“Science and mathematics… have added little to our understanding of such things as Truth, Beauty, and Justice. There may be definite limits to the applicability of the scientific method.”

— Richard Hamming

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

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Richard Hamming 90

American mathematician and information theorist 1915–1998

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Context: The assumptions and definitions of mathematics and science come from our intuition, which is based ultimately on experience. They then get shaped by further experience in using them and are occasionally revised. They are not fixed for all eternity.

“As Uchimaru sees things, an engineer who doesn't think TQM applies to technical activities must not understand either engineering or TQM or both. TQM is the application of the scientific method to business (pick an important problem, get the facts, analyze the facts, find the underlying truth, plan a method of improvement based on the underlying truth, systematically test it to verify that it works, standardize the new method, and then the cycle around again)”

Shoji Shiba (1930) Japanese academic

Shōji Shiba, New American TQM. Productivity press, 1993. p. 463
Shiba talks about Kiyoshi Uchimaru, who was president of NEC's main microchip design subsidiary in the 1980s.

“After years of work in both areas of study, I concluded that the social sciences were different, in many important ways, from the natural sciences, but that the same scientific methods were applicable in both areas, and, indeed, that no very useful work could be done in either area except by scientific methods.”

Carroll Quigley (1910–1977) American historian

Source: The Evolution of Civilizations (1961) (Second Edition 1979), Chapter 1, Scientific Method and the Social Sciences, p. 33

“Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.”

Aristotle book Metaphysics

Book XIII, 1078a.33
Metaphysics

“If scientific reasoning were limited to the logical processes of arithmetic, we should not get far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.”

Vannevar Bush book As We May Think

As We May Think (1945)
Context: If scientific reasoning were limited to the logical processes of arithmetic, we should not get far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability. The abacus, with its beads strung on parallel wires, led the Arabs to positional numeration and the concept of zero many centuries before the rest of the world; and it was a useful tool — so useful that it still exists.