The excitement of learning separates youth from old age. As long as you're learning you're not old. | |
Rosalyn S. Yallow, quoted in The Beacon Book of Quotations by Women, edited by Rosalie Maggio. | 425 |
It is clear that the chief end of mathematical study must be to make the students think. | |
John Wesley Young, | 1021 |
Teaching Ramanujan was like writing on a blackboard covered with excerpts from a more interesting lecture. | |
Laurence Young, from The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel | 881 |
As the twentieth century draws to a close, it has become increasingly clear that Godel's famous Incompleteness Theorem for mathematical logic stands alongside Heisenberg's Uncertainty Principle and Einstein's Theory of Relativity as one of the great mathematical achievements of this - or any other - century. Indeed, these three milestones of twentieth century science have much in common. Although all three represent highwater marks in the most rigorous of mathematical sciences, each constitutes at the same time a fountain of philosophical inspiration. In particular, although each is established by formal methods, each demonstrates, in its own peculiar way, a kind of limitation in principle of the relevant formal science. Heisenberg sets limits to our simultaneous knowledge of the position and momentum of the fundamental particles. Einstein, in turn, sets a limit of the speed of light and indeed to the velocity of any information-bearing signal in the universe. And Godel establishes limits in the ability of any strictly formal, axiomatic mathematical system - in particular, of any computer program - to capture not only all mathematical truth, but even the totality of truths of arithmetic. It is a further, striking fact that all three thinker draw ontological consequences, about the nature of reality, from what are in effect epistemic premises. | |
Palle Yourgrau, from Godel Meets Einstein: Time Travel in the Godel Universe | 1049 |
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