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Journey through Genius: The Great Theorems of Mathematics Paperback – Aug 1 1991


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Product Details

  • Paperback: 320 pages
  • Publisher: Penguin Books; Reprint edition (Aug. 1 1991)
  • Language: English
  • ISBN-10: 014014739X
  • ISBN-13: 978-0140147391
  • Product Dimensions: 13.1 x 1.5 x 19.9 cm
  • Shipping Weight: 222 g
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (39 customer reviews)
  • Amazon Bestsellers Rank: #2,668 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description

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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3 of 3 people found the following review helpful By Gaurav Jain on 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 By Michael P. McGarry on 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 By William Stevenson on 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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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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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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