The Best Books on: The Riemann Hypothesis
Hi there.
Around 2010, as an undergraduate in mathematics I fell absolutely in love with the Riemann hypothesis (RH), as one does. I spent Friday nights researching, reading and trying to understand this most famous of all math problems. In the process, I accrued a bundle of books on the topic. Some were better than others. The following are the ones I would recommend to another 21-year-old interested in understanding the Riemann zeta function, its properties and the implications of Riemann’s hypothesis for the distribution of prime numbers.
1. Prime Obsession (2003)
by John Derbyshire
If you want to understand what the Riemann hypothesis is what its implications are for the distribution of primes numbers, this is the first book you should buy. The book is well-written and contains a sufficient level of technical detail to build a foundation of understanding that you can later expand on with other books and materials. For my money, this is the only narrative-type book you need to buy on the RH.
Type: Narrative | Level: Novice | Price: $17.99
Buy it here
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2. The Riemann Zeta Function (1974)
by Harold M. Edwards
There are many reference books on the Riemann hypothesis, many of which are truly awful to use in practice. This book is not. Although it was first put out in 1974, it is well-written and easy to follow. The book does assume some prior knowledge (approx. math undergrad-level) and some results might be hard to discern on their own. However, if you’re interested in the RH you have to have this book.
Type: Reference | Level: Intermediate | Price: $12.39
Buy it here
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3. Prime Numbers and the Riemann Hypothesis (2016)
by Barry Mazur & William Stein
Few living people know more about number theory than Barry Mazur (1937-). Unfortunately, this book was not available to me back in 2010 but I wish it had been. It’s a wonderful little book that provides thorough explanations of difficult technical results with plenty of examples and curious findings. Highly recommended.
Type: Reference | Level: Novice | Price: $12.39
Buy it here
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4. The Riemann Hypothesis. A Resource for the Afficionado and Virtuoso Alike (2008)
by Borwein, P., Choi, S., Rooney, B. & Weirathmueller, A.
This book became my “bible” as I was writing my dissertation. Although I could not use it outright without having Edwards (1974) at my side, this book provides most if not all of the important results on the RH (as of 2008) in a very clear (albeit technical) format meant for “afficionados and virtuosos”.
A less expensive alternative might be Aleksandar Ivic’s The Riemann Zeta-Function. Theory and Application.
Type: Reference | Level: Expert | Price: $111.75
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5. The Prime Numbers and Their Distribution (2000)
by Tenenbaum, G. & France, M.M.
This is a thin little book that provides some of the results of the other books in a very efficient manner. It is brief, in a good way. More book should be this short. It takes you through some of the basic results in number theory, presents some of the most famous open conjectures and provides some of the stochastic properties of prime numbers. More of a casual read than a reference book, but still recommended.
Type: Narrative | Level: Intermediate | Price: $21.00
Buy it here
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Other books
There are many books on the Riemann hypothesis. Most are probably good books, but might be unnecessary for the casual reader. When I worked on my dissertation, I bought every book I could find, including those below. That was unnecessary. The following books did not provide me (a novice-intermediate reader) with any knowledge (I needed) which was not found in the other books already mentioned.
The Music of the Primes by Marcus du Sautoy
The Riemann Hypothesis by Karl Sabbagh
Stalking the Riemann Hypothesis by Dan Rockmore
Dr. Riemann’s Zeros by Karl Sabbagh
The Riemann Zeta-Function. Theory and Application by Aleksandar Ivic
In Search of the Riemann Zeros by Michel L. Lapidus
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I will probably keep buying RH books until the day I die, but hopefully this guide provided you with some pointers about where to start and what to avoid in building your own collection.
Thank you for reading Privatdozent.
Sincerely,
Jørgen
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Very informative, looking forward to purchasing several of your recommendations