A few years ago I read Prime Obsession by John Derbyshire, a book about the Riemann Hypothesis – a famous unsolved mathematical problem. I was completely captivated by this book. It’s a work of brilliance, written for the “non-mathematical reader” (as Derbyshire puts it). That is, it’s written for someone who understood high school math and perhaps took a few college courses. The book alternates between odd numbered chapters of mathematical exposition that give the mathematical background necessary to understand the Riemann Hypothesis, and even numbered chapters that contain historical and biographical material that help one to understand the players involved and the overall intellectual backdrop of the time. The genius of the book consists of many things: how Derbyshire explains the math so cogently that even when you don’t quite grasp everything, you understand enough to appreciate the importance of what he’s explaining; how the portraits of the mathematical personalities are so vibrant and clear; how a statement so initially esoteric and impenetrable as “All non-trivial zeroes of the zeta function have real part one half” can not only be made understandable, but made to seem worth understanding.
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I’ve re-read Prime Obsession several times, and each time got a little more out of it, understood a little more, grasped a few insights that had previously eluded me. It’s truly one of my favorite books. However, it’s not the only book written in the past few years about the Riemann Hypothesis. Another well-regarded book on the same topic is The Music of the Primes by Marcus du Sautoy. I was aware of this book, but never bothered to read it. Partly this was because of a natural and understandable question: How many books about the Riemann Hypothesis does one person have to read? Isn’t one really enough, especially if that book is excellent? But I think part of it was an odd feeling of loyalty to Prime Obsession, as though I had made my choice in the Riemann Hypothesis book wars (not that there was any such thing) and didn’t want to see how anyone else might approach the topic. It turns out, though, that a friend of mine had The Music of the Primes on his bookshelf. I asked to borrow it, and I’ve really been enjoying it. The book proceeds without the deliberate separation of math and biography that Derbyshire employs, but is still easy to follow structurally. du Sautoy writes beautifully and his emphasis truly is on the “music of the primes.” He keeps coming back to this metaphor in different ways, and he spends more time discussing the many mysteries of prime numbers than does Derbyshire.
If I had to recommend only one book, I would still pick Prime Obsession. I think that Derbyshire does a masterful job of telling the story almost like a suspense thriller, while also building up the math in wonderfully clear, systematic steps. I’m sure that I understand The Music of the Primes as well as I do because I’ve already read Prime Obsession. But The Music of the Primes is also wonderful and I would recommend it with enthusiasm.
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