A History of Mathematics, Second Edition (Perfect Paperback)

by Carl B. Boyer (Author), Uta C. Merzbach (Author), Isaac Asimov (Foreword) "Mathematicians of the twentieth century carry on a highly sophisticated intellectual activity which is not easily defined..." (more)
Key Phrases: solid analytic geometry, harmonic triangle, capable mathematician, Royal Society, École Polytechnique, Euclid's Elements (more...)

Editorial Reviews

Amazon.com Review
What do you mean there's no chapter 0? Whether or not you think that's a deficit, A History of Mathematics more than makes up for it with its depth and engaging analysis of the development of the "flawless science." Historian Carl B. Boyer designed it as a practical textbook for communicating math's complex timelines to interested college students in 1968; Uta C. Merzbach has gently revised it to bring it in line with current thought. Much of the early chapters are untouched, with new 19th- and 20th-century chapters covering Boyer's omissions and new and revised references guiding the reader to additional resources.

From the origins of numbering to the future of computing, the authors strive for comprehensive examination and clear, simple explanations. Some of the math will daunt those who have never taken college-level courses (or have forgotten what they learned), but some of the more elaborate technical material can be skipped if needed. Especially helpful is the extensive timeline-appendix that proceeds from the beginning of time to the late 20th century. Whether you're using it to gain a better understanding of mathematics or to broaden your awareness of the historical record, A History of Mathematics will help you make sense of the wide world of numbers. --Rob Lightner

Product Description
"Boyer and Merzbach distill thousands of years of mathematics into this fascinating chronicle. From the Greeks to Godel, the mathematics is brilliant; the cast of characters is distinguished; the ebb and flow of ideas is everywhere evident. And, while tracing the development of European mathematics, the authors do not overlook the contributions of Chinese, Indian, and Arabic civilizations. Without doubt, this is—and will long remain—a classic one-volume history of mathematics and mathematicians who create it." —William Dunham Author, Journey Through Genius, The Great Theorems of Mathematics "When we read a book like A History of Mathematics, we get the picture of a mounting structure, ever taller and broader and more beautiful and magnificent—and with a foundation, moreover, that is as untainted and as functional now as it was when Thales worked out the first geometrical theorems nearly 26 centuries ago." —From the Foreword by Isaac Asimov "One of the most useful and comprehensive general introductions to the subject." —J. W. Dauben The City University of New York "Both readable and scholarly, this book can serve as a fine introduction to the topic and also a reference book." —J. David Bolter University of North Carolina Author of Turing’s Man Revised to make it more accessible to a general audience, A History of Mathematics paints a vivid picture of humankind’s relationship with numbers. Updated and expanded, it now offers broadened coverage of twentieth century advances in probability and computers, and updated references to further reading. A feature that will be of interest to every reader is an appendix containing an extensive chronological table of mathematical and general historical developments.

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Product Details

• Perfect Paperback: 736 pages
• Publisher: Wiley; 2 edition (March 6, 1991)
• Language: English
• ISBN-10: 0471543977
• ISBN-13: 978-0471543978
• Product Dimensions: 9.2 x 6.1 x 1.8 inches
• Shipping Weight: 2.3 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars See all reviews (12 customer reviews)
• Amazon.com Sales Rank: #172,301 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

84 of 85 people found the following review helpful:

4.0 out of 5 stars Good book, very good book if you already now the basics, September 5, 1999

By	Juergen Kahrs (Bremen, Germany) - See all my reviews (REAL NAME)

The first edition of this book was published in 1968. In the preface to the first edition, Carl Boyer mentions some other books about the history of mathematics and why he thinks it is necessary to write just another one. The most important reason for him is strict adherence to chronological arrangement and a stronger emphasis on historical elements. From my point of view, this aim is (at once) the strength and the weakness of the book. In this single volume of more than 700 pages, the book supplies you with so much detailed historical facts and numbers that it really deserves to be called "A History Of Mathematics". But soon after starting to read the book, I lost interest in reading it. Why was it so boring to read facts and even more facts ? The wealth of material alone does not answer the questions about the history of mathematical ideas.

