“Classical mechanics is mathematical not only in the sense that it makes use of mathematical terms and methods for abbreviating arguments which might, if necessary, also be expressed in the language of everyday speech; it is so also in the much more stringent sense that its basic concepts are mathematical concepts, that mechanics itself is a mathematics.”

Source: The mechanization of the world picture, 1961, p. 499

Adopted from Wikiquote. Last update June 3, 2021. History

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Eduard Jan Dijksterhuis7

Dutch historian 1892–1965

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.”

George Dantzig (1914–2005) American mathematician

Source: Linear programming and extensions (1963), p. 2

“The so-called mysteries of quantum mechanics are in its philosophical interpretation, not in its mathematics.”

Victor J. Stenger (1935–2014) American philosopher

In God and the Folly of Faith: The Incompatibility of Science and Religion (2012)

“The arithmetization of mathematics… which began with Weierstrass… had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics.
These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought.”

Tobias Dantzig (1884–1956) American mathematician

p, 125
Number: The Language of Science (1930)

“Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.”

Leonardo Da Vinci (1452–1519) Italian Renaissance polymath

The Notebooks of Leonardo da Vinci (1883), I Prolegomena and General Introduction to the Book on Painting

“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. The formal and abstract mathematical theory has an independent and sometimes lonely existence of its own. But when an undefined mathematical term such as random is given a definite operational meaning in physical terms, it takes on empirical and practical significance. Every mathematical theorem involving this mathematically undefined concept can then be given the following predictive form: If you do so and so, then such and such will happen.”

Walter A. Shewhart (1891–1967) American statistician

[Shewhart, Walter A., Deming, William E., Statistical Method from the Viewpoint of Quality Control, The Graduate School, The Department of Agriculture, 1939, 18]
Economic Control of Quality of Manufactured Product,1931

“A scientific theory is a concise and coherent set of concepts, claims, and laws (frequently expressed mathematically) that can be used to precisely and accurately explain and predict natural phenomena.
A theory should include a mechanism that explains how its concepts, claims, and laws arise from lower-level theories.”

Mordechai Ben-Ari (1948) Israeli computer scientist

Source: Just a Theory: Exploring the Nature of Science (2005), Chapter 2, “Just a Theory: What Scientists Do” (p. 24)

“Being a language, mathematics may be used not only to inform but also, among other things, to seduce.”

Benoît Mandelbrot (1924–2010) Polish-born, French and American mathematician

Fractals : Form, chance and dimension (1977)

“Phenomena of the external sense are examined and set forth in physics; those of the internal sense in empirical psychology. Pure mathematics considers space in geometry and time in pure mechanics. To these is to be added a certain concept, intellectual to be sure in itself, but whose becoming actual in the concrete requires the auxiliary notions of time and space in the successive addition and simultaneous juxtaposition of separate units, which is the concept of number treated in arithmetic.”

Immanuel Kant (1724–1804) German philosopher

Kant's Inaugural Dissertation (1770), Section II On The Distinction Between The Sensible And The Intelligible Generally

“But we have higher mathematics, haven't we? This gives me freedom from my senses. The language of mathematics is even more inborn and universal than the language of music; a mathematical formula is crystal clear and independent of all sense organs. I therefore built a mathematical laboratory, set myself in it as if I were sitting in a car, and moved along with a beam of light.”

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

Source: Attributed in posthumous publications, Einstein and the Poet (1983), p. 11

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