Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in MathematicsIn August 1859 Bernhard Riemann, a littleknown 32year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark the Riemann Hypothesis that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof and those who have been consumed by it. 
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LibraryThing Review
User Review  palaverofbirds  LibraryThingSeeing as how this is my first exposure to the RH, and I'm only fairly capable in math, I can't say whether or not this is the best place to start. I feel like I have a good sense about this great ... Read full review
LibraryThing Review
User Review  RandyStafford  LibraryThing"This isn't magic. There's a reason this stuff works," my high school math teacher used to say. Of course, there are some contentions, hypotheses, in math where we don't know if they work, if they are ... Read full review
Contents
1 CARD TRICK  3 
2 THE SOIL THE CROP  19 
3 THE PRIME NUMBER THEOREM  32 
4 ON THE SHOULDERS OF GIANTS  48 
5 RIEMANNS ZETA FUNCTION  63 
6 THE GREAT FUSION  82 
7 THE GOLDEN KEY AND AN IMPROVED PRIME NUMBER THEOREM  99 
8 NOT ALTOGETHER UNWORTHY  118 
16 CLIMBING THE CRITICAL LINE  252 
17 A LITTLE ALGEBRA  265 
18 NUMBER THEORY MEETS QUANTUM MECHANICS  280 
19 TURNING THE GOLDEN KEY  296 
20 THE RIEMANN OPERATOR AND OTHER APPROACHES  312 
21 THE ERROR TERM  327 
22 EITHER ITS TRUE OR ELSE IT ISNT  350 
EPILOGUE  362 
9 DOMAIN STRETCHING  137 
10 A PROOF AND A TURNING POINT  151 
11 NINE ZULU QUEENS RULED CHINA  169 
12 HILBERTS EIGHTH PROBLEM  184 
13 THE ARGUMENT ANT AND THE VALUE ANT  201 
14 IN THE GRIP OF AN OBSESSION  223 
15 BIG OH AND MÖBIUS MU  238 
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Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in ... John Derbyshire No preview available  2003 
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actually algebraic analysis analytic number theory Andrew Odlyzko argument arithmetic axis Basel problem Berlin Bernhard Riemann bers big oh bigger calculate cards century Chapter complex function complex numbers complex plane compute conjecture converges course critical line critical strip curve Dedekind Dirichlet eigenvalues ematician ematics error term Euler example Expression fact Figure formula fraction func function value Gauss German going Golden Key Göttingen graph Hadamard Hardy harmonic series Hermitian Hermitian matrix Hilbert imaginary infinite sum infinity integral Jacques Hadamard Landau lecture Leonhard Euler Li(x Littlewood log function math mathematical mathematicians matrix means Möbius multiply natural numbers negative number nontrivial zeros number of primes polynomial positive whole numbers Power Rule Prime Number Theorem problem proof proved random rational numbers real numbers result Riemann Hypothesis Riemann zeta function space subtract Table thing tion true University Vallée Poussin zeta zeros