Praise for William Dunham s Journey Through Genius The Great Theorems of Mathematics "Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions and proofs, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments." Ivars Peterson Author, The Mathematical Tourist Mathematics and Physics Editor, Science News
"It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash." Isaac Asimov
"It is a captivating collection of essays of major mathematical achievements brought to life by the personal and historical anecdotes which the author has skillfully woven into the text. This is a book which should find its place on the bookshelf of anyone interested in science and the scientists who create it." R. L. Graham, AT&T Bell Laboratories
"Come on a time-machine tour through 2,300 years in which Dunham drops in on some of the greatest mathematicians in history. Almost as if we chat over tea and crumpets, we get to know them and their ideas ideas that ring with eternity and that offer glimpses into the often veiled beauty of mathematics and logic. And all the while we marvel, hoping that the tour will not stop." Jearl Walker, Physics Department, Cleveland State University Author of The Flying Circus of Physics
An eloquent exposition of what Dunham (Mathematics/Hanover) calls "the Mona Lisas or Hamlets" of mathematics - 12 classic theorems ranging from Hippocrates' quadrature of the lunes (c. 440 B.C.) and Euclid's proof of the Pythagorean theorem (c. 300 B.C.) to Georg Cantor's theorem of the non-denumerability of the continuum (1874) and his crowning achievement, Cantor's Theorem (1891), which, as Dunham puts it, "pushed mathematics into unexplored territory where it began to merge into the realms of philosophy and metaphysics." Dunham brackets his explanation of each theorem with an accessible discussion of the state of mathematics - and of the world - prior to the theorem, and relevant biographical information about the mathematicians. The theorem explanations themselves, for all their elegance, require a current familiarity with high-school-level math; while not for many of us, then, Dunham's fine tour through the best of mathematics will prove a treat for those who know the difference between a finite cardinal and an infinite one. (Kirkus Reviews)
Hippocrates' Quadrature of the Lune (ca. 440 B.C.).
Euclid's Proof of the Pythagorean Theorem (ca. 300 B.C.).
Euclid and the Infinitude of Primes (ca. 300 B.C.).
Archimedes' Determination of Circular Area (ca. 225 B.C.).
Heron's Formula for Triangular Area (ca. A.D. 75).
Cardano and the Solution of the Cubic (1545).
A Gem from Isaac Newton (Late 1660s).
The Bernoullis and the Harmonic Series (1689).
The Extraordinary Sums of Leonhard Euler (1734).
A Sampler of Euler's Number Theory (1736).
The Non-Denumerability of the Continuum (1874).
Cantor and the Transfinite Realm (1891).