# Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

Joseph Henry Press, Apr 29, 2003 - Science - 429 pages
In August 1859 Bernhard Riemann, a little-known 32-year 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 - LibraryThing

Seeing 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
 NOTES 365 Appendix THE RIEMANN HYPOTHESIS IN SONG 393 PICTURE CREDITS 405 INDEX 407 Pictures 423 Copyright