The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics

This is not the book to learn much of the technicalities of the problem. But if you are interested in the human stories around it, this is a great book.

I think potential readers of this intriguing book need to bear in mind the following: (1) you do not need to understand Riemann's hypothesis to enjoy this book and (2) Mr. Sabbagh does a very fine job of outlining Riemann's hypothesis in layman's terms. Riemann's hypothesis is not easily grasped; what Sabbagh wants to do is to enhance your understanding of it. There is no pretense here that the hypothesis in all its complexity is being conveyed. In fact, near the book's end, he concedes that "you know almost nothing [about R's hypothesis] compared to what there is to know. The hypothesis itself is an outcome of Riemann's zeta function which is the sum of the series 1 + 1/2^s +1/3^s...1/n^s, which means 1 + 1/2^a+ib + 1/3^a+ib (where i is an imaginary number). All sorts of values are possible, but the values of interest center on the Riemann zeta function when it becomes zero. These zeroes, as its turns out, fall on what is known as the "critical strip" and their graph is linked to the fluctation of the primes, which are themselves the building blocks for all the other numbers. The hypothesis is that all the "significant" zeroes line on the critical strip. The proof has become the Mount Everest of mathematics, but it remains unscaled. Many mathematicians, who perhaps found the hypothesis disarmingly approachable, have died before reaching the summit.Sabbagh does want you to understand the hypothesis, but he is also trying to delve into the community of mathematicians generally -- what they are like as people -- in an effort to make them more accessible as well. Inevitably, in this area, Sabbagh often reads like an anthropologist documenting the ritualistic "abnormalities" of some primitive Amazonian sub-culture. What I found surprising is not that Sabbagh finds that the thought processes of mathematicians rarely intersect with that of non-mathematicians; rather what I found striking were the similarities with the "rest of us." They can be collaborative yet guarded, brave yet insecure, intuitive but distrustful of intuition. Several he finds are lousy at simple computations (but brilliant on abstractions). They are a colorful lot, but they are not high IQ aliens from another world. The portrait of Louis de Branges is especially fascinating and forms a strong sub-plot within Sabbagh's text.I don't plow through many books like this, but I do recommend The Riemann Hypothesis. Like Sarah Flannery's "In Code" (which has an excellent chapter on prime numbers), The Riemann Hypothesis is suited for, and ought to be attractive to a wide audience.

a good introduction for this subject.

good book

As a math hobbyist, I've been very eager to learn more about the Riemann Hypothesis. I ordered this book a couple weks ago, and fell ill this week -- so I had some time to spend reading.I didn't get very far before I found a rather glaring error. On page eighteen, the author explains one method for showing that there's no largest prime number. He asserts that:(2 * 3 * 5 * 7 * 11 * 13 * 17 + 1) / 7is equal to2 * 3 * 5 * 7 * 11 * 13 * 17 + (1/7)which is not correct. The left-hand term actually evaluates to2 * 3 * 5 * 11 * 13 * 17 + (1/7).Maybe I'll revise my review after I read more; perhaps the book really does deserve my trust. But after an early blunder like this in a simple topic, maybe I won't read any further.Less astute readers might not have caught this and later become confused. Maybe, in the deeper topics, I won't be able to proof the text and become confused or disillusioned by other errors.