Prime Obsession 325
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics | |
author | John Derbyshire |
pages | 422 |
publisher | Plume |
rating | 9/10 |
reviewer | jkauzlar |
ISBN | 0452285259 |
summary | History of the attempt to prove the Riemann Hypothesis |
Bernhard Riemann came to the University of Goettingen in 1846 at the age of 19, originally to study theology. The University, however, was home to Carl Friedrich Gauss, "the greatest mathematician of his age and possibly of any age," and the impressionable young Riemann, succumbing to the privilege of Gauss's presence and following his already blossoming interest in mathematics, refocused his studies on the area in which he would soon attain distinct immortality. As early as 1851 he was impressing even Gauss with the results of his doctoral dissertation and in 1859 was appointed a corresponding member of the Berlin Academy. To this honor, Riemann responded with his most famous paper, entitled "On the number of prime numbers less than a given quantity," containing therein what became known as the Riemann Hypothesis.
At the heart of the RH is the Zeta function which, in its basic form, looks like this: Z(s)=1 + 1/2^s + 1/3^s + 1/4^s + ... and which, through some simple algebraic manipulation as demonstrated by the mathematically gifted journalist Derbyshire, can be given in the form (1 - 2^-s)^-1 * (1 - 3^-s)^-1 * (1 - 5^-s)^-1 * (1 - 7^-s)^-1 * ... And it is in this second form which Derbyshire calls "The Golden Key" where the non-mathematician gets the first glimpse of the Zeta function's relationship with prime numbers.
But where this Golden Key appears as this "novel's" turning point--its central conflict-- it is not until Prime Obsession's climax when the Key is at last turned and the Zeta function's true relationship to the prime counting function pi(x)--the number of primes less than a given x--is at last made clear. Along the way, from the introduction of the Zeta function to the final explanation of its relevance to prime numbers (the turning of the Key), Derbyshire enlightens us with clear, mostly English language descriptions of the mathematics involved, as well as plentiful anecdotes that give readers a sense of the life and work of the major figures in the history surrounding the RH from Euler, Gauss and Dedekind in the late 18th century through Riemann's 1859 paper, and from 1859 onward to recent advancements in the '80s and '90s.
The Riemann Hypothesis states that "all nontrivial zeros of the Zeta function have real part one-half." Understanding the statement of the hypothesis is Derbyshire's first mission for the reader. In short, most functions with a dependent variable, say f(x)=x^2-2x+1, have a value for which if you replace x with this value, the function returns zero. In the example given, it is at the value x=1 where f(x)=0. The Zeta function has an infinite number of these zeroes and an infinite number of these is "non-trivial." The non-trivial zeroes come from complex number values. Riemann's guess, his hypothesis, is that the real part of each of these non-trivial zeroes is equal to one-half. The imaginary part can be anything.
Derbyshire explains all of the mathematics in very readable language. It's unlikely that anyone who did well in high school mathematics will not be able to follow Derbyshire's mathematics (and it's unlikely that those who didn't do well will pick up a 400-page book on this topic). The Zeta function is explored from a number of angles--numerically, graphically, algebraically, statistically, and there's even a link between the non-trivial zeroes of the Zeta function and quantum physics! By a larger margin, however, Prime Obsession's intrigue lies in Derbyshire's expositions on Riemann, Hilbert, Turing, Gauss, et al, as well as those modern mathematicians he's interviewed personally. The line between the mathematical half of the book and the historical is clearly defined; the odd-numbered chapters are devoted to the former, the even to the latter.
Those fans and foes of Derbyshire's most public line of work as a journalist/editorial writer for National Review will be comforted to know all political polemics have been set aside. John Derbyshire gives a virtuoso performance as an informed journalist and maintains his stance as a personable and careful guide through a sometimes difficult terrain. Anyone with some interest in the topic will find it hard to put down Derbyshire's book once begun. If we are lucky (hint, hint, JD) perhaps Derbyshire's next book will cover the newly-proven Poincare Conjecture ...
You can purchase Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, carefully read the book review guidelines, then visit the submission page.
This is long overdue (Score:5, Funny)
Re:This is long overdue (Score:2, Funny)
Douglas Adams (Score:5, Funny)
The answer? 42.
The question? What is 6 times 9.
The part he didn't tell you is that the question/answer machine was devised by a group of aliens that had 13 fingers. They wouldn't count in base 10, they would count in base 13, naturally.
6 x 9 does in fact equal 42. In base 13.
ISBN not prime (Score:5, Funny)
The author must be sad.
Re:What is bad about him? (Score:2, Funny)
It's entirely people's prerogative to mix politics and pleasure, but my God, what a silly prerogative to exercise.
Re:lay person? (Score:2, Funny)
It should become a classic, alongside with this book: Everyday Math For Dummies http://www.dummies.com/WileyCDA/DummiesTitle/produ ctCd-1568842481.html [dummies.com]
Re:What is bad about him? (Score:2, Funny)
Besides, in the field of mathematics, being conservative is not a bad thing as long as the Earth is still round.
Re:Majored in math, away from it for a year (Score:2, Funny)
Re:Motivation (Score:3, Funny)
Plus chicks will dig you. Yessiree, I'm telling you. If you prove the Riemann Hyphothesis you'll be getting into some prime poontang. If you know what I mean.
Re:lay person? (Score:3, Funny)
I for one welcome our new, math-knowing, Finnish overloards!
And our math-knowing Korean overloards.
And our math-knowing... eh, forget it. At least we beat Portugal [go.com].
Re:lay person? (Score:3, Funny)
Achilles says, 'I think you mean "couldn't be bothered to" rather than "could not." In my experience most people are guilty of lack or interest rather than actual stupidity.'
Re:Propaganda (Score:3, Funny)
Kinda sad actually. If some frothing deaniac at the NYT or somewhere had written a totally non-political book the editors wouldn't have even found it worth mentioning the 'day' job of the author.
But then what do I know... I read Derbyshire's NRO columns so I'm irredeemably wicked in the eyes of the