Journey Through Genius
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Journey Through Genius : The Great Theorems of Mathematics

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Description

Explores the "masterpieces" of mathematics, seventeen landmarks spanning 2,300 years and representing ten mathematicians. Each of these landmarks, to some degree, changed the way the world was perceived. Each theorem is presented with a description of the state of mathematics at the time, the development of the theorem, a biographical sketch of the mathematician and an outline of the proof with explanation.show more

Product details

  • Paperback | 320 pages
  • 126 x 194 x 12mm | 222.26g
  • Penguin Books Ltd
  • London, United Kingdom
  • English
  • Reprint
  • 014014739X
  • 9780140147391
  • 36,354

Review quote

"An inspired piece of intellectual history."-- Los Angeles Times"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"Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments."--Ivars Peterson, author of The Mathematical Touristshow more

Back cover copy

A rare combination of the historical, biographical, and mathematicalgenius, this book is a fascinating introduction to a neglected field of human creativity. Dunham places mathematical theorem, along with masterpieces of art, music, and literature and gives them the attention they deserve.show more

About William Dunham

William Dunham is a Phi Beta Kappa graduate of the University of Pittsburgh. After receiving his Ph.D. 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."show more

Review Text

"An inspired piece of intellectual history."- Los Angeles Times "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 "Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments."-Ivars Peterson, author of The Mathematical Touristshow more

Table of contents

Journey through Genius - William Dunham Preface Acknowledgments Chapter 1. Hippocrates' Quadrature of the Lune (ca. 440 B.C.) The Appearance of Demonstrative Mathematics Some Remarks on Quadrature Great Theorem Epilogue Chapter 2. Euclid's Proof of the Pythagorean Theorem (ca. 300 B.C.) The Elements of Euclid Book I: Preliminaries Book I: The Early Propositions Book I: Parallelism and Related Topics Great Theorem Epilogue Chapter 3. Euclid and the Infinitude of Primes (ca. 300 B.C.) The Elements, Books II-VI Number Theory in Euclid Great Theorem The Final Books of the Elements Epilogue Chapter 4. Archimedes' Determination of Circular Area (ca. 225 B.C.) The Life of Archimedes Great Theorem Archimedes' Masterpiece: On the Sphere and the Cylinder Epilogue Chapter 5. Heron's Formula for Triangular Area (ca. A.D. 75) Classical Mathematics after Archimedes Great Theorem Epilogue Chapter 6. Cardano and the Solution of the Cubic (1545) A Horatio Algebra Story Great Theorem Further Topics on Solving Equations Epilogue Chapter 7. A Gem from Isaac Newton (Late 1660s) Mathematics of the Heroic Century A Mind Unleashed Newton's Binomial Theorem Great Theorem Epilogue Chapter 8. The Bernoullis and the Harmonic Series (1689) The Contributions of Leibniz The Brothers Bernoulli Great Theorem The Challenge of the Brachistochrone Epilogue Chapter 9. The Extraordinary Sums of Leonhard Euler (1734) The Master of All Mathematical Trades Great Theorem Epilogue Chapter 10. A Sampler of Euler's Number Theory (1736) The Legacy of Fermat Great Theorem Epilogue Chapter 11. The Non-Denumerability of the Continuum (1874) Mathematics of the Nineteenth Century Cantor and the Challenge of the Infinite Great Theorem Epilogue Chapter 12. Cantor and the Transfinite Realm (1891) The Nature of Infinite Cardinals Great Theorem Epilogue Afterword Chapter Notes References Indexshow more

Rating details

2,066 ratings
4.17 out of 5 stars
5 45% (940)
4 34% (700)
3 15% (312)
2 4% (78)
1 2% (36)
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