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I would teach the world how the Greeks proved, more than 2,000 years ago, that there are infinitely many prime numbers. In my mind, this discovery is the beginning of mathematics – when humankind realized that, by pure thought alone, it could prove eternal truths of the universe.
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Prime numbers are the indivisible numbers, numbers that can be divided only by themselves and one. They are the most important numbers in mathematics, because every number is built by multiplying prime numbers together – for example, 60 = 2 x 2 x 3 x 5. They are like the atoms of arithmetic, the hydrogen and oxygen of the world of numbers.
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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.
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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.
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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.
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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?
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We have all this evidence that the Riemann zeros are vibrations, but we don't know what's doing the vibrating.
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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.
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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.
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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.
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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."
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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.
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It seems paradoxical that the fundamental objects on which we build our order-filled world of mathematics should behave so wildly and unpredictably.
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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.
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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."
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[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.
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It is the greatest of all mistakes to do nothing because you can only do a little. Do what you can.
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Marcus du Sautoy
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Born:
August 26, 1965
(age 58)
Bio:
Marcus Peter Francis du Sautoy is the Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.
Known for:
The Music of the Primes (2003)
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