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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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From Amazon

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.

Review

"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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Most helpful customer reviews
3 of 3 people found the following review helpful
5.0 out of 5 stars It drove me crazy June 26 2004
Format:Paperback
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 1 people found the following review helpful
5.0 out of 5 stars Sublime beauty Aug. 24 2003
Format:Paperback
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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1 of 1 people found the following review helpful
5.0 out of 5 stars Quite a Journey Dec 12 2002
Format:Paperback
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!) College for a class on Landmarks of Modern Mathematics. With Dunham's sharp lectures, I hardly needed the book, but with his brilliant book, I hardly needed the lectures. The key, however, is that I wanted both, and couldn't get enough of either. Graduation and reaching the back cover does that...
Others have already described what's in the book, but what I must stress is that everything - every single thing - in the book is written in a clear and captivating fashion. You feel like you're sitting right there with the mathematcian under review, solving the problems for the first time with their hints. You wonder if Dunham has a time machine hidden somewhere. What this book adds to the experience is that you get a hint not just about the mathemacians' genius, but also about the personalities of the mathematicians. For example, Cardano is probably one of the humorously psychotic mathematcians that lived.
This book is good for anybody who has had half of a high school education all the way up to people who think in numbers. This isn't a "skim over the math" book like those of many of Dunham's contemporaries - and you wouldn't want to do that anyway. Buy it for yourself and then give it to a budding math student - or heck, buy two!
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5.0 out of 5 stars Another 5 star review for this book Sept. 4 2002
Format:Paperback
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.) The proof by contradiction and infinite descent by Hipparchus that the sqrt(2) is irrational can be found in Newman's "The World of Mathematics" and in various places on the internet; and 2.) on p. 226 Dunham states that a certain formula was known to Euler to be an integer when p was prime. It took me awhile but the terms of this formula are p-choose-k (the combinations of p things chosen k at a time) divided by p ... with a little manipulation one can see that for 1<=k<p and for p prime and with an understanding of the Fundamental Theorem of Arithmetic (basically every integer has a unique prime factorization), that every term is an integer of the form p-choose-k where p has been factored out (and p is prime).
Everything else is there to take a ride from 300BC to 1900AD. Keep paper and pencil handy! And enjoy!
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5.0 out of 5 stars Brings Mathematics To Life! Dec 26 2001
Format:Paperback
William Dunham has brought life to a subject that almost everyone considers dull, boring and dead. Dunham investigates and explains, in easy-to-understand language and simple algebra, some of the most famous theorems of mathematics. But what sets this book apart is his descriptions of the mathemeticians themselves, and their lives. It becomes easier to understand their thinking process, and thus to understand their theorems.
I am a layman with a computer science degree, and a layman's understanding of mathematics, so I am no expert! But I loved this book.
I found Dunham's description of Archimedes' life and his reasoning for finding the area of a circle and volume of a cylinder to be (almost!) riveting.
Dunham's decription of Cantor and his reasoning regarding the cardinality of infinite sets was fascinating to me. But most of all, I loved his chapter on Leonhard Euler. Having in high school been fascinated by Euler's derivation of e^(i*PI) = -1, I was even more amazed at the scope of this man's genius, and Dunham's description of his life.
The chapter on Isaac Newton is an especially good one as well.
Dunham smartly weaves these important theorems of mathematics into the history of mathematics, making this book even more understandable, and, dare I say it, actually entertaining!
This book is a gem, and for anyone interested in mathematics, it is not to be missed.
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Most recent customer reviews
5.0 out of 5 stars Stunning !
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... Read more
Published on July 17 2004 by Guy Zana
4.0 out of 5 stars Solid Math
Dunham selects several mathematical theorems and discusses their meaning and their proof. The book is arranged chronologically beginning with Hippocrates (Quadrature of the Lune)... Read more
Published on Dec 22 2003 by Avid Reader
5.0 out of 5 stars A delicious book and mathematical wonderments
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... Read more
Published on July 11 2003 by Paul J. Papanek
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 A Mathematical Tour de Force!
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. Read more
Published on Jan. 1 2003 by Allan Heydon
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
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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