“In this branch of study exactness is an essential feature; and mathematical difficulties must not be shrunk from when the nature of the subject leads to them.”

— William John Macquorn Rankine

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

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William John Macquorn Rankine 28

civil engineer 1820–1872

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 495

“Among all the studies of natural causes and reasons Light chiefly delights the beholder; and among the great features of Mathematics the certainty of its demonstrations is what preeminently (tends to) elevate the mind of the investigator. Perspective, therefore, must be preferred to all the discourses and systems of human learning. In this branch [of science] the beam of light is explained on those methods of demonstration which form the glory not so much of Mathematics as of Physics and are graced with the flowers of both.”

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 branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics.”

Benjamin Peirce Linear Associative Algebra

§ 2.
Linear Associative Algebra (1882)
Context: The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.

“Geometry can in no way be viewed… as a branch of mathematics; instead, geometry relates to something already given in nature, namely, space. I… realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to geometry.”

Hermann Grassmann (1809–1877) German polymath, linguist and mathematician

Forward, as quoted by Mario Livio, Is God a Mathematician? (2009)
Ausdehnungslehre (1844)

“Geometry is that of mathematical science which is devoted to consideration of form and size, and may be said to be the best and surest guide to study of all sciences in which ideas of dimension or space are involved. Almost all the knowledge required by navigators, architects, surveyors, engineers, and opticians, in their respective occupations, is deduced from geometry and branches of mathematics. All works of art constructed according to the rules which geometry involves; and we find the same laws observed in the works of nature. The study of mathematics, generally, is also of great importance in cultivating habits of exact reasoning; and in this respect it forms a useful auxiliary to logic.”

Robert Chambers (publisher, born 1802) (1802–1871) Scottish publisher and writer

Robert Chambers, Chambers's Information for the People (1875) Vol. 2 https://books.google.com/books?id=vNpTAAAAYAAJ

“It can have no analogy in fact with the descriptions of those who know nothing of the subject; furthermore, it is not to be represented as this or that by any person whomsoever: it is that which it is, drawing from itself only, even as mathematics do, for it is the exact and absolute science of Nature and her laws.”

Eliphas Levi (1810–1875) French writer

Introduction
The History Of Magic (1860)

“Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy.
Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics.”

Joseph Fourier book The Analytical Theory of Heat

Source: The Analytical Theory of Heat (1878), Ch. 1, p. 1

“Mind and matter brought down to the essential, to the consciousness and its object, form a natural whole, and the difficulty does not consist in uniting but in separating them.”

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

Source: The Mind and the Brain, 1907, p. 184

“The subject matter of mathematics has increased so rapidly and extensively that there is some element of truth in maintaining that mathematics is not so much a subject as a way of studying any subject, not so much a science as a way of life. We turn, then, from the attempt to characterize the material object of mathematics to an attempt to determine its formal object, i. e., its methodology.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“I must study politics and war, that our sons may have liberty to study mathematics and philosophy. Our sons ought to study mathematics and philosophy, geography, natural history and naval architecture, navigation, commerce and agriculture in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry and porcelain.”

John Quincy Adams (1767–1848) American politician, 6th president of the United States (in office from 1825 to 1829)

“In this branch of study exactness is an essential feature; and mathematical difficulties must not be shrunk from when the nature of the subject leads to them.”

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William John Macquorn Rankine 28

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