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Journey Through Genius: Great Theorems of Mathematics

Journey Through Genius: Great Theorems of Mathematics

Hardback Wiley Science Editions

By (author) William Dunham

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  • Publisher: John Wiley & Sons Inc
  • Format: Hardback | 320 pages
  • Dimensions: 155mm x 229mm x 18mm | 635g
  • Publication date: 18 April 1990
  • Publication City/Country: New York
  • ISBN 10: 0471500305
  • ISBN 13: 9780471500308
  • Illustrations note: illustrations; portraits
  • Sales rank: 325,801

Product description

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

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Author information

About the author WILLIAM DUNHAM is a Phi Beta Kappa graduate of the University of Pittsburgh. After receiving his PhD from the Ohio State University in 1974, he joined the mathematics faculty at Hanover College in Indiana. He has directed a summer seminar funded by the National Endowment for the Humanities on the topic of "The Great Theorems of Mathematics in Historical Context."

Editorial reviews

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)

Back cover copy

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

Flap copy

There is a remarkable permanence about mathematical ideas. Whereas other scientific disciplines regularly discard the old and outmoded, in mathematics new results build upon their predecessors without rendering them obsolete. The astronomical theories and medical practices of the Alexandrian Greeks, works of undisputed genius in their day, have long since become archaic curios. Yet Euclid's proof of the Pythagorean theorem, set forth in 300 B.C., has lost none of its beauty or validity with the passage of time. A theorem, correctly proved within the rigors of logic, is a theorem forever. Journey Through Genius explores some of the most significant and enduring ideas in mathematics: the great theorems, discoveries of beauty and insight that stand today as monuments to the human intellect. Writing with extraordinary clarity, wit, and enthusiasm, Professor William Dunham takes us on a fascinating journey through the intricate reasoning of these masterworks and the often turbulent lives and times of their creators. Along with the essential mathematics, Professor Dunham uniquely captures the humanity of these great mathematicians. You'll meet Archimedes of Syracuse, who pushed mathematics to frontiers that would stand some 1,500 years. Unchallenged as the greatest mathematician of antiquity, Archimedes was the stereotypically "absent minded" mathematician, capable of forgetting to eat or bathe while at work on a problem. From the sixteenth century you'll encounter Gerolamo Cardano, whose mathematical accomplishments provide a fascinating counterpoint to his extraordinary misadventures. In the next century, there appeared the competitive, bickering Bernoulli brothers, who explored the arcane world of infinite series when not engaged in contentious wrangling with one another. And from more modern times you'll read of the paranoid genius of Georg Cantor, who had the ability and courage to make a frontal assault on that most challenging of mathematical ideas--the infinite. Journey Through Genius is a rare combination of the historical, biographical, and mathematical. Readers will find the history engaging and fast-paced, the mathematics presented in careful steps. Indeed, those who keep paper, pencil, and straightedge nearby will find themselves rewarded by a deeper understanding and appreciation of these powerful discoveries. Regardless of one's mathematical facility, all readers will come away from this exhilarating book with a keen sense of the majesty and power, the creativity and genius of these mathematical masterpieces.

Table of contents

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). Afterword. Chapter Notes. References. Index.