[.uk] Prime Obsession: Bernhard Riemann and the Greatest ... (ISBN 0309085497)

Book Description:
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.

Amazon.com Review:
Bernhard Riemann was an underdog of sorts, a malnourished son of a parson who grew up to be the author of one of mathematics' greatest problems. In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem: proof of the conjecture, "All non-trivial zeros of the zeta function have real part one-half." Though the statement itself passes as nonsense to anyone but a mathematician, Derbyshire walks readers through the decades of reasoning that led to the Riemann Hypothesis in such a way as to clear it up perfectly. Riemann himself never proved the statement, and it remains unsolved to this day. Prime Obsession offers alternating chapters of step-by-step math and a history of 19th-century European intellectual life, letting readers take a breather between chunks of well-written information. Derbyshire's style is accessible but not dumbed-down, thorough but not heavy-handed. This is among the best popular treatments of an obscure mathematical idea, inviting readers to explore the theory without insisting on page after page of formulae. In 2000, the Clay Mathematics Institute offered a one-million-dollar prize to anyone who could prove the Riemann Hypothesis, but luminaries like David Hilbert, G.H. Hardy, Alan Turing, André Weil, and Freeman Dyson have all tried before. Will the Riemann Hypothesis ever be proved? "One day we shall know," writes Derbyshire, and he makes the effort seem very worthwhile. --Therese Littleton

A rambling, long winded book that never makes a point succinctly. 2.5 stars.:
The Prime Number Theorem and its related consequences is a fascinating subject. This book however is a long winded, very poorly written attempt. The author never seems to be able to make a point clearly and succinctly. Instead we are treated to a ramble that confuses more than elaborates. For example the presentation on functions is very poorly done. I have seen basic algebra texts explain the idea of functions far better than in this book. To make matters worse the author takes about ten pages to explain the beautiful idea of a function thus killing a sublime truth. Sorry to say but far better general math books abound. Take a look at Journey Through Genius.

Prime numbers and Riemann:
Very good book, easy to read, no previous knowledge on math is needed but just secondary.

Good Balance Between Math And Biography:
This book is about 2/3 math and 1/3 biography, and these elements are blended well enough to keep nearly everyone's interest. I came away with greater insight into the link between analysis and number theory, and new appreciation for the brilliance of Euler, Gauss, and Riemann. For what it's worth, I think the Riemann Hypothesis is probably true.

A masterpiece of its genre:
There are a number of authors who have tried to esplain difficult scientific or mathematical problems to non-expert readers. I have read and enjoyed many such books. Thus far, Derbyshire is the master.

A great book, which I'll explain later in the review.:
This is a fine book that lays out clearly Riemann's life and times and the mathematical work he did, but I'll explain more about that later in the review. The author certainly knows his subject matter and it thoroughly researched, which I'll touch on a little later. The only thing that drove me to distraction was that at least 2 times in every chapter he would make a point, then say something like "I'll explain more about this in just a bit" or "More about this later" or "In chapter 12 I'll touch on this again". I'm not kidding, it happened EVERY chapter and after a while it got annoying....but I'll show you more about that in my other review. Still, a great read and required reading for anyone into mathematics and number theory.