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Journey through Genius: The Great Theorems of Mathematics [Paperback]

William Dunham
4.8 out of 5 stars  See all reviews (39 customer reviews)
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Book Description

Aug. 1 1991 014014739X 978-0140147391 Reprint
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.

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In Journey through Genius, author William Dunham strikes an extraordinary balance between the historical and technical. He devotes each chapter to a principal result of mathematics, such as the solution of the cubic series and the divergence of the harmonic series. Not only does this book tell the stories of the people behind the math, but it also includes discussions and rigorous proofs of the relevant mathematical results.


"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

Inside This Book (Learn More)
First Sentence
"Our knowledge of the very early development of mathematics is largely speculative, pieced together from archaeological fragments, architectural remains, and educated guesses." Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews

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Most helpful customer reviews
2 of 2 people found the following review helpful
5.0 out of 5 stars It drove me crazy June 26 2004
This book talks some of the most intriguing of classical math problems, and I can not tell you enough about how much of a pleasure it is to read.
It forces us to put some thought over some of the mathematical results that we take for granted today, such as pythagorean theorum, the infinitude of the prime numbers, etc. I read it in just 2 sittings, and have read it over once again after that.
If you have any inclination towards mathematics and its beauty, you will be a different person after you have read through this highly motivating and pleasurable read.
The only thing I wished the book had more was the number of problems it covered :) I seriously wish that William Dunham sets out to write many more such books covering many many more such mathematical problems in his beautiful style! Wish you all the best, William!
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1 of 2 people found the following review helpful
5.0 out of 5 stars A Mathematical Tour de Force! Jan. 1 2003
Mathematical truths possess a beauty quite unlike any other work known to man, and the ability to appreciate that beauty should not be limited to expert mathematicians. In the preface to his book, Journey Through Genius, William Dunham notes that there are books on the great works of art, literature, and music, but that discussions on the mathematical ``classics'' are scarce. His excellent, thoroughly enjoyable, and articulate book fills that void. Most importantly, the book is written for the layperson, requiring only a familiarity with high school geometry and algebra.
A simple elucidation of the greatest mathematical discoveries would be interesting in its own right, but this book goes far beyond that. It also presents fascinating glimpses into the lives of the mathematicians themselves and the cultures in which they worked. For example, we discover that academic positions during the Renaissance were not guaranteed by tenure, but were rather bolstered by successes in public, intellectual ``duels''. As a result, mathematicians kept their discoveries secret, sometimes revealing them only on their deathbeds. We also learn of the ongoing sibling rivalry between the mathematical brothers Jakob and Johann Bernoulli. And we feel sympathy for Georg Cantor, whose counter-intuitive results were widely criticized, driving him to several bouts of mental illness. What emerges overall is an engrossing patchwork presentation of the history of mathematics and of humanity in general.
The book is divided into 12 chapters, each describing and proving a ``great'' theorem. These theorems have been chosen to represent discoveries spanning both time (with the notable exception of the first through 16th centuries) and a diverse range of mathematical disciplines.
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5.0 out of 5 stars Stunning ! July 17 2004
Absolutely one of the most wonderful books i've ever read !
In a chronological way, through each chapter, the book covers the background and history of the current chapter's genius, his great theorem and other achievements, including detailed proofs.
William Dunham writing style is perfect :)
Amazon's service is really good also, I live in Israel and I recieved the book in less than one week since ordered...
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4.0 out of 5 stars Solid Math Dec 23 2003
Dunham selects several mathematical theorems and discusses their meaning and their proof. The book is arranged chronologically beginning with Hippocrates (Quadrature of the Lune) and follows with Euclid, Archimedes through Newton, Euler up to modern scientists. If the subject was ONLY mathematics he would have succeeded. But I expected more of a historical perspective and review that the merely cursory one presented here. Still, the book was arranged well with many graphs, formulae, pictures and charts.
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5.0 out of 5 stars Sublime beauty Aug. 24 2003
Rarely is it properly appreciated that mathematics is one of the arts, and --- like all the other arts --- has created monuments of surpassing beauty through the centuries. Dunham does a wonderful job in this whirlwind tour of the past two thousand years of mathematics. He presents math as a story of triumph after triumph. Each chapter highlights one "great" theorem, and in every chapter he makes clear the context of the theorem by discussing preceding work, the life of the mathematician who proved the theorem, and the applications it opened up. He is masterful at mentioning tidbits in historical context that will be logically necessary to understand a few chapters further. No advanced knowledge of math is necessary, but I will caution: one must be at least reasonably fluent in both geometry and second year algebra in order to get the most out of this book. The more rusty one's algebra skills are, the more burdensome the proofs will be. For someone comfortable with that level of math, the book is breathtaking in the panoply of intellectual vistas it opens up. For anyone doing any kind of work in any technical field, I simply cannot recommend this book highly enough.
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5.0 out of 5 stars A delicious book and mathematical wonderments July 11 2003
This is sumptuous and beautiful writing. Years ago, I took 4 years of math in college, and had forgotten how lovely and surprising these ideas can be, especially when elegantly explained. Would that I had had a professor then, who could have walked through this history so well.
With regard to the theorems themselves, how is it possible that our scientific ancestors were so clever and insightful? How can we explain the genius of men like Euclid, Newton, and Euler?
This book dazzled me, and I predict the same effect for any readers with even a smattering of math education and a taste for scientific wonderments.
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Most recent customer reviews
5.0 out of 5 stars Wonderful book
I came to this book after reading : Uncle Petros and Goldbach's Conjecture , and Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem. Read more
Published on April 11 2003 by Dani Ashkenazi
5.0 out of 5 stars Very stimulating as history
When were algebraic equations formulated with symbols? When were decimal expansions introduced? These questions are answered in readable form, along with examples of some simple... Read more
Published on Jan. 9 2003 by Professor Joseph L. McCauley
5.0 out of 5 stars Quite a Journey
I don't know too many math authors who have consistently written "five-star" books. I had the pleasure of having Dr. Dunham at Muhlenberg (not Muhlendorf! Read more
Published on Dec 12 2002 by William Stevenson
5.0 out of 5 stars A VERY NICE BOOK
this is a fantastic book ..it has a lot of clever ideas from old 2 modern.
easy 2 understand langauge ,i finished this book in a week .. Read more
Published on Nov. 5 2002 by Ahmed Morsi
5.0 out of 5 stars Another 5 star review for this book
This book is outstanding. It is clear and doable for anybody with an interest and motivation in mathematics. Two things I had to find outside the book: 1. Read more
Published on Sept. 4 2002 by Jeffrey L. Cooper
4.0 out of 5 stars Chapters on each of the great theorem.
Also consider: "Zero: The biography of a dangerous idea" by Charles Seife.
* The subject matter of the two books is not the same.
Published on March 17 2002 by Alok Govil
4.0 out of 5 stars Good look at Math thru history and vice versa
The author does a good job of exploring the history of math by looking at 12 great theorems. He does a fairly good job explaining the math. Read more
Published on March 10 2002 by Ronald Brown
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