
“The essence of mathematics lies entirely in its freedom.”
Variant translation: The essence of mathematics is in its freedom.
From Kant to Hilbert (1996)
Source: The Fractalist (2012), Ch. 17, p. 178
“The essence of mathematics lies entirely in its freedom.”
Variant translation: The essence of mathematics is in its freedom.
From Kant to Hilbert (1996)
Harold Davenport, Bryan John Birch, Heini Halberstam (1977), The collected works of Harold Davenport. p. xviii
A Declaration of the Independence of Cyberspace (1996)
Context: You claim there are problems among us that you need to solve. You use this claim as an excuse to invade our precincts. Many of these problems don't exist. Where there are real conflicts, where there are wrongs, we will identify them and address them by our means. We are forming our own Social Contract. This governance will arise according to the conditions of our world, not yours. Our world is different.
Cyberspace consists of transactions, relationships, and thought itself, arrayed like a standing wave in the web of our communications. Ours is a world that is both everywhere and nowhere, but it is not where bodies live.
We are creating a world that all may enter without privilege or prejudice accorded by race, economic power, military force, or station of birth.
We are creating a world where anyone, anywhere may express his or her beliefs, no matter how singular, without fear of being coerced into silence or conformity.
Your legal concepts of property, expression, identity, movement, and context do not apply to us. They are all based on matter, and there is no matter here.
"The Evolution of Chastity" (February 1934), as translated in Toward the Future (1975) edited by by René Hague, who also suggests "space" as an alternate translation of "the ether."
Variants:
"One day after mastering the winds, the waves, the tides and gravity" — after all the scientific and technological achievements — "we shall harness for God the energies of love. And then, for the second time in the history of the world, man will have discovered fire."
As quoted by R. Sargent Shriver, Jr. in his speech accepting the nomination as the Democratic candidate for vice president, in Washington, D. C. (8 August 1972); this has sometimes been published as if Shriver's interjection "after all the scientific and technological achievements" were part of the original statement, as in The New York Times (9 August 1972), p. 18
What paralyzes life is lack of faith and lack of audacity. The difficulty lies not in solving problems but identifying them.
As translated in The The Ignatian Tradition (2009) edited by Kevin F. Burke, Eileen Burke-Sullivan and Phyllis Zagano, p. 86
Love is the only force which can make things one without destroying them. … Some day, after mastering the winds, the waves, the tides and gravity, we shall harness for God the energies of love, and then, for the second time in the history of the world, man will have discovered fire.
As quoted in Seed Sown : Theme and Reflections on the Sunday Lectionary Reading (1996) by Jay Cormier, p. 33
The day will come when, after harnessing space, the winds, the tides, gravitation, we shall harness for God the energies of love. And, on that day, for the second time in the history of the world, humanity will have discovered fire.
As quoted in Fire of Love : Encountering the Holy Spirit (2006) by Donald Goergen, p. 92
The day will come when, after harnessing space, the winds, the tides, gravitation, we shall harness for God the energies of love. And, on that day, for the second time in the history of the world, man will have discovered fire.
As quoted in Read for the Cure (2007) by Eileen Fanning, p. v
Context: What paralyzes life is lack of faith and lack of audacity. The difficulty lies not in solving problems but expressing them. And so we cannot avoid this conclusion: it is biologically evident that to gain control of passion and so make it serve spirit must be a condition of progress. Sooner or later, then, the world will brush aside our incredulity and take this step : because whatever is the more true comes out into the open, and whatever is better is ultimately realized. The day will come when, after harnessing the ether, the winds, the tides, gravitation, we shall harness for God the energies of love. And, on that day, for the second time in the history of the world, man will have discovered fire.
Richard Courant, "Mathematics in the Modern World", Scientific American, Vol 211, (Sep 1964), p. 42
“A great idea invariably creates as many problems as it solves: that is a sign of its greatness.”
page 63 https://books.google.com/books?id=hwpKAAAAIAAJ&pg=PA63
Relativity for All, London, 1922
Source: Linear programming and extensions (1963), p. vii.
Chris Argyris "Teaching smart people how to learn" in: Peter F. Drucker (1998) Harvard Business Review on Knowledge Management. p. 82