Salviati, Third Day. Change of Position
Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638)
“There are, in fact, as I began to say above, not a few principles which are the special property of mathematics, such principles as are discovered by the common light of nature, require no demonstration, and which concern quantities primarily; then they are applied to other things, so far as the latter have something in common with quantities. Now there are more of these principles in mathematics than in the other theoretical sciences because of that very characteristic of the human understanding which seems to be such from the law of creation, that nothing can be known completely except quantities or by quantities. And so it happens that the conclusions of mathematics are most certain and indubitable.”
Vol. VIII, p. 148
Joannis Kepleri Astronomi Opera Omnia, ed. Christian Frisch (1858)
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Johannes Kepler 51
German mathematician, astronomer and astrologer 1571–1630Related quotes
Sections I–II, p. 11–12
Natural Law; or The Science of Justice (1882), Chapter II. The Science of Justice (Continued)
Section VIII, p. 15
Natural Law; or The Science of Justice (1882), Chapter II. The Science of Justice (Continued)
“Bion insisted on the principle that "The property of friends is common."”
As quoted by Diogenes Laërtius, iv. 53.
“Bion insisted on the principle that "The property of friends is common."”
Bion, 9.
The Lives and Opinions of Eminent Philosophers (c. 200 A.D.), Book 4: The Academy
"Will Mathematics Survive? Report on the Zurich Congress" in The Mathematical Intelligencer, Vol. 17, no. 3 (1995), pp. 6–10.
Context: At the beginning of this century a self-destructive democratic principle was advanced in mathematics (especially by Hilbert), according to which all axiom systems have equal right to be analyzed, and the value of a mathematical achievement is determined, not by its significance and usefulness as in other sciences, but by its difficulty alone, as in mountaineering. This principle quickly led mathematicians to break from physics and to separate from all other sciences. In the eyes of all normal people, they were transformed into a sinister priestly caste... Bizarre questions like Fermat's problem or problems on sums of prime numbers were elevated to supposedly central problems of mathematics.
1920s, Sidelights on Relativity (1922)
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)
Rudolf Carnap (1939; 51), as cited in: Paul van Ulsen. Wetenschapsfilosofie http://www.illc.uva.nl/Research/Publications/Inaugurals/IV-10-Arend-Heyting.text.pdf, 6 november 2017.