The music of the primes
"At school, children are taught that prime numbers are divisible only by themselves and the number one. What they are not taught is that primes represent the most tantalising enigma in the pursuit of human knowledge. How can one predict when the next prime number will occur? Is there a formula that could generate primes? In 1859, German mathematician Bernhard Reimann put forward a hypothesis that suggested a solution to the ancient puzzle. Yet he failed to provide a proof and the mystery only deepened. In this breathtaking book, Marcus du Sautoy tells the story of the eccentric and brilliant men who sought a solution that would revolutionise fields as diverse as e-commerce, quantum mechanics and computer science. Du Sautoy's tale is a moving and awe-inspiring evocation of the mathematician's world and the beauties and secrets it contains."
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What Hacker News says
- I am one of those people who finds the universe more beautiful because of its underlying mathematics.
I truly love it when I see fractal broccoli (so pretty I dont want to eat it, lest I disturb the beautiful pattern), the golden spirals in sunflowers and aloe plants (one of my fav!!), the arrangement of ferns, the hexagonal cloud storms on Jupiter, the musical notes that are euphonious, the geometric structures of snowflakes (so many different kinds!!), and on and on...
Marcus du Satoy is a wonderful writer and science communicator. I've loved his _Music of the Primes_. Highly recommended!
- The excellent mathematical history "The Music of the Primes" by Marcus du Sautoy covers this period:
"Within the space of a few weeks, Hitler had destroyed the great Gottingen tradition forged by Gauss, Riemann, Dirichlet and Hilbert. One commentator wrote that it was 'one of the greatest tragedies experienced by human culture since the time of the Renaissance'. Gottingen (and some might argue, German mathematics itself) has never recovered from its destruction by Nazi Germany during the thirties. Hilbert died on St. Valentine's Day in 1943... his death marked the end of the city's position as the Mecca of mathematics."
The central rational for the initial Nazi assault on the Gottingen department of mathematics was its Marxist leanings, with Nazi street protests decrying the 'fortress of Marxism'. Note that 'Landau, who was Jewish, was allowed to stay because he had been appointed before the outbreak of the First World War. The non-Aryan clause in the civil-service law of April 1933 did not apply to long-serving professors or those who had fought in the war.' Later Landau was targeted for his Jewishness, forced to resign, and died in 1938 in Germany after a bried exodus to Britain.
People should be somewhat cautious in applying these historical examples to the USA today - indeed, the corruption of the American academic system began long ago in the 1980s, when Bayh-Dole legislation initiated the corporatization of research via the exclusive licensing of tax-payer funded research to private interests, who then stopped financing their own proprietary industrial research centers like Bell Labs. Now American universities are packed with shady entrepreneurs who routinely cook data and found startups in the hope of large financial payouts via acquistion by large corporations. This has lead to rampant fraud, a culture of secrecy and distrust, and various other ills.
- "The Music of the Primes" by Marcus du Sautoy (2003), has a great section on the work of of Paul Erdòs. eg
> "Erdòs, like so many great mathematicians, was lucky to have a father who could expose him to ideas that would stimulate his passion for numbers. On one occasion his father had shown Erdòs Euclid's proof that there were infinitely many prime numbers. But Erdòs was fascinated when his father twisted Euclid's argument to prove that you could find stretches of numbers of arbitrary length where there were no primes."
(for a stretch of 100 consecutive numbers with no primes, generate n = factorial(101) and then there will be no primes in range(n + 2, n + 102)).
- As a dad to a 7 year old (and another one on the way :)) , I find the following books wonderful. They evoke wonder in me and hopefully I will be able to transmit some of this to the kids .
1. Euclid's Window
2. Music of the primes
- "The Music of the Primes" by Marcus du Sautoy
- "The Music of the Primes" by Marcus du Sautoy, about history of prime number theory and the Riemann hypothesis. Beautiful and inspiring.
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