“Even measured by Wiener's standards Cybernetics is a badly organised work — a collection of misprints, wrong mathematical statements, mistaken formulas, splendid but unrelated ideas, and logical absurdities. It is sad that this work earned Wiener the greater part of his public renown, but this is an afterthought. At that time mathematical readers were more fascinated by the richness of its ideas than by its shortcomings.”

— Hans Freudenthal

Norbert Wiener (2008)

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Hans Freudenthal 27

Dutch mathematician 1905–1990

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“While studying antiaircraft fire control, Wiener may have conceived the idea of considering the operator as part of the steering mechanism and of applying to him such notions as feedback and stability, which had been devised for mechanical systems and electrical circuits. No doubt this kind of analogy had been operative in Wiener’s mathematical work from the beginning and sometimes had even been productive. As time passed, such flashes of insight were more consciously put to use in a sort of biological research for which Wiener consulted all kinds of people, except mathematicians, whether or not they had anything to do with it. Cybernetics, or Control and Communication in the Animal and the Machine (1948) is a rather eloquent report of these abortive attempts, in the sense that it shows there is not much to be reported. The value and influence of Cybernetics, and other publications of this kind, should not, however, be belittled. It has contributed to popularizing a way of thinking in communication theory terms, such as feedback, information, control, input, output, stability, homeostasis, prediction, and filtering. On the other hand, it also has contributed to spreading mistaken ideas of what mathematics really means”

Hans Freudenthal (1905–1990) Dutch mathematician

Norbert Wiener (2008)

“Pure mathematics is in its way the poetry of logical ideas.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

1930s, Obituary for Emmy Noether (1935)
Context: Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.

“Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.”

Freeman Dyson (1923) theoretical physicist and mathematician

The Scientist As Rebel (2006)

“Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

1930s, Obituary for Emmy Noether (1935)

“We are told … statements that are not mathematical or logical formulae may look as if they were necessarily or certainly true, but they only look like that. They cannot really be either necessary or certain.”

Robert Maynard Hutchins (1899–1977) philosopher and university president

Great Books: The Foundation of a Liberal Education (1954)

“Fundamental ideas play the most essential role in forming a physical theory. Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of a quantitative theory, to make possible the comparison with experiment.”

Albert Einstein book The Evolution of Physics

The Evolution of Physics (1938) (co-written with Leopold Infeld)
1930s

“The only possible idea of India is that of a nation greater than the sum of its parts.”

Shashi Tharoor (1956) Indian politician, diplomat, author

The Hindu, "Strengthening Indianness ", Sunday, Jan 19, 2003, Available Online http://www.hinduonnet.com/thehindu/mag/2003/01/19/stories/2003011900240300.htm
2000s

“The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.”

John Von Neumann (1903–1957) Hungarian-American mathematician and polymath

As quoted in Bigeometric Calculus: A System with a Scale-Free Derivative (1983) by Michael Grossman, and in Single Variable Calculus (1994) by James Stewart.

“The more recent concern with complex adaptive organization has led to the notion of contingency as the important key. Thus Wiener, while working in the field of communications and probability theory, became convinced 'that a significant idea of organization cannot be obtained in a world in which everything is necessary and nothing is contingent”

Walter F. Buckley (1922–2006) American sociologist

Source: Sociology and modern systems theory (1967), p. 82 as cited in: Felix Geyer, Johannes van der Zouwen, (1994) " Norbert Wiener and the Social Sciences http://www.critcrim.org/redfeather/chaos/024Weiner.htm", Kybernetes, Vol. 23 Iss: 6/7, pp.46 - 61. Buckley is here referring to Norbert Wiener (1953) I am a Mathematician; The Later Life of a Prodigyan, MIT Press, Cambridge, MA, p. 322.

“The revolution in scientific ideas just mentioned is primarily logical. It is due to recognition that the very method of physical science, with its primary standard units of mass, space, and time, is concerned with measurements of relations of change, not with individuals as such.”

John Dewey (1859–1952) American philosopher, psychologist, and educational reformer

Time and Individuality (1940)

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