“To give here an elaborate account of Pappus would be to create a false impression. His work is only the last convulsive effort of Greek geometry which was now nearly dead and was never effectually revived. It is not so with Ptolemy or Diophantus. The trigonometry of the former is the foundation of a new study which was handed on to other nations indeed but which has thenceforth a continuous history of progress.”

—  Ptolemy

James Gow, A Short History of Greek Mathematics https://books.google.com/books?id=9d8DAAAAMAAJ (1884) p.308.

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Greco-Egyptian writer and astronomer of Alexandria 100–170

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“To give here an elaborate account of Pappus would be to create a false impression. His work is only the last convulsive effort of Greek geometry which was now nearly dead and was never effectually revived. It is not so with Ptolemy or Diophantus. The trigonometry of the former is the foundation of a new study which was handed on to other nations indeed but which has thenceforth a continuous history of progress. Diophantus also represents the outbreak of a movement which probably was not Greek in its origin, and which the Greek genius long resisted, but which was especially adapted to the tastes of the people who, after the extinction of Greek schools, received their heritage and kept their memory green. But no Indian or Arab ever studied Pappus or cared in the least for his style or his matter. When geometry came once more up to his level, the invention of analytical methods gave it a sudden push which sent it far beyond him and he was out of date at the very moment when he seemed to be taking a new lease of life.”

James Gow (scholar) (1854–1923) scholar

p, 125
A Short History of Greek Mathematics (1884)

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“Nationalism is always an effort in a direction opposite to that of the principle which creates nations. The former is exclusive in tendency, the latter inclusive.”

José Ortega Y Gasset book The Revolt of the Masses

Source: The Revolt of the Masses (1929), Chapter XIV: Who Rules The World?
Context: Nationalism is always an effort in a direction opposite to that of the principle which creates nations. The former is exclusive in tendency, the latter inclusive. In periods of consolidation, nationalism has a positive value, and is a lofty standard. But in Europe everything is more than consolidated, and nationalism is nothing but a mania, a pretext to escape from the necessity of inventing something new, some great enterprise.

Thomas Little Heath photo

“It would be inconvenient to interrupt the account of Menaechmus's solution of the problem of the two mean proportionals in order to consider the way in which he may have discovered the conic sections and their fundamental properties. It seems to me much better to give the complete story of the origin and development of the geometry of the conic sections in one place, and this has been done in the chapter on conic sections associated with the name of Apollonius of Perga. Similarly a chapter has been devoted to algebra (in connexion with Diophantus) and another to trigonometry”

Thomas Little Heath (1861–1940) British civil servant and academic

under Hipparchus, Menelaus and Ptolemy
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

Oliver Wendell Holmes Jr. photo

“The only simplicity for which I would give a straw is that which is on the other side of the complex — not that which never has divined it.”

Oliver Wendell Holmes Jr. (1841–1935) United States Supreme Court justice

"Holmes-Pollock Letters : The Correspondence of Mr. Justice Holmes and Sir Frederick Pollock, 1874-1932" (2nd ed., 1961), p. 109.
Often quoted as "I wouldn't give a fig for the simplicity on this side of complexity; I would give my right arm for the simplicity on the far side of complexity" and attributed to Oliver Wendell Holmes, Sr..
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Paul Karl Feyerabend photo

“After Aristotle and Ptolemy, the idea that the earth moves - that strange, ancient, and "entirely ridiculous", Pythagorean view was thrown on the rubbish heap of history, only to be revived by Copernicus and to be forged by him into a weapon for the defeat of its defeaters. The Hermetic writings played an important part in this revival, which is still not sufficiently understood, and they were studied with care by the great Newton himself.”

Paul Karl Feyerabend book Against Method

Pg 48
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Context: Progress was often achieved by a "criticism from the past"… After Aristotle and Ptolemy, the idea that the earth moves - that strange, ancient, and "entirely ridiculous", Pythagorean view was thrown on the rubbish heap of history, only to be revived by Copernicus and to be forged by him into a weapon for the defeat of its defeaters. The Hermetic writings played an important part in this revival, which is still not sufficiently understood, and they were studied with care by the great Newton himself. Such developments are not surprising. No idea is ever examined in all its ramifications and no view is ever given all the chances it deserves. Theories are abandoned and superseded by more fashionable accounts long before they have had an opportunity to show their virtues. Besides, ancient doctrines and "primitive" myths appear strange and nonsensical only because their scientific content is either not known, or is distorted by philologists or anthropologists unfamiliar with the simplest physical, medical or astronomical knowledge.

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“M. Desargues puts me under obligations on account of the pains that it has pleased him to have in me, in that he shows that he is sorry that I do not wish to study more in geometry, but I have resolved to quit only abstract geometry, that is to say, the consideration of questions which serve only to exercise the mind, and this, in order to study another kind of geometry, which has for its object the explanation of the phenomena of nature… You know that all my physics is nothing else than geometry.”

René Descartes (1596–1650) French philosopher, mathematician, and scientist

Letter to Marin Mersenne (July 27, 1638) as quoted by Florian Cajori, A History of Mathematics (1893) letter dated in The Philosophical Writings of Descartes Vol. 3, The Correspondence (1991) ed. John Cottingham, Robert Stoothoff, Dugald Murdoch

“With Diophantus the history of Greek arithmetic comes to an end. No original work, that we know of, was done afterwards.”

James Gow (scholar) (1854–1923) scholar

p, 125
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“Though the defects in Diophantus' proofs are in general due to the limitation of his symbolism, it is not so always. Very frequently indeed Diophantus introduces into a solution arbitrary conditions and determinations which are not in the problem. Of such "fudged" solutions, as a schoolboy would call them, two particular kinds are very frequent. Sometimes an unknown is assumed at a determinate value… Sometimes a new condition is introduced.”

James Gow (scholar) (1854–1923) scholar

A Short History of Greek Mathematics (1884)

Mark Rothko photo

“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

“The cultural tradition of which the Greek language is the focal point has the longest unbroken history of any in Europe. The Greek state, however, was newly born out of the conflict of 1821-8 and was without precedent in the history of the Greeks. The newly defined nation therefore had, as a matter of urgency, to create its own past, that is, to select and endorse those elements of earlier Greek history which retrospectively could claim to have made the present existence and future aspirations of the nation inevitable. Since the state itself was in many ways the creation of European Romanticism, it was only natural that the means to hand for defining and justifying its existence should derive from the same source.”

Roy Porter (1946–2002) British historian

[Roderick Beaton, Mikuláš Teich & Roy Porter, Romanticism in national context, Cambridge University Press, Cambridge, UK, 1988, 99, 0-521-33913-8]

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