Customer Reviews

A History of Mathematics, Second Edition

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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.

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.

Hey I read this book loved it, and everyone should read it! Hey I am no brain, I do not belong to Mensa, nor am I endowed with any superior intelect, I am an average guy, Just a B student, who fell in love with this book. Anybody if they really want can understand this book and really appreciate what math is. Mathmatics before this book was just a bunch of numbers on a page any countless formulas to memorize, however this book changed me, I see math a whole different way now. Studying the history of mathmatics is like studying the history of the world. It is a shame this information is never taught in elementry school, it would make kids a lot more interested in math and actually be able to see what the numbers mean. After reading this book a door has been opened. I now am more curious about mathmatics and well everything! I understand where those numbers came from, Pie no longer is something I eat or some funy thing in a formula to find the area of a circle, it actually means something to now.

When I was a high school student, I loved math, but hated math classes, with their tedious emphasis on going over things until even the most mathematically ungifted either got the stuff (or gave up!) the repetitive teaching necessary to inculcate it into the densest heads, and the problem solving that went on long after I had "got it."

Would that I'd then had this book. Boyer has written a great introductory work to both the history of math and math itself, which you can read at your own pace, study until you get it and then move on, with lots of references if you for some reason want to understand something even better. By grouping the chapters around eras of mathematicians, and various mathematicians, he makes the history of math approachable even to those without degrees in mathematics.

This is not necessarily THE book you'd want to read if you're working on a masters or PhD in math, but the sort of book you'd really love to read as a bright high school student or undergraduate student. All in all a great book, but, as other reviewers have written, not exactly the Encyclopaedia Britanica, but then, how many people read the Britanica for pleasure?

I picked up this and Burton's similarly named book, and I just wanted to make a few comments and comparisons of the two.

First off, both are excellent reads, and although they cover the same subject they approach it in two different manners. Boyer's text takes the style of a history book to approach the topic. It often focuses on the people and on the time period, commenting on political/cultural going-on. Its an enjoyable book to read, almost in the sense of reading a novel. Usually the mathematics is brought up in the text, but most of the proofs and derivations are often glossed over. Possible many of those mathematical details were in the questions that are no longer at the end of the chapters. But I found missing those details to be somewhat frustrating.

Conversely Burton takes the approach of a mathematics textbook that follows the story line of history. Its filled with proofs and examples, but isn't quite as rich in historical content. Each chapter ends with numerous "homework" problems, often times relating to specific solutions to a problem found by different mathematicians.

Both are excellent books, but depending on your personal taste and interests you may prefer one approach over the other. If you are looking to sit down and work through historical mathematical problems, Burton is probably right for you. If you want to cozy up and imagine what life and thought was like throughout different times in civilization, Boyer is probably your answer.

Hope this is helpful.

An interesting exposition of the history of mathematics up to the mid-20th century, but the author's attitude is somewhat irritating. I would describe him somewhat of a "purist fundamentalist". His denigration of the contributions of applied mathematicians shows throughout the book. His best praise for someone is "so and so did not only contribute to applied mathematics", as if pure mathematics is the superior art.

Nevertheless, the book is an interesting read and the exercises are full of interesting mathematical puzzles. A word of caution is that the reader needs some college-level mathematics to understand much of the book, despite its being written in simpler language. Some of the latter chapters also get confusing since he talks about 5 mathematicians at any one time, jumping from the contributions of one to another in mid-sentence, then going back to someone else described earlier. It would have been more helpful if his sections were better-defined and had titles. Could also use an update to the 21st century.

Practically any page you open this book to presents fascinating insight into some step in the development of mathematics.

I first bought the firt edition about 25 years ago when I was still a matriculation student preparing the examination to university. This book has been with me for more than one fourth of a decade. I also own the second edition of the same book.
It is a pity that the new author did not take the opportunity to expand the book to a much wider scale. ( what I mean is not to a encycoplaedic but at least expand the history of mathematics in the 20 the century. Now back to the book. What makes this book different other ones, I think it is the historical intuition of Boyer makes this book eternal. Some book arrange the content chronologically and somes book arrange the content according to the topics. However, Boyer cleverly combined that two . Also, he also extinctly discuss the topics proportional to their importance in the history. There is not too much mathematics and
there is not too few mathematics, Just a few words to describe that is " that book is really well balanced " and gives you everything and also the range of audience is wide, coupled with the very very reasonable price, it is the book on mathematical history who are interested should own one.

Excellent organization and coverage. Type size limits effectiveness for practical reference on a routine basis. Subject matter being oriented toward those accustomed to frequent reference should serve as guide.

I learned so much from this book. It's like 5 textbooks wrapped into one!