“The geometrical spirit is not so tied to geometry that it cannot be detached from it and transported to other branches of knowledge. A work of morals or politics or criticism, perhaps even of eloquence, would be better (other things being equal) if it were done in the style of a geometer. The order, clarity, precision and exactitude which have been apparent in good books for some time might well have their source in this geometric spirit. …Sometimes one great man gives the tone to a whole century; [Descartes], to whom one might legitimately be accorded the glory of having established a new art of reasoning, was an excellent geometer.”

— Bernard Le Bovier de Fontenelle

"The Utility of Mathematics," i.e. "Préface sur l'utitlité des mathématiques et de la physique et sur les travaux de le Académie des Sciences," Œuvres de Monsieur de Fontenelle (1753) Vol. 6, pp.37-50, as quoted by Herbert Butterfield, The Origins of Modern Science 1300-1800 (1949).

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Bernard Le Bovier de Fontenelle 13

French writer, satirist and philosopher of enlightenment 1657–1757

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“One of the most curious of these cases [geometrical paradoxers] was that of a student, I am not sure but a graduate, of the University of Virginia, who claimed that geometers were in error in assuming that a line had no thickness. He published a school geometry based on his views, which received the endorsement of a well-known New York school official and, on the basis of this, was actually endorsed, or came very near being endorsed, as a text-book hi the public schools of New York.”

Simon Newcomb (1835–1909) American astronomer

Simon Newcomb, The Reminiscences of an Astronomer, (Boston and New York, 1903), p. 388. Reported in Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book https://archive.org/stream/memorabiliamathe00moriiala#page/81/mode/2up, (1914), p. 368

“The last thirty years [1925 to 1955] have seen an enormous improvement in the position of geometry as a branch of mathematics, or, rather, have seen the re-integration of geometry into the main fabric of mathematics. Indeed, one can go further and say that with the restoration of geometry to its rightful place in the mathematical scheme the process of fragmentation which had been doing so much harm to mathematics has been reversed, and we may look forward to the day in which there are no longer analysts, algebraists, geometers and so on, but simply mathematicians. Mathematical research has two aspects, motivation and technique, and when the latter gains control the result is apt to be excessive specialisation. The revolution of geometrical thought, and the reinstatement of geometry as one of the major mathematical disciplines, have helped to bring about a unification of mathematics which we may justly regard as one of the major contributions of the last quarter century to the subject.”

W. V. D. Hodge (1903–1975) British mathematician

W. V. D. Hodge, Changing Views of Geometry. Presidential Address to the Mathematical Association, 14th April, 1955, The Mathematical Gazette 39 (329) (1955), 177-183.

“The progression of a painter's work, as it travels in time from point to point, will be toward clarity: toward the elimination of all obstacles between the painter and the idea, and between the idea and the observer. As examples of such obstacles, I give (among others) memory, history or geometry, which are swamps of generalization from which one might pull out parodies of ideas (which are ghosts) but never an idea in itself. To achieve this clarity is, inevitably, to be understood.”

Mark Rothko (1903–1970) American painter

In Tiger’s Eye, Vol. 1, no 9, October 1949; as quoted in Abstract Expressionism Creators and Critics, ed. Clifford Ross, Abrams Publishers New York 1990, p. 170
1940's

“Your description of Troyon and Rousseau, for instance, is lively enough to give me some idea of which of their manners they are done in. There were other paintings from the time of Troyon's municipal pasture that had a certain 'mood' that one would have to call 'dramatic', even though they aren't figure paintings.”

