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Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics Paperback – May 25, 2004
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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 --This text refers to an out of print or unavailable edition of this title.
Bernhard Riemann would make any list of the greatest mathematicians ever. In 1859, he proposed a formula to count prime numbers that has defied all attempts to prove it true. This new book tackles the Riemann hypothesis. Partly a biography of Riemann, Derbyshire's work presents more technical details about the hypothesis and will probably attract math recreationists. It requires, however, only a college-prep level of knowledge because of its crystalline explanations. Derbyshire treats the hypothesis historically, tracking increments of progress with sketches of well-known people, such as David Hilbert and Alan Turing, who have been stymied by it. Carrying a million-dollar bounty, the hypothesis is the most famous unsolved problem in math today, and interest in it will be both sated and stoked by these able authors. Gilbert Taylor
Copyright © American Library Association. All rights reserved --This text refers to an out of print or unavailable edition of this title.
Top customer reviews
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.
However, just as the other book, the paper quality is not so good. I feel that people tend to use good paper for textbook while bad paper for "pop" book. This is not a textbook but I hope the publisher can use better quality paper for this kind of serious pop-science book, just as most mathematics textbook.
The theme of the book is the Riemann Hyphotesis, concerning the zeros of the Zeta-function, and starts with a detailed treatment of the Prime Number Theorem: a statement about the number of primes smaller than a given number. Beautiful connections and amazing results are produced all along.
What about this: One of the best approximations for the number of primes is the Logaritmic Integral function Li(x) (the integral of 1/lnx). This function gives a number that is always a little too high, the error steadily increasing (but the relative error is decreasing). For the number of primes less than one million, the function gives a number only 130 higher than the true number of primes. For the number of primes less than 1000 billion, the error has increased to 38 000, and for the number 10 to the power of 23 (a very big number!) the error is 7.25 billions. And continued increase in the number results in increasing error. So what a surprise, when in 1914 it was proved that the difference between Li(x) and the true number of primes changes from positive to negative and back, and even do this infinitely many times!! This happening for the first time when the number is probably (!) somewhere around 10 to the power of 316.
This example shows that even though the first 10 000 billion zeros (!) of the Zeta function has been computed, all confirming the Riemann hypothesis, this is very, very far from a proof. There is a long, long way to infinity!
To read the book you should have some basic (not detailed) knowledge of calculus, the exponential and logarithmic functions, complex numbers and above all: infinite series. Some knowledge of complex functions could be helpful, but probably not necessary.
The text is always clear, logical and easy to follow, bringing a lot of surprises and pleasures. Can be read over again many times, as there are plenty of stuff for thinking and wondering.
A truly amazing book!
Most recent customer reviews
reads like a page-turner, despite the sophistication of the subject matter.
the melding of history and biography adds great background to development
If you struggle with algebra, trig.Read more