Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers

by Dan Rockmore

For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.

Genres: Mathematics, Science, Nonfiction, Number

292 pages, Paperback

First published April 5, 2005

Reviews

[Joe · Rating 3 out of 5]

A very good book, but I'm not sure if Dan Rockmore knows who his audience is. Throughout the book, he switches back and forth between incredibly simple mathematical concepts and painfully abstract inside baseball.

For example, he spends almost an entire chapter explaining what a prime number is and then devotes only a few pages to detailing the Critical Strip, a concept integral to understanding WHAT mathematicians are looking for to prove the Reimann Hypothesis.

If the book was written for a math newbie, there's way too much rarefied air in its pages. If his intended audience is mathematicians, the book is terribly watered down. Being somewhere in the middle of these two extremes, I found the book periodically enjoyable but pretty frustrating.

The historical account is terrific, though. It's rare to find such a comprehensive chronology with names, dates and charming anecdotes about science dweebs, so the book is worth the read if only for this.

[Brian · Rating 3 out of 5]

(3.0) A history of the Riemann Hypothesis, as translated by a mathematician

I've often regretted never having taken 'real' math (calculus, linear algebra, diffeq all seem like applied math to me), so there's a lot that I don't know that I wish I did. I was kind of hoping that I'd gain a better understanding of one of the most famous unresolved problems in mathematics by reading this. However, I get the feeling (from the sections that I followed well) that in translating math into prose, a little understanding is lost, and you kind of need to already understand the topic well to properly interpret his presentation. My hyperbolic geometry is a little fuzzy, shall we say, so much of the latter history of the Riemann Hypothesis was a rough qualitative understanding at best. But I did enjoy the early history quite a bit. Definitely makes mathematicians look like pretty cool guys (and girls, though I don't think there were (m)any in the narrative. :( ).

I'm sure many of you smarter than I out there can get a lot more out of this book. I guess I would've appreciated at least a few Greek symbols and proofs in there for me... ;)

[Steffi Greeff · Rating 5 out of 5]

About as effective in stealing the reader from this world than Lord of the Rings or Alice in Wonderland. Only, rather than being lured into the world of elves or Cheshire cats, the reader is drawn into a world of numbers, theorems and graphs. A must read for anyone who truly enjoys algebra, is fascinated by prime numbers and is endlessly drawn to infinites

[James Swenson · Rating 3 out of 5]

This was a fairly good effort at what was probably a doomed project. I have a Ph.D. in mathematics, and I ended up just letting the last 4 or 5 chapters wash over me. It was fun to see Rockmore name-check some familiar names from my grad school, though.

[Benjamin Manning · Rating 4 out of 5]

I read this book for two reasons - first, over the last few years I've become more entranced with the magic that is mathematics; the fact that the Riemann Hypothesis is (probably) true is for me, as compelling as possible evidence that some deity exists (albeit still unlikely). Second, I'm try to read books by people I know and Dan Rockmore is a family friend who's the man! I enjoyed this book a lot, although I'll admit Dan took on a MASSIVE task in attempting to distill some incredibly hard mathematical material for the laymen (which he admits in the first pages). I think he did a superb job in creating a compelling story, but some of the math was simply too hard to simplify and i found myself lost more often than I'd like to admit. Clearly though, Dan is a mathematical master and the history of the Reimann hypothesis is CRAZY.

3 of the MANY things I learned:

1. I've recently been more an more skeptical of asymptotics with the use of monte carlo and bayesian methods, but learning that Gauss's original prediction for the distribution of primes is an underestimate until around 10^1024, and yet equally above and below towards infinity is nothing short of mind-twisting.

2. It's incredible that there are both infinite prime numbers and that the twin primes conjecture has been whittled down to infinite pairs 246 apart; once again, mindblowing.

3. I'm always shocked reading about the 19th century mathematicians who created the foundation for higher mathematics entirely by hand and barely with electricity. Even more shocking is euclid coming up with a damn compelling proof for infinite primes over 2300 years ago!

[Joseph Schrock · Rating 4 out of 5]

I found Dan Rockmore's treatment of the Riemann Hypothesis engaging, but I was not persuaded that matrices and their eigenvalues are going to play a serious role in the eventual solution to the RH. As with all highly complex mathematics, for me, the technical aspects of the book were a bit daunting -- especially segments about matrices.

I thought that the book makes a valuable contribution to the discussions about a notoriously intransigent mathematical hypothesis.

[Andrew · Rating 3 out of 5]

Information overload.
Historically ordered, which is nice. Unfortunately, it's hard to keep up with all the math, which makes it difficult to stay focused on the content. I'm not sure how much I'll retain, but I'll probably read it a second time.

