Marcus du Sautoy - The Music of the Primes (2003)

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Gauss liked to call [number theory] 'the Queen of Mathematics'. For Gauss, the jewels in the crown were the primes, numbers which had fascinated and teased generations of mathematicians.

Marcus du Sautoy
Armed with his prime number tables, Gauss began his quest. As he looked at the proportion of numbers that were prime, he found that when he counted higher and higher a pattern started to emerge. Despite the randomness of these numbers, a stunning regularity seemed to be looming out of the mist.

Marcus du Sautoy
As we shall see, Riemann's Hypothesis can be interpreted as an example of a general philosophy among mathematicians that, given a choice between an ugly world and an aesthetic one, Nature always chooses the latter.

Marcus du Sautoy
A solution to the Riemann Hypothesis offers the prospect of charting the misty waters of the vast ocean of numbers. It represents just a beginning in our understanding of Nature's numbers. If we can only find the secret of how to navigate the primes, who knows what else lies out there, waiting for us to discover?

Marcus du Sautoy
We have all this evidence that the Riemann zeros are vibrations, but we don't know what's doing the vibrating.

Marcus du Sautoy
The primes have been a constant companion in our exploration of the mathematical world yet they remain the most enigmatic of all numbers. Despite the best efforts of the greatest mathematical minds to explain the modulation and transformation of this mystical music, the primes remain an unanswered riddle.

Marcus du Sautoy
Gauss had heard the first big theme in the music of the primes, but it was one of his students, Riemann, who would truly unleash the full force... of the hidden harmonies that lay behind the cacophony of the primes.

Marcus du Sautoy
Despite their apparent simplicity and fundamental character, prime numbers remain the most mysterious objects studied by mathematicians. In a subject dedicated to finding patterns and order, the primes offer the ultimate challenge.

Marcus du Sautoy
In an interview, Hilbert explained that he believed the Riemann Hypothesis to be the most important problem "not only in mathematics but absolutely the most important."

Marcus du Sautoy
Littlewood's proof... revealed that prime numbers are masters of disguise. They hide their true colours in the deep recesses of the universe of numbers, so deep that witnessing their true nature may be beyond the computational power of humankind. Their true behavior can be seen only through the penetrating eyes of abstract mathematical proof.

Marcus du Sautoy
It seems paradoxical that the fundamental objects on which we build our order-filled world of mathematics should behave so wildly and unpredictably.

Marcus du Sautoy
As mathematicians navigate their way across the mathematical terrain, it as though all paths will necessarily lead at some point to the same awesome vista of the Riemann Hypothesis.

Marcus du Sautoy
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."

Marcus du Sautoy
[The Riemann] zeros did not appear to be scattered at random. Riemann's calculations indicated that they were lining up as if along some mystical ley line running through the landscape.

Marcus du Sautoy