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The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities 1st Edition

46 customer reviews
ISBN-13: 978-0471176619
ISBN-10: 0471176613
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Editorial Reviews

Amazon.com Review

The Mathematical Universe is a solid collection of short essays, with each addressing a particular mathematical topic. Titles range from "Isoperimetric Problem" to "Where Are the Women?" Author Dunham manages to maintain a conversational tone while referencing diagrams, equations, and rigorous arguments throughout the book.

From Library Journal

Like John Allen Paulos's Beyond Numeracy (LJ 4/1/91), this is an A-to-Z collection of mathematical essays. The advantage of this format is that it lets the author hit the highlights in essays that can be read independently. This collection is less cantankerous than Paulos's, and it is also somewhat more focused and mathematically challenging, though still written for a popular audience. Dunham (Journey Through Genius: The Great Theorems of Mathematics, Wiley, 1990) is winner of the 1993 George Polya Award for excellence in math writing, an honor he richly deserves. He is fascinated by the nature of mathematical genius, and the theme of these essays is the personality and eccentricities of mathematicians and the brilliance of their discoveries. For sophisticated readers who don't mind equations (including algebra, geometry, and calculus), this is a rewarding and entertaining look at the history of mathematics.
Amy Brunvand, Fort Lewis Coll. Lib., Durango, Col.
Copyright 1994 Reed Business Information, Inc. --This text refers to the Hardcover edition.
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Product Details

  • Paperback: 320 pages
  • Publisher: Wiley; 1 edition (February 18, 1997)
  • Language: English
  • ISBN-10: 0471176613
  • ISBN-13: 978-0471176619
  • Product Dimensions: 6.2 x 0.8 x 9.3 inches
  • Shipping Weight: 13.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (46 customer reviews)
  • Amazon Best Sellers Rank: #568,595 in Books (See Top 100 in Books)

More About the Author

William Dunham, Koehler Professor of Mathematics at Muhlenberg College, is the author of "Journey Through Genius: The Great Theorems of Mathematics"; "The Mathematical Universe"; and "Euler: The Master of Us All". He has received the Mathematical Association of America's George Polya, Trevor Evans, and Lester R. Ford awards, as well as its Beckenbach Prize for expository writing.

Customer Reviews

Most Helpful Customer Reviews

55 of 55 people found the following review helpful By Timothy Haugh VINE VOICE on November 11, 2000
Format: Paperback
I first read this book a number of years ago and recently read it again. I still think it is a magnificent overview of basic mathematics. In fact, it is one of the best overviews of basic mathematics that I have ever read. Dunham covers a wide range of topics and he does so in a very readable and understandable manner without giving up reasonable mathematical rigor. Someone with elementary algebra and geometry can follow all of Dunham's arguments and enjoy.
Of course, it is impossible to cover the entire range of mathematics in a book such as this but Dunham has chosen well. He sticks mainly to the fundementals of the major fields. In addition, his book reminds us that people with personalities have developed mathematics and that it's not a field created merely to strike fear into the hearts of schoolkids (and adults).
This book will always hold a special place for me: it was the catalyst for an epiphany. I had been teaching high school geometry for a few years when this book came out and I was very good at teaching the modern methods of proof and problem-solving. On the other hand, I didn't really like teaching constructions, because, though I could do them quite well, I didn't truly understand their place and function in geometry and its development. When I first read chapter "G" of this book ("Greek Geometry"), however, it was like a thousand puzzle pieces fell into place and I knew more than how to do constructions, I understood them and was able to teach them more effectively.
If you have any interest in mathematics at all, I recommend this book. It will not disappoint.
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39 of 39 people found the following review helpful By Allan Heydon on January 5, 2003
Format: Paperback
In this follow-on to his excellent "Journey Through Genius", William Dunham once again breathes life into a variety of mathematical topics. Whereas "Journey" was arranged around 12 great mathematical theorems, this book is arranged around the 26 letters of the alphabet. Some chapters cover the work of individuals (e.g., "Euler", "Knighted Newton", "Lost Leibniz", and "Russell's Paradox"), while others describe important mathematical results (e.g., "Isoperimetric Problem", "Spherical Surface", and "Trisection"). Still others, such as "Mathematical Personality" and "Where are the Women?", address social aspects of the field.
As in the previous book, Dunham's descriptions are entertaining and enlightening. The main difference is that this book has broader coverage. As a result, it tends to omit more of the proofs, which I found disappointing, but perhaps that will make it of interest to a wider audience. For people with a deeper interest in mathematics, I recommend you read either "Journey Through Genius" or "Euler: The Master of Us All", another Dunham masterpiece that includes detailed proofs throughout.
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21 of 21 people found the following review helpful By A Customer on August 5, 2000
Format: Paperback
I have now read Dunhams 'Journey through Genius', 'Euler, the master of us all' and 'The Mathematical Universe'. These are three great books on Mathematics and choosing can become difficult. My personal favourite is 'Journey through Genius'.If you are mainly interested in magnificent proofs (real gems)with a historical account, then I would recommend 'Journey through Genius', for lots of nice eulerian proofs, then I recommend 'Euler, the master of us all' and if you want more a overview with some proofs and less depth, then buy 'The mathematical Universe'.
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31 of 36 people found the following review helpful By Winfried Corduan on February 7, 2007
Format: Paperback Verified Purchase
I really enjoy this book, and I keep consulting it. But I really don't know whether what I'm learning from it is correct or not. Here's the problem: The two entries with which I have the most familiarity are just plain wrong.

The entry on the "Russell Paradox" reads like a hagiography of Bertrand Russell. It makes it appear that Russell ceased working on the Principia Mathematica because he could not find a solution to his paradox--whether a set, all of whose members are not members of themselves, contains itself. According to Dunham, his inability to find a satisfactory solution spelled the end of his quest for the development of a logical foundation for mathematics, which he communicated to Frege, who gave up on his attempts as well. This is pure fiction. The entire Principia Mathematica is based on Russell's theory of ramified types (the stipulation that a set cannot be a member of itself), which he confidently asserted as being the solution to the paradox throughout the work. What put an end to Russell and Whitehead's project, as well as Frege's, was Goedel's incompleteness theorem, totally ignored by Dunham.

Dunham's treatment of Venn diagrams is even worse because it is deprecating of John Venn and his work--and totally wrong. Dunham states that the diagrams that are named after him were Venn's only contribution to mathematics and then makes disparaging remarks about them, particularly that they lacked any originality. Here's the reality: John Venn was an extremely competent mathematician/logician whose many contributions included the furtherance of George Boole's innovations.
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