The most beautiful quotation:
“It is evident that the primes are randomly distributed but, unfortunately, we don’t know what ‘random’ means.”,Vaughan
Ok, what is random?
(Sound of primes, Sautoy)
music (repeatedly), sense of wonder, timeless, Nature’s gift, ultimate challenge, secret source, inner harmony, elixir, metamorphosis, miraculous, stunning, yearning, enthralled, frightened, fascinated and teased, embarrassment, anathema, misty waters, vast ocean, vast expanse, awesome vista, looming out of the mist, utterly alien, unleash the full force, radically new vistas, hidden harmonies, cacophony, poetry, alchemist, treasure, jewels, crown, riddle, cryptic, most enigmatic, mystical ley line, masters of disguise, diabolical malice
Next, this thing.
“Probability is not a notion of pure mathematics, but of physics or philosophy.“, Hardy, Littlewood
“Although the prime numbers are rigidly determined, they somehow feel like experimental data.”, Gowers
The consequences [of the Riemann Hypothesis] are fantastic: the distribution of primes, these elementary objects of arithmetic. And to have tools to study the distribution of these of objects”, Iwaniec
“The Riemann Hypothesis is the most basic connection between addition and multiplication that there is, so I think of it in the simplest terms as something really basic that we don’t understand about the link between addition and multiplication.”, Conrey
“Concerning Littlewood, I am working on a monograph on computations of zeros of the zeta function , which will feature an extended discussion of various conjectures and the numerical evidence for them. Perhaps when I am done I might be willing to write a commentary on Littlewood’s opinions. Personally I am a bit of an agnostic about the R.H., but would definitely not agree with Littlewood to the fullest. “, Odlyzko on Littlewoods’ doubts about R.H.
“Despite the stunning advances linking Riemann’s zeta function to 20th century physics, no one is predicting an imminent proof of the Riemann hypothesis. Odlyzko’s numerical experiments and evidence amassed by physicists have convinced everyone that a spectral interpretation of the zeta zeros is the way to go, but number theorists say they are at least one ‘big idea’ away from even the beginnings of a proof. Mathematicians aren’t yet sure what to aim at, says [Princeton University mathematician Peter] Sarnak.“, Cipra
“…there have been very few attempts at proving the Riemann hypothesis, because, simply, no one has ever had any really good idea for how to go about it.” , Selberg
“I still think that some major new idea is needed here” , Bombieri
“…there is no apparent reason why one number is prime and another not. To the contrary, upon looking at these numbers one has the feeling of being in the presence of one of the inexplicable secrets of creation.”, Zagier
“The mystery that clings to numbers, the magic of numbers, may spring from this very fact, that the intellect, in the form of the number series, creates an infinite manifold of well distinguishable individuals. Even we enlightened scientists can still feel it e.g. in the impenetrable law of the distribution of prime numbers.”, Weyl
“Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate.”, Euler
“The primes have tantalized mathematicians since the Greeks, because they appear to be somewhat randomly distributed but not completely so.”, Gowers
“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, …)?”, Stewart
“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.”, Zagier
“Given the millennia that people have contemplated prime numbers, our continuing ignorance concerning the primes is stultifying.”, Crandall, Pomercance
“Littlewood wrote to Hardy about [Ramanujan]: ‘it is not surprising that he would have been [misled], unsuspicious as he presumably is of the diabolical malice inherent in the primes’.”, Littlewood in a letter to Hardy
“We show that counting different configurations that give rise to black hole entropy in loop quantum gravity is related to partitions in number theory.” , Garcia-Islas
“In 1859, a German mathematician called Bernhard Riemann, a ‘timid diffident soul with a horror of attracting attention to himself,’ published a paper that drew more attention to him than to almost any other mathematician in the 19th century,. In it he made an important statement: the non-trivial zeros of the Riemann zeta function all have real part equal to 1/2. That is the Riemann Hypothesis: 15 words encapsulating a mystery at the heart of our number system.”, Sabbagh
“When reading these, take note of the profusion of emotional/poetic/ecstatic and religiously-oriented language which is used throughout. The words mystery, mysterious and secretsappear numerous times, but also sense of wonder, strange, stunning, astonishing, baffling, bafflement, devilment, surprise, endless surprises, exasperating, perplexing, bedevilled, diabolical malice, teased, cruel and compelling, stultifying, fascinating, (strange) fascination, yearning, obsession, mysterious attraction, breathtaking(ly), beautiful, most beautiful, incredibly beautiful, immense beauty, beautiful harmonies, elegant, elegance, gorgeous, glamorous, enthralled, incredible, exalted, majestic, fantastic, miraculous, amazed, amazing, absolutely amazing, awed, impenetrable, impenetrability, tantalized, tantalizing, tantalizingly, tantalizingly vulnerable, unveil, blazed…fearlessly, wreath its conqueror with glory, awesome vista, most ancient, cryptic, riddle, formidable enigmas, most enigmatic, strange conundrum, great white whale, quest, vast toil, unthinkable complexity, utterly alien, secret source, profundity, profound mystery, great mystery, magic, alchemist, elixir, aesthetic appeal, works of art, poetry”,Watkins
Chosen quotations from http://empslocal.ex.ac.uk/people/staff/mrwatkin/