[Henry Jones · Rating 3 out of 5]

It's a good read for anyone interested in math, particularly prime numbers.

[Ulf Kastner · Rating 3 out of 5]

In terms of thorough comprehension of the mathematical concepts touched upon in this book, I think I held my own until about page 72 or so when the book switched (for me, anyway) into high gear with the introductions of the imaginary number and the complex plane (both of which happen to be rather crucial for an intermediate-level understanding of the eponymous hypothesis).

For the 200 pages or so that followed I read on with what can only be described as a tenuous grasp of the math, where periods of comforting lucidity where interspersed with frustrating Gordian knots of incomprehension that I decided weren't going to hinder my progress through the book and its retellings of the wide-ranging efforts to find a proof for Bernhard Riemann's hypothesis about the fundamental nature of prime numbers.

By the conclusion of the book I thought I'd regained a modest nimbleness with the sort of math I hadn't had any close encounters with in going on 20 years.

Considering my compulsive need to read books cover to cover and my suffering from an innate averseness to moving on through a text without adequate understanding of every one of its finer details, it's a testament to the author's ability to tell a compelling story that I managed to make an exception when it came to the latter.

So the writing of author Dan Rockmore proved sufficiently accessible for me to keep reading despite my inadequacies and I hope it set me up well for the other pop math book on prime numbers in my to-read stack—"The Music of the Primes" by Marcus du Sautoy—as well as what I expect to be a slightly more challenging pop math book, "Meta Math! The Quest for Omega" by Gregory Chaitin.

[Nick · Rating 2 out of 5]

There is an incredible amount of mathematics being hinted at in this book. I don't feel like I understand much of it any better than before I read the book though. Instead, I have a list of keywords of starting points for further reading. I suppose this is fair, for a general audience book, but I was still frustrated by it.

I didn't like the way the book was written. The language was frequently... fruity is the best word I've come up with to desribe it, from my meager vocabulary. I almost gave up after the first chapter or two because of this.

But I guess I'm glad I hung in there, picking up plenty about the history of work on the Riemann hypothesis, and some interesting tidbits (mathematics = "that which is learned", elleipein = "to fall short" (ellipse), hyperballein = "throw beyond" (hyperbola)). There were interesting stories about big names in the field, and it's always fascinating to see a huge number of topics I've heard about all related. I wish, a little, that I'd been keeping notes throughout, but the flowery beginning threw me off.

[Randall Scalise · Rating 3 out of 5]

p70: "Such constructible numbers ... include pi ..."

Absolutely not!

p237: "Gravity is the last of the fundamental forces of nature to resist "unification," electricity, magnetism, and quantum mechanics having been knit together (with Dyson's help) into the Feynman-Schwinger-Tomonaga theory of quantum electrodynamics (QED), which was then incorporated into a theory of quantum chromodynamics (QCD) that could also account for the theories of the weak and strong nuclear forces."

No. Very no. Not even wrong, as Pauli would say.

Read John Derbyshire's "Prime Obsession" instead.

[Mangzilla · Rating 4 out of 5]

A fascinating look at the many connections to the unproven Reimann Hypothesis. Necessarily glossing over technicalities it nevertheless gives a strong flavor of the surprising mathematical breadth of this problem. It connects to hyper geometry, eigenvalues of random matrices, quantum chaos, and billiards.

[Joel · Rating 4 out of 5]

This is a real page-turner, a romp through many of the hot topics in math for the last several centuries. It hits the high spots, with just enough explanation for the non-math person to grasp what's going on. Still an unsolved mystery.

[William Derksen · Rating 4 out of 5]

A fun book exploring the history of one of the largest unsolved questions in mathematics. While it does bounce around a little in terms of mathematical difficulty, even if you don’t quite follow all the math, it’s a pretty interesting read!

[Dan · Rating 3 out of 5]

Enjoyable read, but I still have a lot of unanswered questions about the function, imaginary exponents, and those relations to the random numbers of quantum mechanics.

[Brian Page · Rating 3 out of 5]

Definitely includes some gems but the author's attempt at literary flourish is a bit tiresome.

[Nick Black · Rating 4 out of 5]

Pretty tolerable pop math

[Joshua · Rating 3 out of 5]

I understand that the author wanted to write for the public and therefore avoided using equations by the assumption that they might make reading math harder. But I also wonder how likely a person who will be turned off by equations should find more comforts in reading Riemann zeta function in words even if the book was intended to overview the history. Certain balance between using plain language and math notations would be actually necessary to achieve readability. Otherwise, this is a good book.