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“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*

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

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