“Unless a grain of wheat falls into the earth and dies, it remains alone; but if it dies, it bears much fruit.” – John 12:24
“The last enemy to be destroyed is death...Death is swallowed up in victory.” – 1 Corinthians 15:26, 54
"The greater the sin, the greater the mercy, the deeper the death and the brighter the rebirth.” - C. S. Lewis
"This story...has the very taste of primary truth." - J. R. R. Tolkien

Monday, December 22, 2008

More Quotes on the Beauty and Mystery of Prime Numbers

Some more quotes from this site on number theory and physics:

"There are two facts about the distribution of prime numbers which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that despite their simple definition and role as the building blocks of the natural numbers, the prime numbers... grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behaviour, and that they obey these laws with almost military precision."
Don Zagier, Bonn University inaugural lecture

“Why do the primes achieve such a delicate balance between randomness and order? And if their patterns do encode the behaviour of quantum chaotic systems, what other jewels will we uncover when we dig deeper? Those who believe mathematics holds the key to the Universe might do well to ponder a question that goes back to the ancients: What secrets are locked within the primes?"
E. Klarreich, "Prime Time" (New Scientist, 11/11/00)

The metamorphosis provided by Riemann's mirror, where chaos turns to order, is one which most mathematicians find almost miraculous."
Marcus du Sautoy's, The Music of the Primes (Fourth Estate, 2003), p. 9
"The prime numbers…have fascinated mathematicians and others since ancient times, and the richness and beauty of the results of research in this field have been astonishing."
C.H. Denbow and V. Goedicke, Foundations of Mathematics (Harper, 1959)
"[It has been] said that the zeros [of the Riemann zeta function] weren't real, nobody measured them. They are as real as anything you will measure in a laboratory - this has to be the way we look at the world."
P. Sarnak, professor of mathematics at Princeton University, from 1999 MSRI lecture "Random matrix theory and zeroes of zeta functions - a survey"
"317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way."
G.H. Hardy, A Mathematician's Apology, (Cambridge Univ. Press, 1940) p. 70.
I read the other day that mathematicians are intuitively platonists. They approach mathematics as something real (abstract realities, but no less real than atoms and molecules), and strive to discover mathematical truth in the same way that physicists or chemists try to discover how the physical world works. But what is it that causes this intuition that numbers are real just like quarks and electrons? Why these sentiments of "depth" and "beauty," this seeming assumption that in numbers there is something of value, something that has worth? The common sense answer is that mathematicians perceive correctly - numbers are real, and there is something of of value in mathematical truth. For more philosophical thoughts on math and numbers, see my posts on "A Theology of Mathematics."

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