“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

Sunday, December 21, 2008

Quotes on the Beauty and Mystery of Prime Numbers

A while ago I wrote a little about "mathematical beauty," the idea that certain equations, patterns, or proofs in mathematics have been perceived as having a certain sort of abstract beauty to them. For example, consider these descriptions of Euler's equation, eiπ+1=0:

It “reaches down into the very depths of existence” - Stanford mathematics professor Keith Devlin

"[A] mathematics professor at MIT, an atheist, once wrote this formula on the blackboard, saying, ‘There is no God, but if there were, this formula would be proof of his existence’" - Charles Edward White, professor of Christian thought and history at Spring Arbor University
Some time ago I also ran ran across this website about connections between number theory and mathematics, particularly with respect to the distribution of prime numbers and the Riemann Hypothesis. I've copied below some of the most interesting quotes listed on this site. Words that are frequently used include mystery, depth, treasures, secrets, wonder, elegance, beauty, miraculous, tantalizing, and awesome vista:
"Who would have imagined that something as straightforward as the natural numbers (1, 2, 3, 4,...) could give birth to anything so baffling as the prime numbers (2, 3 ,5, 7, 11, ...)?"
Ian Stewart, "Jumping Champions", Scientific American, December 2000

Prime numbers are “a great mystery indeed, worthy of the most exalted intelligence.”
A. Doxiadis, from the novel Uncle Petros and Goldbach's Conjecture, p. 84 (Faber 2000)

"The primes have music in them".
M.V.Berry and J.P.Keating from "The Riemann Zeros and Eigenvalue Asymptotics" (SIAM Review 41, no.2 (1999), page238.)

"To me, that the distribution of prime numbers can be so accurately represented in a harmonic analysis is absolutely amazing and incredibly beautiful. It tells of an arcane music and a secret harmony composed by the prime numbers."
E. Bombieri from "Prime Territory: Exploring the Infinite Landscape at the Base of the Number System" (The Sciences, Sept/Oct 1992)

"It's a whole beautiful subject and the Riemann zeta function is just the first one of these, but it's just the tip of the iceberg. They are just the most amazing objects, these L-functions - the fact that they exist, and have these incredible properties are tied up with all these arithmetical things - and it's just a beautiful subject. Discovering these things is like discovering a gemstone or something. You're amazed that this thing exists, has these properties and can do this."
B. Conrey, Dr. Riemann's Zeros (Atlantic, 2002), p.166

"I sometimes have the feeling that the number system is comparable with the universe that the astronomer is studying...The number system is something like a cosmos."
M. Jutila, quoted in K. Sabbagh, "Beautiful Mathematics", Prospect, January 2002

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