Vincent Van Gogh (1853–1890) Dutch post-Impressionist painter (1853-1890)

In his letter to Theo, from the Hague, c. 11 July 1883 - original manuscript at Van Gogh Museum, location Amsterdam - inv. nos. b322 a-c V/1962, http://vangoghletters.org/vg/letters/let361/letter.html
At the exhibition 'Les cent chefs d'oeuvre' at Galerie Georges Petit - in Paris, 1883 there were 9 paintings of Troyon. Vincent had asked Theo in Paris to give him a description of the works at this exhibition. Vincent already appreciated Troyon's painting style, which he knew from his Paris' years at art-gallery Goupil where he worked
1880s, 1883

“This book raises issues that might not be apparent from the table of contents.
It sketches some of the difficulties faced by our civilization — a civilization which might be perhaps described as aiming at humanness and reasonableness, at equality and freedom; a civilization which is still in its infancy, as it were, and which continues to grow in spite of the fact that it has been so often betrayed by so many of the intellectual leaders of mankind. It attempts to show that this civilization has not yet fully recovered from the shock of its birth — the transition from the tribal or "enclosed society," with its submission to magical forces, to the 'open society' which sets free the critical powers of man. It attempts to show that the shock of this transition is one of the factors that have made possible the rise of those reactionary movements which have tried, and still try, to overthrow civilization and to return to tribalism.”

Karl Popper book The Open Society and Its Enemies

Introduction; part of this has sometimes been paraphrased : Our civilization has not yet fully recovered from the shock of its birth — the transition from the tribal or 'closed society', with its submission to magical forces, to the 'open society' which sets free the critical powers of man.
The Open Society and Its Enemies (1945)

“His notions fitted things so well,
That which was which he could not tell;
But oftentimes mistook th' one
For th' other, as great clerks have done.”

Samuel Butler (poet) Hudibras

Canto I, line 131
Hudibras, Part I (1663–1664)
Context: Whatever sceptic could inquire for,
For ev'ry why he had a wherefore;
Knew more than forty of them do,
As far as words and terms cou'd go.
All which he understood by rote
And, as occasion serv'd, would quote;
No matter whether right or wrong,
They might be either said or sung.
His notions fitted things so well,
That which was which he could not tell;
But oftentimes mistook th' one
For th' other, as great clerks have done.

“I cannot find in Chatterton's works any thing so extraordinary as the age at which they were written. They have a facility, vigour, and knowledge, which were prodigious in a boy of sixteen, but which would not have been so in a boy of twenty. He did not show extraordinary powers of genius, but extraordinary precocity. Nor do I believe he would have written better, had he lived. He knew this himself, or he would have lived. Great geniuses, like great kings, have too much to think of to kill themselves.”

Thomas Chatterton (1752–1770) English poet, forger

William Hazlitt Lectures on the English Poets (Philadelphia: Thomas Dobson, 1818) p. 243.
Criticism

“The seeing of things as they really are — the seeing of a proportion veiled from other eyes (together with the power of expression), is what makes a man an artist. What makes him a great artist is a high fervour of spirit, which produces a superlative, instead of a comparative, clarity of vision.”

John Galsworthy (1867–1933) English novelist and playwright

Vague Thoughts On Art (1911)

“Newton… (after having remarked that geometry only requires two of the mechanical actions which it postulates, namely, to describe a straight line and a circle) says: geometry is proud of being able to achieve so much while taking so little from extraneous sources. One might say of metaphysics, on the other hand: it stands astonished, that with so much offered it by pure mathematics it can effect so little.”

Immanuel Kant book Metaphysical Foundations of Natural Science

In the meantime, this little is something which mathematics indispensably requires in its application to natural science, which, inasmuch as it must here necessarily borrow from metaphysics, need not be ashamed to allow itself to be seen in company with the latter.
Preface, Tr. Bax (1883) citing Isaac Newton's Principia
Metaphysical Foundations of Natural Science (1786)

“I have come to believe that a great teacher is a great artist and that there are as few as there are any other great artists. It might even be the greatest of the arts since the medium is the human mind and spirit.”

John Steinbeck (1902–1968) American writer

"...like captured fireflies" (1955); also published in America and Americans and Selected Nonfiction (2003), p. 142

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Bernard Le Bovier de Fontenelle 13

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