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    Journey through Genius

    The Great Theorems of Mathematics

    Author William Dunham
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    Paperback
    $19.00 US
    Penguin Adult HC/TR | Penguin Books
    On sale Aug 01, 1991 | 320 Pages | 9780140147391
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    Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve.

    Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    “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
    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
    Index
    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." View titles by William Dunham
    "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 Tourist

    About

    Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve.

    Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    “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

    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
    Index

    Author

    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." View titles by William Dunham

    Praise

    "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 Tourist

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