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Wednesday, July 25, 2012

Quote… Unquote

Yet again, I'm pulled back to prime numbers for a post… GREAT compendium of quotes pertaining to prime numbers, the zeta function, and Riemann Hypothesis here:


The page comes from (Brit) Matthew Watkins, who co-authored "The Mystery of the Prime Numbers," a volume I haven't read myself, but have seen several uniformly positive reviews of. His webpage linking to prime number-related stuff is here:


And here a small sampling of quotes from the initially-cited page:
"How can so much of the formal and systematic edifice of mathematics, the science of pattern and rule and order per se, rest on such a patternless, unruly, and disorderly foundation? Or how can numbers regulate so many aspects of our physical world and let us predict some of them when they themselves are so unpredictable and appear to be governed by nothing but chance?"
   -- H. Peter Aleff, from the 'e-book' Prime Passages to Paradise
"We may - paraphrasing the famous sentence of George Orwell - say that "all mathematics is beautiful, yet some is more beautiful than the other." But the most beautiful in all mathematics is the zeta function. There is no doubt about it."   -- Polish cosmologist Krzysztof Maslanka
"In [his 1859 paper], Riemann made an incidental remark - a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years...

...it is that incidental remark - the Riemann Hypothesis - that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant at work - subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age...

It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. ...Hunting down the solution to the Riemann Hypothesis has become an obsession for many - the veritable 'great white whale' of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution."
  -- J. Derbyshire, from the dustjacket description of Prime Obsession (John Henry Press, 2003)
 "For many mathematicians working on it, $1m is less important than the satisfaction that would come from finding a proof. Throughout my researches among the mathematicians' tribe (I have interviewed 30 in the past year), Riemann's Hypotheis was often described to me in awed terms. Hugh Montgomery of the University of Michigan said this was the proof for which a mathematician might sell his soul. Henryk Iwaniec, a Polish-American mathematician, sounded as if he were already discussing terms with Lucifer"

'I would trade everything I know in mathematics for the proof of the Riemann Hypothesis. It's gorgeous stuff. I'm only worried that I'll be unable to understand it. That would be the worst...'"
   -- K. Sabbagh, "Beautiful Mathematics", Prospect, January 2002

"Proving the Riemann hypothesis won't end the story. It will prompt a sequence of even harder, more penetrating questions. 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)

 There now exist a great many volumes related to prime numbers for lay folks (it's been a hot topic in recent years). Among my own favorites are (in no particular order):

"The Music of the Primes" -- Marcus du Sautoy
"The Riemann Hypothesis" -- Karl Sabbagh
"Stalking the Riemann Hypothesis" -- Dan Rockmore
"Prime Numbers" by David Wells, a more encyclopedic/academic (but still interesting) offering.

And finally, John Derbyshire's "Prime Obsession" was another hugely popular volume on the subject, though I didn't enjoy it quite as much as the preceding titles.

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