On Randomness XVII (Mathematics)

"Comparing the rough data of our senses with that extremely complex and subtle conception which mathematicians call magnitude, we are compelled to recognise a divergence. The framework into which we wish to make everything it is one of our own construction; but we did not construct it at random, we constructed it by measurement so to speak; and that is why we can it the facts into it without altering their essential qualities." (Henri Poincaré, "Science and Hypothesis", 1901)

"The definition of random in terms of a physical operation is notoriously without effect on the mathematical operations of statistical theory because so far as these mathematical operations are concerned random is purely and simply an undefined term." (Walter A Shewhart and W. Edwards "Deming, Statistical Method from the Viewpoint of Quality Control", 1939)

"I suspect that even if the random walkers announced a perfect mathematic proof of randomness I would go on believing that in the long run future earnings influence present value, and that in the short run the dominant factor is the elusive Australopithecus, the temper of the crowd." (Adam Smith, "The Money Game", 1968)

"The popular image of mathematics as a collection of precise facts, linked together by well-defined logical paths, is revealed to be false. There is randomness and hence uncertainty in mathematics, just as there is in physics." (Paul Davis, "The Mind of God", 1992)

"Mathematics, far from being stymied by this situation, finds enormous value in it. The fecundity of ‘randomness’ is astounding; it is an inexhaustible source of scientific riches. Could ‘randomness’ be such a rich notion because of the inner contradiction that it contains, not despite it? The depth we sense in ‘randomness’ comes from something that lies behind any specific mathematical definition." (William Byers," How Mathematicians Think", 2007)

"The key to understanding randomness and all of mathematics is not being able to intuit the answer to every problem immediately but merely having the tools to figure out the answer." (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"The randomness which lies at the very foundations of pure mathematics of necessity permeates every human description of nature" (Joseph Ford)