The music of primes is not a book that would explain to you how the Reimann Hypothesis can be approached. It is not a rigorous mathematical book that tries to link all the pieces of the puzzle. What it is, is a compedium of the various attempts made by the greatest minds of Mathematics over the past few centuries (mostly decades) over this rather simple sounding problem – is there an order within the prime numbers ?. The book traces the history of the attempts made by Gauss,Euler, Reimann, Ramanjuman, Hilbert, Turing to mention a few. The initial chapters unravel the genius of Euler. Even though it was Reimann who conjenctured about the location of prime numbers on the imaginary line, the foundation of that was laid by Gauss and Euler (which I guess is in line with the general scientific progress). What is the most interesting part is that after Reimann’s hypothesis more than 150 years ago, none of the brilliant minds were able to conclusively prove the hypothesis. And if you are wondering why the hypothesis is important (apart from it being a millenium problem). The most basic application of the hypothesis is to find out the next prime number – this makes it very easy to find large prime numbers, and potentially large prime factors for all the PKI transactions. So, what was considered an insurmountable problem when the public-private key proofs were presented, might become very easy, which essentially implies that the PKI might not be as secure as thought.
Coming back to the book, the book is a good historical insight into prime numbers. I have not read the Prime Obsession, which is supposed to be another good book for the history of prime numbers. Music of Primes, is like a compedium of all the work done and being done to unravel the mystery behind these numbers. The chapter were the Reimann Hypothesis is presented, starts off well, with the necessary building blocks about imaginary numbers. But it falls short in helping the reader visualize the hypothesis. Bernhard Reimann was a mathematician, and his abstract thinking levels can’t be achieved by mere mortals like me. So, I had to look up more information regarding the hypothesis to be able to visualize the zeta function and its zeroes. But, like I said, this book is not expected to help you get a major in mathematics.
Another interesting chapter of the book is Ramanujan, the Mathematical mystic. In this chapter, Marcus du Sautoy tries to present Ramanujan’s genius with respect to the research on prime numbers. Simply superb is what I’d call this chapter. Another very good read are the final two chapters wherein the author tries to present the work done by physicists and mathematicians to try and link the quantum world with the prime numbers. Even though, some parts of it were OHT for me, I sure did enjoy it.
So, should you buy the book. I’d say if you want something more than a light read, but not something which is very dense w.r.t mathematics you might be able to enjoy this book. And if you are someone who is interested in history of things (like I am), then you will relish it more. I’d give the book, a 6 out of 10, because, there were parts of the book which I thought were skimmed way too fast for the average reader to understand – YMMV. An aside, if you want to visualize how the prime numbers spread, check the prime number spiral