Derbyshire John. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

Washington, D.C.: Joseph Henry Press, 2003. — 422 p.Bernhard Riemann was an underdog of sorts, a malnourished son of a parson who grew up to be the author of one of mathematics' greatest problems. In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem: proof of the conjecture, "All non-trivial zeros of the zeta function have real part one-half." Though the statement itself passes as nonsense to anyone but a mathematician, Derbyshire walks readers through the decades of reasoning that led to the Riemann Hypothesis in such a way as to clear it up perfectly. Riemann himself never proved the statement, and it remains unsolved to this day. Prime Obsession offers alternating chapters of step-by-step math and a history of 19th-century European intellectual life, letting readers take a breather between chunks of well-written information. Derbyshire's style is accessible but not dumbed-down, thorough but not heavy-handed. This is among the best popular treatments of an obscure mathematical idea, inviting readers to explore the theory without insisting on page after page of formulae.Prologue
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
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 Möbius 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
Epilogue
Notes