Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

By John Derbyshire

Book Overview

In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark -- a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false?

Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic -- defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark -- the Riemann Hypothesis -- that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows -- subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age.

It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many -- the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution.

Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof -- and those who have been consumed by it.

• Format: Hardcover
• Language: English
• ISBN: 0309085497
• ISBN13: 9780309085496
• Release Date: April 2003
• Publisher: Joseph Henry Press
• Length: 446 Pages
• Weight: 1.50 lbs.
• Dimensions: 9.3" x 1.3" x 6.0"

Customer Reviews

It's got that certain "can't put it down" feel

This is a fascinating and very well-written book about a singular problem in mathematics history. Derbyshire presents a look at the history of the Riemann hypothesis (or is it "conjecture"? Derbyshire asks, as an aside, what the real difference is between the two, in mathematical terminology) -- the people and their political context as well as the equation and efforts to prove it.As a blessing to those of us who are not hard-core mathematicians, Derbyshire takes the approach of alternating chapters between (even numbered chapters) math and (odd chapters) people and context. This gives the effect of telling two intimately linked stories simultaneously, and keeping the reader in just a bit of suspense in each while telling the other. I found myself enjoying each of the two tales, yet impatient to see where the other was going next.Derbyshire's style of writing is thoroughly entertaining, as well. His personality comes through as someone who is a "fan" of math. In "Peanuts", the late, great Charles Shultz has Lucy commenting to Schroeder that Beethoven couldn't have been so great, because he never had his picture on bubble-gum cards. It is apparent that if there was ever a set of mathematical gurus bubble-gum cards, Derbyshire would have been a collector. His admiration for genius only added to my enjoyment of the book. Derbyshire directly lets you know which people he holds in high esteem. He clearly honors those with a work ethic, those with dedication to their craft, family, and faith. He almost apologetically admits his appreciation for these sympathetic characters with a style reminiscent of a sports broadcaster who is also quietly rooting for "the good guys" -- not the home team, but the high-character-quality players. Thomas Boswell and George Will both use a similar "aw shucks, I just LIKE the guy" style when writing about Cal Ripken.In any case, Derbyshire reveals his own character by telling which mathematicians he likes best and why. Similarly, his humility in how he presents the mathematical concepts is also telling. Derbyshire has obviously had to cut some strong math chops to be able to understand and present all that he does, as clearly as he does, and he repeatedly comments on keeping the level down to where most readers can comprehend -- yet he does all this in a self-deprecating fashion that made me comfortable to keep reading and learning. Even when the math was more than I wanted to plow through, I just read those parts lightly and kept going, and Derbyshire's style kept the story together through that.As an engineer and semi-pop-science geek wannabe, I found this book to be a bit heavy on math theory and a bit light on applications for my tastes. Derbyshire admits this tendency, to the effect that once the theoretical knowledge is gained, people will find applications for it. That's Derbyshire's point of view, and another glimpse of his character. It makes me want to meet him -- he seems to be the type of perso

A great popular math book

There seems to be a plethora of books about the Riemann Hypothesis (RH) lately. This book is very through for the non-mathematician. Every other chapter is mathematical in nature but is tractable with plenty of illustrations to guide the weary reader along the way. For the most part I couldn't see how Mr. Derbyshire could make it any easier. The other chapters are historical in nature and describe not only Mr. Riemann's life but how RH has touched mathematicians, physicists and the rest of humanity until present day.

Reads Like a Gripping Mystery

Prime Obsession is a delight: a book about a hypothesis on the distribution of prime numbers that reads like a gripping mystery. Most fiction isn't this vivid, moving, and well written, and this is no fiction. It is history, biography, philosophy, and, yes, mathematics brought to life with wit and wonder. You have to read this extraordinary book.This is the story of the Reimann Hypothesis, the greatest unsolved problem in mathematics today. Here it is in all its glory: "All non-trivial zeros of the zeta function have real part one-half."What on earth does it mean? Mr. Derbyshire, a gifted storyteller, takes the reader on an exhilarating journey of discovery as he painstakingly illuminates the meaning, mystery, and power of those eleven short words. I have never taken a course in calculus and am intimidated by even moderately complex math notation. There's lots of that in this book, and I had my doubts I could get through it. But Mr. Derbyshire knows that some of his readers will have fear of flying, or only be able to fly for short distances, so he patiently breaks scary-looking formulae into bite-size pieces and gives you the general rules you need to know to digest them. He knows how to explain things with crystal clarity and easy wit. And the man knows how to turn a phrase.Still, he does not coddle his readers, so you need to be prepared to roll up your sleeves and fasten your seat belt. This is a challenging book, no bones about it. I needed to read it twice just to get a passing feel for chunks of it. Why, you may ask, would I twice read a book I had difficulty comprehending? Because with Mr. Derbyshire's gentle urging I could glimpse the beauty and feel the deep wonder of Bernhard Riemann's hypothesis, even if it remained just beyond grasp. And this was enough, more than enough, to rivet my attention for days and give me hours of entertaining, informative reading.This is a gem of book. It left me gasping for air and wanting more. I cannot more strongly recommend it.

A Beautiful Read. Well Done

John Derbyshire has done a great job with Prime Obsession. I am not a mathematician and I'd never even heard of the Riemann Hypothesis, but Derbyshire feeds it to you a bite at a time, and I think I now at least understand what all the excitement is about. Derbyshire doesn't pretend it's easy and doesn't spare you any of the necessary math, but he makes it as palatable as it can be made, I think, and gives just as much as you need.I agree with the statement in his prologue: "If you don't understand the Hypothesis after finishing my book, you can be pretty sure you will never understand it." When you get overloaded with math, there is plenty of historical and biographical detail to keep your attention--some physics, too. The writing is fluent and occasionally beautiful. The book's epilogue, where we say goodbye to Bernhard Riemann, is actually very moving.And the footnotes are wonderful! This is a nonfiction book, but Derbyshire is a natural novelist, and it shows--he has made a really good story out of the Riemann Hypothesis.---------------------------------------------------------------

Excellent Reading for Math and Non-Math Types

Mr. Derbyshire has written an absolutely excellent book on the Riemann hypothesis. The Riemann hypothesis, which relates to prime and complex numbers, has yet to be proved. It is the most famous unproved problem in mathematics. In fact, the first person to prove the Riemann hypothesis will be awarded a large sum of money from the Clay Mathematics Institute.Mr. Derbyshire's book is perfect for folks like me with a mathematics background and also for those who lack formal training but are interested nonetheless. The mathematics are very well explained, and much of the book requires no understanding of mathematics at all. "Prime Obsession" is easily the most accessible book ever written on the Riemann hypothesis.Pure mathematics is more of a mysterious art than a science, and this work serves to illuminate one very important mathematical mystery. This book is on my shelf, and it should be on yours too!