A History of Mathematics

Rating:
Summary: Not for the serious student of history of mathematics
Review: 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.

Rating:
Summary: Not for the serious student of history of mathematics
Review: 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.

Rating:
Summary: The best book on history of mathematics
Review: 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.

Rating:
Summary: This book tells you everything
Review: I learned so much from this book. It's like 5 textbooks wrapped into one!

Rating:
Summary: This book tells you everything
Review: In this book the historian of mathematics Carl Boyer exposes the development of mathematics from the pre-history to modern times in a wide view, covering all the important mathematics and mathematicians from ancient times to our modern times. This reviewed version by Uta Merzbach is easier to read than the first edition by Boyer and its updated. I disagree that you need to be a mathematician or so to read this, all you need is the interest. In fact when I read this book I was entering high school and I found it easy and enjoyable to read. The author will not spent any time with hard mathematics, rather he is just going to cite (so all you need to know is what thouse technical names means superficially, but you don't need to know the math undergoing). This book is very nice if you want to have a deep and wide view on the history of math, so don't think this is an ultimate guide or something. Actually I think this book can be considered as a general introduction to the history of mathematics and to mathematics itself, it will make you get used to many technical terms and their intuitive meaning before getting deep in the formal math.

Rating:
Summary: Guide to the Temple of Mathematics...
Review: So far this is the best book I have ever read on the history of mathematics. I have read a bundle of books on the history of mathematics, but no book is as interesting and as concise as this. But one deficit: this book concentrates too much on the Western part. Why shouldn't it put a chapter on the Chinese mathematics of recent years? I think this will surely add more to the content of the books. I have read a lot of intereting biography of mathematicans in this books. The narractive is good. The explanation of the theorems is clear. All in all, a good book and a good try.

Rating:
Summary: Good book, very good book if you already now the basics
Review: 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.