“It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, “Economics is what economists do,” and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.”

—  Kenneth E. Boulding

Source: 1970s, Economics As a Science, 1970, p. 97

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Kenneth E. Boulding photo
Kenneth E. Boulding 163
British-American economist 1910–1993

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C. West Churchman (1913–2004) American philosopher and systems scientist

Mathematics is a way of preparing for decisions through thinking. Sets and classes provide one way to subdivide a problem for decision preparation; a set derives its meaning from decision making, and not vice versa.

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“A distinguished economist, on being asked to define the subject matter of his science, once replied, "Economics is what economists do."”

Kenneth E. Boulding (1910–1993) British-American economist

Source: 1940s, Economic Analysis, 1941, p. 3

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“What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else.”

Stanislaw Ulam (1909–1984) Polish-American mathematician

Source: Adventures of a Mathematician - Third Edition (1991), Chapter 15, Random Reflections on Mathematics and Science, p. 273-274

“We have defined the main task of economic analysis as the explanation of the magnitudes of economic quantities. The student will find also that the main part of this, as of most other works on the subject, is concerned with the theory of the determination of prices, wages, interest rates, incomes, and the like. He may well inquire, therefore, in the midst of so much mathematics, whether the first task of economics is not the investigation of wealth, or welfare. Some economists have endeavored to restrict the boundaries of the science to the investigation of those quantities which are numerically measurable. Well-being, under such a restriction, would not be part of economics at all.”

Kenneth E. Boulding (1910–1993) British-American economist

Source: 1940s, Economic Analysis, 1941, p. 7-8

“As far as the use of mathematics in economics is concerned, there is an abundance of formulas where such are not needed. They are frequently introduced, one fears, in order to show off. The more difficult the mathematical theorem, the more esoteric the name of the mathematician quoted, the better.”

Oskar Morgenstern (1902–1977) austrian economist

Oskar Morgenstern, " Limits of the Use of Mathematics in Economics https://www.princeton.edu/~erp/ERParchives/archivepdfs/M49.pdf," in: James C. Charlesworth (Hg.), Mathematics and the Social Science. The Utility and Inutility of Mathematics in the Study of Economics, Political Sciences and Sociology, Philadelphia 1963, S. 12-29, hier S. 18.

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“It is not of the essence of mathematics to be conversant with the ideas of number and quantity.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 12; Cited in: Alexander Bain (1870) Logic, p. 191

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“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

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“Economic theory deals with two concepts, Value and Economy. Abstract reasoning regarding these concepts rests ultimately on mathematical concepts of quantity, time and energy. The three are inseparable, for quantity and time are dimensions of energy. The quantity relationships of energy, usually termed "statics," turn on the problem of the relation of the parts to the whole, while the time relationships, usually termed "dynamics," are the relations of a process that connects past, present and future.”

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“Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”

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Source: 1910s, Mysticism and Logic and Other Essays http://archive.org/stream/mysticism00russuoft/mysticism00russuoft_djvu.txt (1918), Ch. 5: Mathematics and the Metaphysicians

“The only generally agreed upon definition of mathematics is "Mathematics is what mathematicians do." […]
In the face of this difficulty [of defining "computer science"] many people, including myself at times, feel that we should ignore the discussion and get on with doing it. But as George Forsythe points out so well in a recent article*, it does matter what people in Washington D. C. think computer science is. According to him, they tend to feel that it is a part of applied mathematics and therefore turn to the mathematicians for advice in the granting of funds. And it is not greatly different elsewhere; in both industry and the universities you can often still see traces of where computing first started, whether in electrical engineering, physics, mathematics, or even business. Evidently the picture which people have of a subject can significantly affect its subsequent development. Therefore, although we cannot hope to settle the question definitively, we need frequently to examine and to air our views on what our subject is and should become.”

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

Hamming cites Forsythe, G.E., "What to do until the computer scientist comes", Am. Math. Monthly 75 (5), May 1968, p. 454-461.
One Man's View of Computer Science (1969)

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