Richard von Mises - Collected Quotes

"A collective appropriate for the application of the theory of probability must fulfil two conditions. First, the relative frequencies of the attributes must possess limiting values. Second, these limiting values must remain the same in all partial sequences which may be selected from the original one in an arbitrary way. Of course, only such partial sequences can be taken into consideration as can be extended indefinitely, in the same way as the original sequence itself." (Richard von Mises, "Probability, Statistics and Truth", 1928)

"A great number of popular and more or less serious objections to the theory of probability disappear at once when we recognize that the exclusive purpose of this theory is to determine, from the given probabilities in a number of initial collectives, the probabilities in a new collective derived from the initial ones." (Richard von Mises, "Probability, Statistics and Truth", 1928)

"The rational concept of probability, which is the only basis of probability calculus, applies only to problems in which either the same event repeats itself again and again, or a great number of uniform elements are involved at the same time. Using the language of physics, we may say that in order to apply the theory of probability we must have a practically unlimited sequence of uniform observations." (Richard von Mises, "Probability, Statistics and Truth", 1928)

"The result of each calculation appertaining to the field of probability is always, as far as our theory goes, nothing else but a probability, or, using our general definition, the relative frequency of a certain event in a sufficiently long (theoretically, infinitely long) sequence of observations. The theory of probability can never lead to a definite statement concerning a single event. The only question that it can answer is: what is to be expected in the course of a very long sequence of observations? It is important to note that this statement remains valid also if the calculated probability has one of the two extreme values 1 or 0." (Richard von Mises, "Probability, Statistics and Truth", 1928)

"All followers of the axiomatic method and most mathematicians think that there is some such thing as an absolute ‘mathematical rigor’ which has to be satisfied by any deduction if it is to be valid. The history of mathematics shows that this is not the case, that, on the contrary, every generation is surpassed in rigor again and again by its successors." (Richard von Mises, "Positivism: A Study in Human Understanding", 1951)

"If the concept of probability and the formulae of the theory of probability are used without a clear understanding of the collectives involved, one may arrive at entirely misleading results." (Richard von Mises, "Probability, Statistics, and Truth"2nd Ed., 1957)

"Remember that algebra, with all its deep and intricate problems, is nothing but a development of the four fundamental operations of arithmetic. Everyone who understands the meaning of addition, subtraction, multiplication, and division holds the key to all algebraic problems." (Richard von Mises, "Probability, Statistics, and Truth"2nd Ed., 1957)

"Starting from statistical observations and applying to them a clear and precise concept of probability it is possible to arrive at conclusions which are just as reliable and ‘truth-full’ and quite as practically useful as those obtained in any other exact science." (Richard von Mises, "Probability, Statistics, and Truth"2nd Ed., 1957)

"The main interest of physical statistics lies in fact not so much in the distribution of the phenomena in space, but rather in their succession in time." (Richard von Mises, "Probability, Statistics, and Truth"2nd Ed., 1957)

"The problems of statistical physics are of the greatest in our time, since they lead to a revolutionary change in our whole conception of the universe." (Richard von Mises, "Probability, Statistics, and Truth"2nd Ed., 1957)

"The theory of probability can never lead to a definite statement concerning a single event." (Richard von Mises, "Probability, Statistics, and Truth" 2nd Ed., 1957)

"The probability concept used in probability theory has exactly the same structure as have the fundamental concepts in any field in which mathematical analysis is applied to describe and represent reality." (Richard von Mises, "Mathematical Theory of Probability and Statistics", 1964)