Journey through genius: the great theorems of mathematicsPraise 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 timemachine 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 
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8 pages matching Cantor's theorem in this book
Page 296
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User Review  datrappert  LibraryThingThis is a brilliant intellectual journey through some of the great theorems of mathematics. The author writes very clearly and evocativelythen, there is the math. I am not a mathematician, and I ... Read full review
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User Review  nmarun  LibraryThingIt felt great reading this book because it took me back to my school days where we learned these concepts/theorems along with their proofs. The book brings history and mathematics together which was ... Read full review
Contents
Hippocrates Quadrature of the Lune ca 440 b c  1 
Euclids Proof of the Pythagorean Theorem ca 300 b c  27 
Euclid and the Infinitude of Primes ca 300 b c  61 
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appeared Archimedes argument binomial Book calculus Cantor's theorem Cardano Carl Friedrich Gauss century Chapter circle circle's circumference classical Common Notion compass and straightedge congruent construct continuum hypothesis contradiction course cube decimal place definition denumerable depressed cubic diameter discovery divides evenly divisor Elements Epilogue equal equation Euclid Euclidean Eudoxus excerpt fact factor Fauvel and Gray Fermat finite formula Gauss genius geometry Georg Cantor Greek harmonic series Heath Heron Heron's formula Hippocrates infinite series inscribed instance irrational Isaac Newton Jakob Johann Bernoulli Leibniz length Leonhard Euler likewise logical lune matching mathe mathematicians mathematics modern natural numbers nonEuclidean noted number theory onetoone correspondence parallel postulate perfect numbers plane polynomial problem proof Proposition proved Pythagorean theorem quadrature radius rational real numbers regular polygons result right angles right triangle segment semicircle sides simple solid solution solving sphere square straight line subset Tartaglia tion transfinite cardinal triangle's whole numbers