathematical method of studying causal ties. The idea of a differential equation as alaw uniquely determining the forthcoming evolution of a system, given its present state,occupied an even more exclusive place in the mathematical natural science than it doesnowadays.For this branch of knowledge, the theory of probability is required when the deterministicpattern of differential equations is not effective anymore; at the same time, the concretenatural-scientific material for applying the theory in a calculating, or, so to say, business-likeway, was yet lacking. Nevertheless, the inevitability of coarsening real phenomena whenfitting them in with deterministic patterns of the type provided by systems of differentialequations, was already sufficiently understood. It was also clear that quite discernibleregularities may occur in the mean out of the chaos of an enormous number of phenomenadefying individual account and unconnected one with another. Exactly here the fundamentalrole of probability theory in theoretical philosophy was foreseen. Of course, just this aspectrather than the servicing of the applied problems posed by Chevalier de Méré, so stronglyattracted Pascal to probability, and (already explicitly) guided Jakob Bernoulli during thetwenty years when he was searching for a proof of his limit theorem that also nowadays isthe basis of all applications of probability theory. This proposition solved with sufficientcompleteness the main problem of theoretical philosophy encountered in the theory’s first