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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
|Publisher:||Penguin Publishing Group|
|Product dimensions:||7.78(w) x 4.98(h) x 0.57(d)|
|Age Range:||18 Years|
About the 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."
Table of Contents
Journey through Genius - William Dunham Preface
Chapter 1. Hippocrates' Quadrature of the Lune (ca. 440 B.C.)
The Appearance of Demonstrative Mathematics
Some Remarks on Quadrature
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
Chapter 3. Euclid and the Infinitude of Primes (ca. 300 B.C.)
The Elements, Books II-VI
Number Theory in Euclid
The Final Books of the Elements
Chapter 4. Archimedes' Determination of Circular Area (ca. 225 B.C.)
The Life of Archimedes
Archimedes' Masterpiece: On the Sphere and the Cylinder
Chapter 5. Heron's Formula for Triangular Area (ca. A.D. 75)
Classical Mathematics after Archimedes
Chapter 6. Cardano and the Solution of the Cubic (1545)
A Horatio Algebra Story
Further Topics on Solving Equations
Chapter 7. A Gem from Isaac Newton (Late 1660s)
Mathematics of the Heroic Century
A Mind Unleashed
Newton's Binomial Theorem
Chapter 8. The Bernoullis and the Harmonic Series (1689)
The Contributions of Leibniz
The Brothers Bernoulli
The Challenge of the Brachistochrone
Chapter 9. The Extraordinary Sums of Leonhard Euler (1734)
The Master of All Mathematical Trades
Chapter 10. A Sampler of Euler's Number Theory (1736)
The Legacy of Fermat
Chapter 11. The Non-Denumerability of the Continuum (1874)
Mathematics of the Nineteenth Century
Cantor and the Challenge of the Infinite
Chapter 12. Cantor and the Transfinite Realm (1891)
The Nature of Infinite Cardinals
What People are Saying About This
"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
Most Helpful Customer Reviews
This book was actually the course material for a 'History of Mathematics' course at a certain University. Needless to say, it was written very well. Instead of sticking directly to chronological order in every chapter there is an epilogue of the modern progress to certain subjects. For instance, on the chapter about the discovery of the circular length of a circle, we get the ancient values for pi. The epilogue helps us to appreciate down to our time the increasing advances made to approximate the constant pi. There is a few 'errors' in this book, that is in quotes since the statements are just outdated. Since the publication of this book, Fermat's Last Theorem has been proved by Andrew Wiles, and pi has been calculated to more decimal places, things such as these. Of course, there are gaps in the history, this is more of a guide to the 'greatest' of all theorems that influenced and changed the way mathematics worked. For instance, I was shocked that E.Galois was not given more than a few paragraphs even though he 'along with Abel' showed fifth-degree polynomials and higher could not be solved algebraically. Thus discovering Group Theory. Moving on to the subject matter: the book promises its readers that only high school math is necessary...which is interesting since the final 2 chapters deal with set theory, which is taught as an upper division course in an undergraduate university. Also, when trigonometry is mentioned, the author states: 'which is beyond the scope of this text.' Which I find contradictory since trigonometry is taught in high school! Otherwise though, I highly recommend this book to anyone, especially math majors so they can see the history of their own study.
'Journey Through Genius' is a collection of proofs that are important in the history of mathematics, along with biographical information on the mathematicians who created these proofs. The major branches of elementary mathematics are well represented: geometry, number theory, algebra. The proofs are all explained well. Many readers will probably leave each proof thinking 'I understand it, but I could never have created it.' The title perfectly captures the essence of the book.
This was one of two textbooks for a Math History class. I kept this one and sold the other one back at the end of the semester. I found this book delightful to read and have reread it long after my course work was done. I found the book very accessible though at times I had to work at understanding some of the proofs.