Stalking the Riemann Hypothesis: the quest to find the hidden law of prime numbers

When Albert Einstein sought the mathematics to bring his general theory of relativity to life, he found his solution in the works of none other than Bernard Reimann. And although Reimann died young (at 39) apparently the special math necessary for relativity was not Reimann's only masterstroke. He also developed a theta function or formula for predicting the placement of prime numbers in the number line. As you may recall from elementary mathematics, prime numbers are those numbers only divisible by themselves and one. Though casual thought on the matter may initially lead one to conclude that prime numbers would eventually be exhausted (indeed the higher you go the more rare they do become) mathematical proofs dating back to Euclid show that like the integer line they accompany they go on forever. But again figuring out how they can be located algorithmically within that forever was long a mathematics holy grail until 1859 when Bernard Reimann posited a hypothesis for locating them. His hypothesis or zeta function involves incredibly complicated mathematics certainly beyond the scope of this book so if you want to understand it you may do better to read Reimann's Zeta Function. However if you want the outlines of search that goes from ancient Greece all the way to modern times, this book makes quick accessible reading.

You can see why the Riemann Hypothesis allegedly led to John Nash's label of mental instability. This book is the best math book out there and it's definitely out there. All the best mathematicians should go insane but then hopefully make it back to acceptable society (without having to undergo secret CIA drug experiments like the Unabomber did at Harvard). And so we STALK -- but what exactly? That's the point isn't it? (to conjure up Dedekind, Godel, Cantor, and so many other greats that challenged the norms of demented ecstasy). I think the grand message of this book is that not only do we get a very clear and concise overview of the whole history of mathematics but in the end we find out that the logic on which math is based is totally a mystery. Call it the "abduction" logic, as created by C.S. Pierce (a sort of intuitive inference). Nevertheless the promo by Professor Strogatz (on the first edition) calls the Riemann Hypothesis a conspiracy which F.W. Schelling would say is totally accurate -- a great spiral of asymmetrical time reversal arising out of pure empty awareness. It appears that math has always been a spectator sport, that the grand paradoxes created by Euler really were proofs for God, that all the power based on math really is an illusion.

This is another fine book on the Riemann Hypothesis that, in my view, strongly complements the volumes by John Derbyshire and Marcus du Sautoy. Readers of the book should have some prior exposure to the Riemann Hypothesis (including a basic understanding of complex variables), some understanding of linear algebra, and a modicum of understanding of quantum physics. I say this because, unlike for Derbyshire and du Sautoy, the mathematics underlying the Riemann Hypothesis are more talked about than developed. The strengths of the book are (1) the author's strong historical perspective, (2) his ability to make extremely esoteric mathematical concepts understandable (and fun!), and (3)a better discussion than provided by either Derbyshire or du Sautoy of the connection between the distribution of the zeta zeroes and the distribution of the prime numbers -- in short, why it is that the Riemann Hypothesis is viewed amongst mathematicians as being so important.

Rockmore's treatment of the Riemann hypothesis does the challenging job of introducing lay readers to the Prime Number theorem, the Euler factorization, Mobius inversion, and the eigenvalues of random matrices. The history is covered beautifully, detailing the partial successes and false starts along the way. Rockmore assumes very little on the part of the reader, and if you're already familiar with the complex plane and infinite series you will read between the lines a bit (actual equations are confined to footnotes) but even mathematically-inclined readers can gain a lot from the book. I enjoyed it a great deal.

In 1900 Dave Hilbert, the most famous mathematician of his day, and quite likely of any day, gave a speech where he listed 23 mathematical problems that he expected to be solved during the 1900's. Most of the problems got solved, several by the invention of new fields of mathematics. Problem Number 8 was simply "Prove the Riemann Hypothesis." It wasn't solved. (To see the other 22, do a Google Search.) Riemann wrote a short paper on prime numbers stating his hypothesis. He then became very ill and died at the age of thirty-nine. The proof has remained elusive for a century and a half. While watching the play "Proof" I found myself wondering if this was the "Proof" in the play. This book is the story of the recent attempts to prove Riemann's hypothesis. It doesn't use any (or very little) mathematics so it is much easier for the layman to read. But the problem isn't solved, after you read the book perhaps you will. If you do, you would be a good candidate for the Fields medal the math equivalent of the Nobel.