“There cannot be a greater mistake than that of looking superciliously upon the practical applications of science. The life and soul of science is its practical application; and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.”

— William Thomson

Lecture on "Electrical Units of Measurement" (3 May 1883), published in Popular Lectures Vol. I, p. 73, as quoted in The Life of Lord Kelvin (1910) by Silvanus Phillips Thompson

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William Thomson 18

British physicist and engineer 1824–1907

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“A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range. The increased complexity and specialisation of all branches of knowledge makes it true in the present, however it may have been in former times, that important advances in such a department as Mathematics can be expected only from men who are interested in the subject for its own sake, and who, whilst keeping an open mind for suggestions from outside, allow their thought to range freely in those lines of advance which are indicated by the present state of their subject, untrammelled by any preoccupation as to applications to other departments of science. Even with a view to applications, if Mathematics is to be adequately equipped for the purpose of coping with the intricate problems which will be presented to it in the future by Physics, Chemistry and other branches of physical science, many of these problems probably of a character which we cannot at present forecast, it is essential that Mathematics should be allowed to develop freely on its own lines.”

E. W. Hobson (1856–1933) British mathematician

Source: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 286; Cited in: Moritz (1914, 106): Modern mathematics.

“The great advances in mathematics have not been made by logic but by creative imagination.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)
Context: Logical analysis is indispensable for an examination of the strength of a mathematical structure, but it is useless for its conception and design. The great advances in mathematics have not been made by logic but by creative imagination.

“There have been applied sciences throughout the ages. … However this so-called practice was not much more than paper in nearly all of these cases, and the various applied sciences were only lacking a bagatelle, namely proper scientific practice. The applied sciences show the application of theoretic doctrines in existing events; but that is precisely what it does, it merely shows. Whereas the scientific practice autonomously puts to use these theories.”

Christian Doppler (1803–1853) mathematician, physicist

in his review of Joseph Beskiba's textbook, published in the Österreichische Blätter für Literatur und Kunst (September 7, 1844), as quoted by [Peter Schuster, Moving the stars: Christian Doppler, his life, his works and principle, and the world after, Living edition, 2005, 3901585052, 78]

“At present, when the prevailing forms of society have become hindrances to the free expression of human powers, it is precisely the abstract branches of science, mathematics and theoretical physics, which … offer a less distorted form of knowledge than other branches of science which are interwoven with the pattern of daily life, and the practicality of which seemingly testifies to their realistic character.”

Max Horkheimer (1895–1973) German philosopher and sociologist

Source: "The Latest Attack on Metaphysics" (1937), p. 133.

“Some of the evils which are caused by the fallacy of an incompatibility between theory and practice having been described, it must now be admitted, that at the present time those evils show a decided tendency to decline. The extent of intercourse, and of mutual assistance, between men of science and men of practice, the practical knowledge of scientific men, and the scientific knowledge of practical men, have been for some time steadily increasing; and that combination and harmony of theoretical and practical knowledge—that skill in the application of scientific principles to practical purposes, which in former times was confined to a few remarkable individuals, now tends to become more generally diffused.”

William John Macquorn Rankine (1820–1872) civil engineer

p, 125
"On the Harmony of Theory and Practice in Mechanics" (Jan. 3, 1856)

“The fundamental doctrines of motion have [herein]… been more immediately referred to axioms simply mathematical than has hitherto been usual; and the application of these doctrines to practical purposes has [herein]… been facilitated.”

Thomas Young (scientist) (1773–1829) English polymath

Preface (March 30, 1807)
A Course of Lectures on Natural Philosophy and the Mechanical Arts (1807)

“While it is never safe to affirm that the future of Physical Science has no marvels in store even more astonishing than those of the past, it seems probable that most of the grand underlying principles have been firmly established and that further advances are to be sought chiefly in the rigorous application of these principles to all the phenomena which come under our notice. It is here that the science of measurement shows its importance — where quantitative work is more to be desired than qualitative work. An eminent physicist remarked that the future truths of physical science are to be looked for in the sixth place of decimals.”

Albert A. Michelson (1852–1931) American physicist

1894, dedication of Ryerson Physical Laboratory, quoted in Annual Register 1896, p. 159 https://books.google.com/books?id=HysXAAAAYAAJ&pg=PA159.
Variants of this quote have been misattributed to Lord Kelvin since the 1980s, though there is no evidence that he said anything of the sort. The identity of the unnamed "eminent physicist" is unknown.

“An engineering science aims to organize the design principles used in engineering practice into a discipline and thus to exhibit the similarities between different areas of engineering practice and to emphasize the power of fundamental concepts. In short, an engineering science is predominated by theoretical analysis and very often uses the tool of advanced mathematics.”

Qian Xuesen (1911–2009) Chinese rocket scientist

Source: Engineering cybernetics, (1954), p. vii

“[Knowing how to suffer without complaining is the only practical thing, it's the great science, the lesson to learn, the solution to the problem of life. ]”

Irving Stone book Lust for Life

Source: Lust for Life

“More than any of his predecessors Plato appreciated the scientific possibilities of geometry... By his teaching he laid the foundations of the science, insisting upon accurate definitions, clear assumptions, and logical proof. His opposition to the materialists, who saw in geometry only what was immediately useful to the artisan and the mechanic is… clear. …That Plato should hold the view… is not a cause for surprise. The world's thinkers have always held it. No man has ever created a mathematical theory for practical purposes alone. The applications of mathematics have generally been an afterthought.”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1923) Vol.1, p. 90

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William Thomson 18

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