“The science of the age, in short, is physical, chemical, physiological; in all shapes mechanical. Our favourite Mathematics, the highly prized exponent of all these other sciences, has also become more and more mechanical. Excellence in what is called its higher departments depends less on natural genius than on acquired expertness in wielding its machinery. Without undervaluing the wonderful results which a Lagrange or Laplace educes by means of it, we may remark, that their calculus, differential and integral, is little else than a more cunningly-constructed arithmetical mill; where the factors, being put in, are, as it were, ground into the true product, under cover, and without other effort on our part than steady turning of the handle. We have more Mathematics than ever; but less Mathesis.”

— Thomas Carlyle

1820s, Signs of the Times (1829)

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Thomas Carlyle 481

Scottish philosopher, satirical writer, essayist, historian… 1795–1881

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“Science Of Energetics. Although the mechanical hypothesis just mentioned may be useful and interesting as a means of anticipating laws, and connecting the science of thermodynamics with that of ordinary mechanics, still it is to be remembered that the science of thermodynamics is by no means dependent for its certainty on that or any other hypothesis, having been now reduced, to a system of principles, or general facts, expressing strictly the results of experiment as to the relations between heat and motive power. In this point of view the laws of thermodynamics may be regarded as particular cases of more general laws, applicable to all such states of matter as constitute Energy, or the capacity to perform work, which more general laws form the basis of the science of energetics, — a science comprehending, as special branches, the theories of motion, heat, light, electricity, and all other physical phenomena.”

William John Macquorn Rankine (1820–1872) civil engineer

Source: A Manual of the Steam Engine and Other Prime Movers (1859), p. 31

“It took from a hundred to a hundred and fifty or two hundred years for the astronomy of Kepler to become the astronomy of Newton and Laplace], and for the mechanics of [[Galileo to become the mechanics of d'Alembert and Lagrange. On the other hand, less than a century has elapsed between the publication of Adam Smith’s work and the contributions of Cournot, Gossen, Jevons, and myself.”

Léon Walras (1834–1910) French mathematical economist

In : John Cunningham Wood (1993), Léon Walras: The life of Léon Walras and perspectives on his thought. Taylor & Francis, p. 32-33.

“In general the position as regards all such new calculi is this - That one cannot accomplish by them anything that could not be accomplished without them. However, the advantage is, that, provided such a calculus corresponds to the inmost nature of frequent needs, anyone who masters it thoroughly is able - without the unconscious inspiration of genius which no one can command - to solve the respective problems, yea to solve them mechanically in complicated cases in which, without such aid, even genius becomes powerless. Such is the case with the invention of general algebra, with the differential calculus, and in a more limited region with Lagrange's calculus of variations, with my calculus of congruences, and with Mobius's calculus. Such conceptions unite, as it were, into an organic whole countless problems which otherwise would remain isolated and require for their separate solution more or less application of inventive genius.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

As quoted in Gauss, Werke, Bd. 8, page 298
As quoted in Memorabilia Mathematica (or The Philomath's Quotation-Book) (1914) by Robert Edouard Moritz, quotation #1215
As quoted in The First Systems of Weighted Differential and Integral Calculus (1980) by Jane Grossman, Michael Grossman, and Robert Katz, page ii

“The calculus is to mathematics no more than what experiment is to physics, and all the truths produced solely by the calculus can be treated as truths of experiment. The sciences must proceed to first causes, above all mathematics where one cannot assume, as in physics, principles that are unknown to us. For there is in mathematics, so to speak, only what we have placed there… If, however, mathematics always has some essential obscurity that one cannot dissipate, it will lie, uniquely, I think, in the direction of the infinite; it is in that direction that mathematics touches on physics, on the innermost nature of bodies about which we know little.”

Bernard Le Bovier de Fontenelle (1657–1757) French writer, satirist and philosopher of enlightenment

Elements de la géométrie de l'infini (1727) as quoted by Amir R. Alexander, Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice (2002) citing Michael S. Mahoney, "Infinitesimals and Transcendent Relations: The Mathematics of Motion in the Late Seventeenth Century" in Reappraisals of the Scientific Revolution, ed. David C. Lindberg, Robert S. Westman (1990)

“Mathematics is more than a tool and language for science. It is also an end in itself, and as such, it has, over the centuries, affected our worldview in its own right.”

Stephen Hawking book God Created the Integers

Preface
God Created the Integers (2007)

“The more advanced the sciences have become, the more they have tended to enter the domain of mathematics, which is a sort of center towards which they converge. We can judge of the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation.”

Adolphe Quetelet (1796–1874) Belgian astronomer, mathematician, statistician and sociologist

Edward Mailly, Essai sur la vie et les ouv rages de Quetelet in the Annuaire de Vacadimie royale des sciences des lettres et des beaux-arts de Belgique (1875) Vol. xli pp. 109-297 found also in "Conclusions" of Instructions populaires sur le calcul des probabilités p. 230

“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

“Every breath you draw, every accelerated beat of your heart in the emotional periods of your oratory depend upon highly elaborated physical and chemical reactions and mechanisms which nature has been building up through a million centuries.”

Henry Fairfield Osborn (1857–1935) American geologist, paleontologist, and eugenist

As quoted in the closing address by Dr. Henry Sloane Coffin, president of the Union Theological Seminary, New York, at the Memorial Service for Osborn at St. Bartholomew's Church, N.Y. (18 December 1935); published in "Henry Fairfield Osborn", Supplement to Natural History, Vol. 37, no. 2 (February 1936), p. 133 
Context: Every breath you draw, every accelerated beat of your heart in the emotional periods of your oratory depend upon highly elaborated physical and chemical reactions and mechanisms which nature has been building up through a million centuries. If one of these mechanisms, which you owe entirely to your animal ancestry, were to be stopped for a single instant, you would fall lifeless on the stage. Not only this, but some of your highest ideals of human fellowship and comradeship were not created in a moment, but represent the work of ages.

“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.”

Eduard Jan Dijksterhuis (1892–1965) Dutch historian

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

“By following up this idea, also, we might go a little further. We might arrive at the conviction that our present science is human, petty, and contingent; that it is closely linked with the structure of our sensory organs; that this structure results from the evolution which fashioned these organs; that this evolution has been an accident of history; that in the future it may be different; and that, consequently, by the side or in the stead of our modern science, the work of our eyes and hands—and also of our words—there might have been constituted, there may still be constituted, sciences entirely and extraordinarily new—auditory, olfactory, and gustatory sciences, and even others derived from other kinds of sensations which we can neither foresee nor conceive because they are not, for the moment, differentiated in us. Outside the matter we know, a very special matter fashioned of vision and touch, there may exist other matter with totally different properties. …We must, by setting aside the mechanical theory, free ourselves from a too narrow conception of the constitution of matter. And this liberation will be to us a great advantage which we shall soon reap. We shall avoid the error of believing that mechanics is the only real thing and that all that cannot be explained by mechanics must be incomprehensible. We shall then gain more liberty of mind for understanding what the union of the soul with the body may be.”

Alfred Binet (1857–1911) French psychologist and inventor of the first usable intelligence test

Source: The Mind and the Brain, 1907, p. 43

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