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Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, by John Derbyshire
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The definitive story of the Riemann Hypothesis, a fascinating and epic mathematical mystery that continues to challege the world.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.
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Product details
Paperback: 448 pages
Publisher: Plume; First Edition edition (May 25, 2004)
Language: English
ISBN-10: 9780452285255
ISBN-13: 978-0452285255
ASIN: 0452285259
Product Dimensions:
5.3 x 1 x 8 inches
Shipping Weight: 13.4 ounces (View shipping rates and policies)
Average Customer Review:
4.6 out of 5 stars
184 customer reviews
Amazon Best Sellers Rank:
#119,237 in Books (See Top 100 in Books)
No, this is not for math dummies. IF you got good grades in Pre-Calc and IF you remember it you will love this book.If you struggle with algebra, trig. you will quickly bog down. I don't fault the author who really does a man's job of makingall this rarified math intelligible. And it's a great story too. Well written. But it is NOT easy if you lack the math. Truth said.If you've enjoyed popular documentaries of this subject and want more, buy this book, smarten up, and the author will richlyreward you.
Riemann Hypothesis states that "all non-trivial zeros of zeta function have real part one-half". Ever since it was introduced by a German mathematician, Bernhard Riemann in 1859, in his famous paper on prime numbers, it has not been proven yet, although many great mathematicians worked on it. It was one of 23 Hilbert problems that were unsolved when published, and were considered to be highly influential for 20th century and is still one of six Millennium problems stated by Clay Institute that offers $1 million to whomever proves or disproves it. It is the holy grail of number theory, as the hypothesis concerns the distribution of prime numbers. Prime Obsession tells us what the the hypothesis is about, brief biographies of mathematicians related to the hypothesis such as Riemann, Gauss, Euler, Hardy, Littlewood, Hilbert and so on and history of mathematical advances made when mathematicians worked on it. In doing so, John Derbyshire does a fantastic job. He seizes the reader's attention from very first page until the very last one as if a reader reads a very absorbing thriller. As far as I am concerned, Prime Obsession was one of the best books I read in the last few years. If you like mathematics, you would fall in love with this book. It is such a great read.
Really, No hyperbole, because of this book I have a Masters in Maths(sic). Well actually I have a Masters in Maths because I studied for it, but yes the inspiration came from this book.Having decided to review my (old) Physics knowledge and study The Theory of General Relativity. I chanced across this book whilst browsing Math books on this site, it was of course Riemann's name that caught my eye, since his geometry is (one of) the basis behind Einstein's previously mentioned seminal theory. The reviews made the book look interesting, but I was a bit skeptical as most Math/Science books for layman I found to be well... crap!!! Though I will immediately state an exception for Kip Thorne's excellent Black Holes etc.This book captivated me from the get go. I liked the structure, some Math (it's mostly simply Elementary Number Theory and some really basic Analysis) alternating with some history, I learned a lot from both. I'd never studied Number Theory before and learned about a lot of mathematicians I'd never or fleetingly heard of. The tone wasn't too condescending and the Math was just about right for his task, at least until the last chapter or so.Anyway, when I hit the proof of the Euler Equation, I read it and read it again and again and got hooked on Number Theory and started my own Prime Obsession. Now by the end of book I never fully understood what the Riemann Hypothesis truly meant or implied; this may be also due to the fact that by the end of the book I was already starting to study more Math and its Queen... Number Theory, as I'd signed up for a Masters in Maths and wanted to be fully prepared for it not having studied for a quite a few years by then. And by the end of the course I got to study Riemann's original paper. All in all it was an enjoyable few years.Now to be honest to really understand what Riemann was up to, you do need a wee bit more Math than Derbyshire offers here, and Riemann's paper is a bit of a read as he makes a lot of assumptions on the part of the reader (he of course assumes you're a Mathematician), this makes the paper relatively short, but means you need to be up on your Complex Analysis, Elementary and Analytic Number Theory help to. We used Apostal's excellent Analytic Number Theory and I found Edward's Riemann Zeta Function to be extremely helpful too; it also has a copy of the original paper.To conclude I highly recommend this book by Derbyshire as a great starting point to Riemann's and Number Theory in general. It was for me!
I am often asked to recommend an engaging 'high level' popular math book. I have taught math at the university level as well as the precollege level (the latter 6 years). This is the book I recommend. It's truly outstanding! Moreover, in 2007 it won the prestigious Euler Prize as the "outstanding mathematics book of the year". The prize is given by the Mathematical Association of America. Other winners include books by Ian Stewart, Edward Frankel, Steven Strogatz, Persi Diaconis, Timothy Gowers,...If you're still intrigued by the subject the next step is to read the more hands-on book: Prime Numbers and the Riemann Hypothesis by Barry Mazur and William Stein which only requires high school math and some effort. The Riemann Hypothesis problem is a great way to understand modern mathematics.
From the perspective if getting the reader from A to B, the composite of biography and mathematics is getting to be popular for a good reason - it actually works very well. As with all things, mathematics doesn't just happen, there's no maths fairy that will put a theory under your pillow at night (oh, if only there were...), You need context. The history and biographical details give that context.Good methods can be used badly, but aside from a little awkward phrasing, there was nothing obviously bad here. If someone wanted to understand the elements of maths talked about and how they came about, the book is very respectable.Ok, defects. Some of the tables are broken because whoever adapted the book wasn't very good with HTML. The text is awkward to read in places for the same reason.Any factual defects? Just the usual ones, issues of infinities, some domains not being quite orthodox, etc. Nothing that impacts the accuracy of the main subject, merely side notes where the phrasing could confuse. The main topic is what matters, so just smile and nod when it comes to the maths that simply doesn't matter.If I could rate chunks of book, most would be a 5, with a few scattered 3s throughout. The average is more than 4, but not so high that I'm ok just giving a 5 and having done with it.
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