
Source: Achimedes (1920), Ch. I. Archimedes, p.1
Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 5
1900s
Context: The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself.
Source: Achimedes (1920), Ch. I. Archimedes, p.1
“The presentation of facts in logical form contributes to a confusion between discovery and proof.”
Internet Encyclopedia of Philosophy
Context: The presentation of facts in logical form contributes to a confusion between discovery and proof. If the process of discovery were mere synthesis, any mechanical manipulator of prior partial concepts would have reached the insight and it would not have taken a genius to arrive at it.
Source: The Integration of the Personality (1939), p. 72
“The golden age of mathematics - that was not the age of Euclid, it is ours.”
Source: The Human Worth of Rigorous Thinking: Essays and Addresses, p. 268
as translated by Arnold Dresden from: Brouwer, L. E. J. (1913). Intuitionism and formalism. Bulletin of the American Mathematical Society, 20(2), 81–96. (quote on p. 84)
Source: 1910s, Introduction to Mathematical Philosophy (1919), Ch. 18: Mathematics and Logic
“There is a logic of language and a logic of mathematics.”
The Secular Journal of Thomas Merton (1959)
Context: There is a logic of language and a logic of mathematics. The former is supple and lifelike, it follows our experience. The latter is abstract and rigid, more ideal. The latter is perfectly necessary, perfectly reliable: the former is only sometimes reliable and hardly ever systematic. But the logic of mathematics achieves necessity at the expense of living truth, it is less real than the other, although more certain. It achieves certainty by a flight from the concrete into abstraction. Doubtless, to an idealist, this would seem to be a more perfect reality. I am not an idealist. The logic of the poet — that is, the logic of language or the experience itself — develops the way a living organism grows: it spreads out towards what it loves, and is heliotropic, like a plant.
Attributed in Princeton & Mathematics: A Notable Record, Chaplin, Virginia, Princeton Alumni Weekly, May 9, 1958 http://www.princeton.edu/~mudd/finding_aids/mathoral/pmcxpaw.htm,