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Journey Through Genius: The Great Theorems of Mathematics

William Dunham
Publisher: 
Penguin Books
Publication Date: 
1990
Number of Pages: 
320
Format: 
Paperback
Price: 
14.95
ISBN: 
014014739X
Category: 
Textbook
BLL Rating: 

The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

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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

akirak's picture

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:

  • The font size is too small and it is particularly difficult to read some of the fractions.
  • I found two typographical errors: On page 170 the fraction should be 5/128 and not 5/12; on page 238 the factorization should be over 2a and not just a.
  • On page 235 the first Fermat prime 3 is missing.

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.

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