Music of the Primes Searching to Solve the Greatest Mystery in Mathematics Book

There’s surprisingly little maths in this book about an unsolved maths problem, only a few scattered and rather simple equations and some graphs, all of which should be understandable for non-mathematicians. And even if you don’t, you can still follow the text easily. Marcus du Sautoy works a lot with metaphors, which is frowned upon by real mathematicians, but which help to keep the layman in line.

So, what’s the deal? In short: a hitherto unsolved problem in the field of number theory, the so called Riemann hypothesis, which the German mathematician Bernhard Riemann mentioned in his paper in 1859, and whose effect, if it ever turns out to be true, will make an important contribution to the understanding of prime numbers and their inner workings (those whole numbers greater than 1 that have no factors other than 1 and the number itself, staring with 2, 3, 5, 7, 11, 13, … and of which there are infinitely many). Riemann has assumed that the zeros of a certain (admittedly rather complex) function, the Zeta-function, all lie on a certain critical line. There are an infinite number of these zeros, so one cannot simply determine and check them all with the help of a super computer, because even the most powerful computer cannot perform an infinite number of calculations in a finite time. In order to refute the hypothesis, it would be sufficient to find a single zero outside the critical line. This has been tried over the centuries, but without success: over 100 billion zeros have been checked by now (you can explore them here) and they all fit the hypothesis, but although this strongly suggests the hypothesis is true, it doesn’t count as an acceptable proof in maths.

This problem is at the centre of the book. But around it the author builds up a whole cultural history of mathematics. Almost all mathematicians who dealt with prime numbers at some point and made their contributions found their rightful place here. The baton has been handed down over the centuries: Euklid, Euler, Gauss, Riemann, Hilbert, Hardy/Littlewood, Ramanujan, Gödel, Turing, to name but only a few of the best known actors. The book is filled with anecdotal stuff about all of these intriguing characters. In addition, one learns about the current state of cryptography, without which secure Internet communication would not be possible, and in which large prime numbers (100 digits and more) play an essential role.

Should you read this? I would say, yes. If you’re interested in the history of maths/science in general (on the basis of a prominent example), I guess it’s hard to come by a presentation that is more simple but has the same high level of seriousness, fun, and sophistication.

By the way, if it’s fame and wealth you’re after: The Riemann hypothesis belong to the list of the so called Millennium Prize Problems stated by the Clay Mathematics Institute in 2000. Solving any of these problems will get you a US$1,000,000 prize and, of course, will give you immortal fame among mathematicians. Good luck!

PS. The words in this review at prime positions are underlined.


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