Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
- A Plume Book 2003
- xv, 422 pages : illustrations, portraits ; 21 cm
Part I. The prime number theorem. Card trick -- The soil, the crop -- The prime number theorem -- On the shoulders of giants -- Riemann's zeta function -- The great fusion -- The golden key, and an improved prime number theorem -- Not altogether unworthy -- Domain stretching -- A proof and a turning point. Part II. The Riemann hypothesis. Nine Zulu queens ruled China -- Hilbert's eighth problem -- The argument ant and the value ant -- In the grip of an obsession -- Big oh and Mobius Mu -- Climbing the critical line -- A little algebra -- Number theory meets quantum mechanics -- Turning the golden key -- The Riemann operator and other approaches -- The error term -- Either it's true, or else it isn't.
In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled "On the Number of Prime Numbers Less Than a Given Quantity." Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it. 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.