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1. Prime Obsession: Bernhard Riemann

1. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
by John Derbyshire
Paperback: 448 Pages (2004-05-25)
list price: US$16.00 -- used & new: US$7.77
(price subject to change: see help)
Asin: 0452285259
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

Bernhard Riemann was an underdog of sorts, a malnourished son of aparson who grew up to be the author of one of mathematics' greatestproblems. In Prime Obsession, John Derbyshire deals brilliantlywith 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 amathematician, Derbyshire walks readers through the decades of reasoningthat led to the Riemann Hypothesis in such a way as to clear it upperfectly. Riemann himself never proved the statement, and it remainsunsolved to this day. Prime Obsession offers alternating chaptersof step-by-step math and a history of 19th-century European intellectuallife, letting readers take a breather between chunks of well-writteninformation. Derbyshire's style is accessible but not dumbed-down,thorough but not heavy-handed. This is among the best popular treatmentsof an obscure mathematical idea, inviting readers to explore the theorywithout insisting on page after page of formulae.

In 2000, the Clay Mathematics Institute offered a one-million-dollarprize to anyone who could prove the Riemann Hypothesis, but luminarieslike David Hilbert, G.H. Hardy, Alan Turing, André Weil, and FreemanDyson have all tried before. Will the Riemann Hypothesis ever be proved?"One day we shall know," writes Derbyshire, and he makes the effort seemvery worthwhile. --Therese LittletonBook Description
In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled “On the Number of Prime Numbers Less Than a Given Quantity.” Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it.

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. ... Read more

Customer Reviews (77)

4-0 out of 5 stars My first review
Really good book for beginners,it explainsbasic concepts for all audiences, the way of mixing history and concepts is original (i prefer The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics) , but sometimes slow for advanced readers.
ugly/strange typography of ecuations and errors.

5-0 out of 5 stars A wonderful read for the inclined
For the person with an interest in mathematics this book is a wonderful read.It is written for the general lay person, but I would generally recommend the book to someone who has already completed high school level calculus.The author does a wonderful job of breaking down the Riemann Hypothesis and presenting it in the easiest way possible.I preferred the actual math explanations more than the math history sections myself.The only real complaint I can make are the poorly presented graphs, which are often so small to make the axis or values unreadable.

3-0 out of 5 stars The calculation of the very first example is wrong!
I just start reading this book. The writing is very good and easy to understand. However, I am upset by the fact that the author calculated wrongly the very first example he gave: the maximum length of the deck of cards.

The error started from the third card. The total length of the top three cards is (1 + 1/4 + 1/2) = 7/4. So the center of their gravity is (7/4)/2 = 7/8. This means that the third card can be pushed by (1 - 7/8) = 1/8 without falling, not 1/6 as stated by the author! The total overhang of the 52-card deck is 1/2 + 1/4 + 1/8 + ... + 1/(2^51). So we get the same series as the second example (the ruler working) given by the author. And with infinite number of cards, the lenght of the above series is 1!

The author wanted to use the example to introduce the harmonic series (1/2 + 1/3 + 1/4 + 1/5 + ...), which can go infinite given infinite cards. Unfortunately, he needs to find another one.

5-0 out of 5 stars Zeta functionmade easy
Prime Obsession is one of the best books for people interested in mathematics but do not have an advanced background in it. John Derbyshire builds the entire edifice brick by brick making clear at every step what he may be leaving out and why he is doing so. I highly recommend this book. Thank you Dr. Derbyshire.

5-0 out of 5 stars A wonderful primer on a very complicated topic
Derbyshire's style of writing lends itself well to imagining this Brit-turned-American actually providing the audio track in your head. If you have a chance to catch his Radio Derb on Nation Review Online, you'll see what I mean.

The book is quite good at providing a historical survey of number theory, how natural numbers and primes work and how all this eventually relates to a very difficult, unsolved modern math puzzle: Riemann's Hypothesis. Through most of the book, Derbyshire does a good job explaining the fundamental math in play on the way to our modern understanding of the puzzle. In fact, I dare say these explanations are vastly superior to the ways most folks are taught math in schools and universities. There are points near the end where the math is so complicated for a newcomer that he makes explicit note to jump over some of these areas and provide the result of the jump. Probably a wise move but it does leave some wanting the full background.

On the whole, it's a great tour of a field of math (and a way of thinking) that eludes 99.99% of the populace -- but is now more accessible.

I was going to say that I hope he write more of these books to popularize advanced math. However, it seems he already has with a book on algebra: Unknown Quantity. ... Read more

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