Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
To get the free app, enter your mobile phone number.
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics Hardcover – International Edition, April 23, 2003
Frequently bought together
Customers who bought this item also bought
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
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
Top customer reviews
There was a problem filtering reviews right now. Please try again later.
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.
enjoyment of the book . A fine writer makes math as well as the rarified world of mathematicians interesting and enjoyable .
Derbyshire's mathematical exposition is quite good, especially for an author who is not a practicing mathematician and apparently spends much of his professional life writing conservative political polemics. I found his explanations to be very clear and really enjoyed his detailed, nuts-and-bolts explanation of how to extract the prime counting function given the zeros of the Riemann zeta function.
Naturally, he had to omit some of the more mathematically sophisticated details, including questions of convergence, how to extend the domain of the zeta function from the series definition, and how exactly you calculate the zeros of the zeta function.
Some of these details can be found in, e.g., Conway's Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) and Apostol's Introduction to Analytic Number Theory (Undergraduate Texts in Mathematics).
The rest appear to be covered in Harold Edwards' Riemann's Zeta Function (which is now at the top of my reading pile). As a bonus, Edwards' book includes in an appendix an English translation of Riemann's original paper containing the hypothesis, "On the Number of Primes Less Than a Given Magnitude."
Right at the first page of the book, the author introduced the origin of the Riemann Hypothesis. The hypothesis was first introduced by Bernhard Riemann's paper "On the Number of Prime Numbers Less Than a Given Quantity" in August 1859. The paper leads to the proof of the Prime Number Theorem (PNT) in 1896. PNT states that the number of prime numbers less than a given number x is approximated by x/ln(x). "If either...or...could have proved the truth of the [Riemann] Hypothesis, the PNT would have followed at once...They couldn't of course...The PNT [could] follows from a much weaker result...: All non-trivial zeros of the zeta function have real part less than one." Riemann Hypothesis is similar to the above weaker result: all non-trivial zeros of the zeta function have real part one-half. In 1914, Hardy proved that "there is infinity of non-trivial zeros...infinitely many of them have real part one-half." But "this did not settle the Hypothesis." Since then, mathematicians discovered or conjectured that the zeta function has relationships with the Mobius function, the J step function, the Li function, field theory, and with some Hermitian operator. The zeta function is also related to quantum mechanics through the Montgomery-Odlyzko Law (GUE operator). However, nobody is able to prove or disprove the hypothesis yet.
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