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Journey through Genius: The Great Theorems of Mathematics |  | Author: William Dunham
Publisher: Penguin (Non-Classics)
List Price: $16.00
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Seller: Booyah Bay
Rating:  74 reviews
Sales Rank: 13769
Media: Paperback
Pages: 320
Number Of Items: 1
Shipping Weight (lbs): 1.1
Dimensions (in): 7.7 x 5 x 0.7
ISBN: 014014739X
Dewey Decimal Number: 510.9
EAN: 9780140147391
ASIN: 014014739X
Publication Date: August 1, 1991
Availability: Usually ships in 1-2 business days
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Amazon.com Review
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.
Product Description
Praise for William Dunhams Journey Through Genius The Great Theorems of Mathematics "Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions and proofs, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments." —Ivars Peterson Author, The Mathematical Tourist Mathematics and Physics Editor, Science News "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 "It is a captivating collection of essays of major mathematical achievements brought to life by the personal and historical anecdotes which the author has skillfully woven into the text. This is a book which should find its place on the bookshelf of anyone interested in science and the scientists who create it." —R. L. Graham, AT&T Bell Laboratories "Come on a time-machine tour through 2,300 years in which Dunham drops in on some of the greatest mathematicians in history. Almost as if we chat over tea and crumpets, we get to know them and their ideas—ideas that ring with eternity and that offer glimpses into the often veiled beauty of mathematics and logic. And all the while we marvel, hoping that the tour will not stop." —Jearl Walker, Physics Department, Cleveland State University Author of The Flying Circus of Physics
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Showing reviews 1-5 of 74
Informative. Inspiring. Intriguing. August 20, 2009
Harshad Patil (Toronto, ON, Canada)
This book is an amazing journey through the centuries of human struggle to enhance the language of mathematics in order to understand the nature. It sheds light on the human story behind evolving of mathematics. There are no dry mathematical theorems. Rather, these theorems and proofs are written in a way that fascinates and inspires the reader. This lucidly written book inspires to study more about the subject and number of polymaths it refers to.
Note on how to read: The book refers to many great human minds, throughout. I had little knowledge about Cicero or Leibniz. So, I usually google and read about them. It is a little digression and slows you down; but you learn much more. Similarly, a theorem or topic of interest, briefly discussed in epilogue of each chapter, can be studied in more detail, as you go along.
 Good on mathematics July 10, 2009
Viktor Blasjo
This is a good book. I shall offer some minor points of criticism, but only because the praise that the book deserves would be too repetitive. First we should note that the originality lies in the mathematics (esp. chs. 7 and 8 are pretty original); the historical narrative is basically just a compilation of the standard anecdotes (often tangentially related at best to the mathematics discussed). My main problem with this book is that Dunham is too uncritical and faithful to the canon: where the canon is silent, so is Dunham, no matter how glaring the omission may be. There is one serious illustration of this: Archimedes on the circle (ch. 4). We read that "Archimedes' bold proposition easily implied Euclid's relatively tame result that the areas of two circles are in the same ratio as the squares upon their diameters" (p. 96). I suggest that "bold" and "tame" are euphemisms for "taught today" and "not taught today" respectively. Durham, being a slave to the current canon, is happy with this test and does not provide any additional evidence or arguments for his claim. This is great shame for anyone who is not willing to salute the reigning flag for the sake of it. Why is Archimedes' result "bold" and "great" enough to warrant inclusion here? How exactly does it go beyond Euclid's "tame" result? It can hardly be "the critical link between circumference and circular area" (p. 90) since "the importance of this ratio had been recognized long before Archimedes" (p. 106). Nor can the answer be found in a link between "one-dimesional constants" (p. 90) such as that of circumference to diameter and "two-dimensional constants" (p. 90) having to do with areas, since Euclid's "tame" result provides precisely that. Archimedes' work on the circle is surely related to his work on the sphere (if only conceptually). The latter is discussed here at some length, though no indication of its relation, if any, to the former is provided. Since the canon in silent on this matter, so is Dunham, even though critical readers will all be asking this question.
The Bible June 29, 2009
Ld Seaver
I can't tell you how often I go back to Journey through Genius. If you love deep math and want an historical perspective of key theorems you can't do better. Keep in mind it's not for everyone - but of those who "get it" you won't be able to put it down. Advanced thinking required (I hope that doesn't sound too elitist!)
Excellent book for people with some mathematical background June 7, 2009
Nona (CA United States)
In the considerably crowded field of popular science/math writing, this book really stands out. William Dunham guides the reader through twelve great topics in mathematical history and actually provides serious (but accessible!) mathematical exposition on those topics. As such, it's probably necessary to have some mathematical background (but no more than what one covers in a typical high school curriculum) to fully appreciate this book, although there is also a fair amount of non-mathematical content as well. Mathematically interested adults and talented middle or high school students are probably the ideal audience for this book.
The actual mathematics in the book is of the highest quality - after all, Dunham selects some of the greatest ideas in all of mathematical history to cover. Fortunately, the exposition is also of superb quality. While there is a lot of real math in the book, Dunham does a great job in guiding the reader from step to step and explaining the general strategy behind the approach to each mathematical problem. Actually, even if you don't have a great mathematical background, a lot of this book can still be read profitably, and may actually inspire you to brush up on math or talk to people more experienced in mathematics.
This book isn't like most popular books in science or mathematics, in that it contains actual mathematical arguments. Since the author is trying to make this book accessible to a wide audience, certain great topics in mathematical history need to be omitted since they would require too many mathematical pre-requisites. For example, do not expect anything about 20th century mathematics (which is by and large far too technical for a book like this), despite the fact that many great theorems have been proven in the 20th century (and the first decade of the 21st!). Nevertheless, the math in this book is truly of the first-order and the author does a superb job of communicating it to his audience. If you have any interest in seeing some of the actual great ideas from mathematics, you can't go wrong with this book.
Fantastic!!! April 23, 2009
Brad Young
Dunham squared the circle with this book.
The math is both deep and clear, more than many other historical overview books, but at the same time is a wonderful read, with personalities (of the mathematicians and also of Dunham himself) jumping from the pages.
Showing reviews 1-5 of 74
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