The Music of the Primes: Why an Unsolved Problem in Mathematics Matters

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The most unsettling thing about these new numbers was working out where they were. There wasn't any room on the number line, which contained places for numbers like 2, -3, pi or e. It was Gauss, Riemann's teacher, who suggested creating a new direction for this new imaginary number i. The ordinary numbers (or real numbers as mathematicians call them) sat on the number line

The music of the primes : Marcus Du Sautoy : Free Download The music of the primes : Marcus Du Sautoy : Free Download

Riemann was very shy as a schoolchild and preferred to hide in his headmaster's library reading maths books rather than playing outside with his classmates. It was while reading one of these books that Riemann first learnt about Gauss's guess for the number of primes one should encounter as one counts higher and higher. Based on the idea of the prime number dice, Gauss had produced a function, negative times a negative is always positive. But the French revolution gave mathematicians the courage to think of new ideas. They invented new months and new days of the week, so why not new numbers? So came about the birth of the new number i, the square root of minus one. All the other imaginary numbers were got by taking combinations of this new number with the ordinary numbers, forWhen reading Maths books, I think it’s important to distinguish between books about Maths or the history of Maths, and books where you actually get to learn and do Maths. You should try to have a good balance of both types on your personal statement. As you can tell The Music of the Primes is one of the books about the history of Maths. Access-restricted-item true Addeddate 2013-06-17 14:37:53 Bookplateleaf 0004 Boxid IA1127404 Camera Canon EOS 5D Mark II City New York, NY Donor running East-West in this map of imaginary numbers, while the North-South direction corresponded to the imaginary part. So each imaginary number, like -3+4 i, just became a point in this map: go 3 units west and 4 units north. Suddenly a two-dimensional map of the world of imaginary numbers emerged, making these numbers far more tangible. du Sautoy takes the reader into a long journey exposing the ideas of the greatest minds ever, starting from Fermat, moving to Gauss, Riemann, Gödel, the enigma code breaker and father of AI and computing Alan Turing .. and many many others. However, I felt more and more at sea as the book went on. Given that I have studied the Riemann Hypothesis at Masters level, and even written an essay on it and the Riemann Zeta Function (in 2019), you would think I’d do better – however, my maths brain has not done well since I gave up in 2021, and I have forgotten so much.

Music of the Primes by Marcus du Sautoy | Goodreads The Music of the Primes by Marcus du Sautoy | Goodreads

Edwards, Harold M. (December 2004), "Prime obsession; The Music of the Primes; The Riemann Hypothesis", The Mathematical Intelligencer, 26 (1): 55–59, doi: 10.1007/bf02985403, S2CID 122755808 There is a good reason for the religious, even spiritual, interpretation of mathematics - particularly number theory, and especially prime numbers. In the first instance, unlike any other area of human inquiry - even theology - the results obtained in mathematics never change. Euclid’s proofs may be superseded by more general analysis but they are nevertheless entirely correct and need no modification in a world of radically different cosmology and technology.

The Music of the Primes

But the hypothesis still stands strong. Some believe its time has come while others feel that it'll survive its bicentenary. Some believe it is false where other think that it is true but unprovable. six-sided dice would land exactly one in six times on the prime side. But of course it is very unlikely that a dice thrown 6,000 times will land exactly 1,000 times on the prime side. A fair dice is allowed to over- or under-estimate this score. But was there any way to understand how to get from Gauss's theoretical guess to the way the prime number dice had really landed? Aged 33, Riemann, now We take it for granted now that evolutionary biology, among other things, helps us understand human behaviour, but we're not entirely sure why maths matters - if, indeed, it matters at all. Hence books like this, which strain to assert their importance: 'Why an Unsolved Problem in Mathematics Matters'. Hence Marcus du Sautoy, whose combination of brains and charm should soften up even the most wilfully innumerate of readers.