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Unknown Quantity: A Real and Imaginary History of Algebra by John Derbyshire  (26)

Riemann's Zeta Function by Harold M. Edwards  (16)  $10.85

An Imaginary Tale: The Story of "i" [the square root of minus one] by Paul J. Nahin  (42)  $11.53

e: The Story of a Number by Eli Maor  (52)  $13.57

Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills by Paul J. Nahin  (13)  $19.77

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Amazon.com
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.

In 2000, the Clay Mathematics Institute offered a one-million-dollar prize to anyone who could prove the Riemann Hypothesis, but luminaries like David Hilbert, G.H. Hardy, Alan Turing, André Weil, and Freeman Dyson have all tried before. Will the Riemann Hypothesis ever be proved? "One day we shall know," writes Derbyshire, and he makes the effort seem very worthwhile. --Therese Littleton

From Booklist
Bernhard Riemann would make any list of the greatest mathematicians ever. In 1859, he proposed a formula to count prime numbers that has defied all attempts to prove it true. This new book tackles the Riemann hypothesis. Partly a biography of Riemann, Derbyshire's work presents more technical details about the hypothesis and will probably attract math recreationists. It requires, however, only a college-prep level of knowledge because of its crystalline explanations. Derbyshire treats the hypothesis historically, tracking increments of progress with sketches of well-known people, such as David Hilbert and Alan Turing, who have been stymied by it. Carrying a million-dollar bounty, the hypothesis is the most famous unsolved problem in math today, and interest in it will be both sated and stoked by these able authors. Gilbert Taylor
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First Sentence:
In August 1859, Bernhard Riemann was made a corresponding member of the Berlin Academy, a great honor for a young mathematician (he was 32). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
argument ant, total overhang, prime counting function, argument plane, critical strip, computational thread, squaring function, zeta function, value ant, prime number theorem, lead diagonal, complex function theory, card length, critical line, value plane, positive whole numbers, analytic number theory, log function Key Phrases - Capitalized Phrases (CAPs): (learn more)
Golden Key, Power Rule, Bernhard Riemann, Vallée Poussin, Andrew Odlyzko, Jacques Hadamard, Fermat's Last Theorem, Leonhard Euler, David Hilbert, Hugh Montgomery, Edmund Landau, World War, Alain Connes, Andrew Wiles, Harold Edwards, Montgomery-Odlyzko Law, United Sta