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

## Comments

## Kuldeep Singh

This book gives a thorough treatment of the history of some important mathematical results. There are a number of interesting mathematical examples set in an historical context which makes the book very joyful to read. The author has hit the right balance between the mathematics (such as proofs of theorems) and the history behind each theorem. It is good to see the author does not shy away from producing proofs of results which many popular writers tend to eschew so that they can increase their sales. The result can be challenging at times for the reader, but these parts can be skipped without losing the flow. Dunham has a fantastic writing style which keeps the reader hooked and intrigued.

Another great asset of the book is that it is portable and reasonably cheap at around £10. I managed to read most of it in Starbucks, with pen and paper of course. However I have following reservations:

A less serious issue is that once the author has covered a particular concept he expects the reader to have fully digested it. Dunham has tackled this by signposting his earlier results, but I think it would have been more readable for the layman to see the statement of the result again.

This is a book for anybody interested in history of mathematics or mathematics in general. You do not need to be a mathematician to appreciate this book. Overall I would say this is an excellent book and would recommend anybody interested in mathematics to purchase this.