1 Studies in the History of Statistics and Probability ... - Sheynin, Oscar

What objections can be made? First, since the problem concerns aninterval of a few centuries of time, it will be advisable to turn tohistory and look whether there are examples of what is happening withsome fields of intellectual activity the interest in which is preserved aslong as that. An example of such an activity is the scholasticism of theMiddle Ages.Scholastics were clever and diligent. In any case, the volume oftheir contributions was of the same order as, say, those of Laplace (theamount of paper that a man can cover with writing during his lifetimelikely little depends on the contents of the written). Universities andacademies had been initially created for scholastics because of theimportance of the moral and ethical applications of their work, actualor imagined. No one had expelled them from those institutions with ared-hot broom 25 , but it somehow happened all by itself that scientists,physicists, mathematicians, chemists etc., had occupied their places.Why did that occur?I believe that the reason was that scholasticism had graduallywithdrawn into its own business and quit to provide society solutionsof moral problems essential for everyday life. For example, now, as inthe Middle Ages, each solves for himself whether to marry or not.Scholastics naturally discussed that problem but their answers becamelong summaries of the diverse opinions of fathers of the church andancient philosophers 26 . What then should have done a practicallyworking clergyman when asked by his parishioner?Such questions gradually occurred unbecoming to serious scienceand then it somehow happened all by itself that the society had begunto consider unbecoming scholasticism as a whole. This examplecompels us to think carefully what would have happened tomathematics had it been for centuries cut off from all the streams ofactivities. The action of the ensuing phenomenon would have beenvery simple: the number of young men wishing to devote themselvesto mathematics would have gradually decreased since those otherstreams indeed play the most important part in attracting their interest.However, finally it is possible to admit, and Dieudonne’s articleconvinces us, that there exists mathematics of different types; one isdirected towards its own interests, the other one, towards applications.Both have a quite lawful right to exist because, for example, theKolmogorov axiomatics of the theory of probability, necessary in asense for applications as well, had emerged on the basis of the theoryof functions of a real variable (obviously belonging to the first type).But then, to which type does the theory of probability belong?The distinguishing feature of mathematics of the first type is itssomewhat special elegance (presenting a comparative simplicity whichmakes it possible to perceive that quality). The theory of probabilityhas rather many results of exactly that kind, mostly connected with theKolmogorov axiomatics and resembling the theory of functions of areal variable. However, the main contents of that science having beenformed at the time of Laplace 27 , developing after him and beingelaborated nowadays is not, alas! beautiful at all. For example, limittheorems are usually rather decently formulated, but as a rule theirproofs are helplessly long, difficult and entangled. Their sole raison117