Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime NumbersFor 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics. |
Contents
| 7 | |
3 | 20 |
Primal Cartographers | 30 |
Shoulders to Stand Upon | 46 |
Riemann and His Very Likely Hypothesis | 63 |
7 | 71 |
A Dutch Red Herring | 95 |
Good but Not Good Enough | 118 |
First Steps | 128 |
A Chance Meeting of Two Minds | 154 |
Making Order Out of Quantum Chaos | 213 |
God May Not Play Dice but What about Cards? | 232 |
15 | 261 |
Glossary | 267 |
Further Reading and Sources | 277 |
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Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime ... Dan Rockmore No preview available - 2006 |
Common terms and phrases
accumulation algebraic algorithm analysis asymptotic atom axis basic behavior billiard ball calculations cards chaotic complex numbers complex plane conjecture count critical line critical strip curve Deift describe Diaconis Dirichlet Dyson eigenvalues energy levels equations Euclid Euler example famous Figure finite formula Fourier Gauss Gauss's estimate Gaussian integers Gaussian primes geometry graph Hadamard Hamiltonian harmonic series Hilbert hyperbolic imaginary infinity intellectual Legendre Legendre's logarithm mann hypothesis mathe mathematical mathematicians Möbius Möbius function natural numbers nontrivial zeta zeros number line number of primes Odlyzko pair correlation particles physicist physics Poincaré disk Pólya primal Prime Number Theorem primes less problem proof quantum chaos quantum mechanics random matrix real numbers reciprocals Riemann hypothesis Riemann's zeta function Riemannian rising sequence Sarnak Selberg sort spacing distribution square root Stieltjes string theory tion Tracy transformations understanding University Vallée-Poussin waves Widom zeta zeros