But Boyer also supplied the solution to this problem. Among the books he recommends in the preface of the first edition is a much shorter book by Howard Eves (Foundations and Fundamental Concepts Of Mathematics, ISBN 0-486-69609-X). Eves' book emphasizes the historical development of the most important ideas and methods through more than 2000 years. After reading Eves' book, you can return to Boyer's book and you will appreciate the wealth of details much more because your mind is equipped with a guideline.

There is one other fact worth mentioning about the book. The avaiable second edition has been revised by Uta C. Merzbach and Isaac Asimov has written a foreword. Merzbach left the first 22 chapter virtually unchanged. The chapters about more recent developments have been expanded. In revising the references and the bibliography, Merzbach replaced Boyer's references (often non-English sources) by works in English. That is good for the English-speaking readers, but is it also good for people who are interested in the history of mathematics (which mostly took place in Europe: Greece, Italy, France, Germany) ? The second major change Merzbach made was dropping the exercises. For a history book, this was probably the right decision. But in Eves' book (focused on the development of ideas), the exercises are a valuable means of deepening the understanding of the era and its problems.

To whom can I recommend this book ? I recommend this book to the initiated readers. If you have never heard about the axiomatic method, you should probably first read Eves' book and then return to this one.

31 of 32 people found the following review helpful:

4.0 out of 5 stars Mathematics for Mathematicians, January 27, 1998

By A Customer

OK, I admit that it took me about five years to finish reading this book. But it isn't because it's dry and boring but because I spent most of that time trying to solve the problems that were the obsession of mathematicians throughout the ages without reading ahead. I started just after acquiring my degree in Mathematics and it showed me just how little of the vast field I had learned. The book starts from the earliest evidence we have of mathematics and how it pre-dates writing and traverses the development of mathematical thought throughout the ages to the present. From developments of notation to deep mysteries such as why mathematics is doomed to leave us with questions we cannot answer. One of the nice touches of the book is that it recognizes that the development of math occurred in places other than Europe and that men were not the only ones who discovered its mysteries. Make no mistake, however: If you hate math, you aren't going to like this book. While it is, indeed, a historical account of the development of mathematics, it is still a book about mathematics. You will need a decent understanding of how math works to truly appreciate what is laid out.

71 of 82 people found the following review helpful:

3.0 out of 5 stars Not for the serious student of history of mathematics, October 8, 2003

By	Chan-Ho Suh (Davis, CA USA) - See all my reviews (REAL NAME)

Boyer can write pretty well. His tendency to wax on about the virtues of the people he writes about can get annoying, but overall this probably works to make a more engaging style. This kind of writing style is entirely appropriate for a textbook designed to draw readers into the world of mathematics, but is prone to wide, sweeping generalizations and ill-supported assumptions and occasionally, factually incorrect statements.

The reader who is serious about studying the development of mathematics will learn something from this book, but there are better places to learn it. Boyer, as indicated above, seems intent on "cleaning up" history to fit the nice picture he has of it. Unfortunately, merely reciting well-known mathematical legends does more harm than good; it obscures the real process of discovery, and the way mathematics has, and still does, develop.

There are errors in the book that indicate Boyer did not do his research. To keep this review short, I'll name one: Boyer credits Poincare with the Poincare disc model of hyperbolic geometry. Anyone that has actually looked at Riemann's very important 1854 lecture (one of the most important documents of 19th century mathematics) will realize this model is due to Riemann! Since Boyer spends quite a bit of time on Riemann, this is rather puzzling.

Boyer also relies on E.T. Bell for some biographical information. No serious historian of mathematics would (or should) reference Bell for biographies of mathematicians. Bell's caricatures are entertaining, but do a disservice to the subject.

This book is only recommended for those who want to get a vague idea of the history of mathematics, but do not particularly care about the details being correct. For that purpose, Boyer does a better job than most.