on September 29, 2001
As the book's subtitle suggests, it is a journey through some of the world's greatest mathematical achievements. It is a collection of quasi-independent essays, loosely patterned after children's ABC picture books.
For me there were two things that made this book a joy to read. One was that, as the preface states, "each chapter provides a strong dose of history." This way each topic was considered in some human context that revealed just how remarkable its development was. The other trait I liked was that while each chapter followed the same basic formula, i.e., some history and then some math, no two chapters were presented in the same way. Thus, Dr. Dunham was able to avoid predictability.
Though the mathematics in this book was not terribly challenging, the reader should be fairly mathematically inclined. The historical periods covered were weighted in favor of the classical Greeks and the 17th century Europeans, and the corresponding developments paralleled current curricula through lower division college math courses.
On the minus side, I would like to have seen a bibliography in addition to the notes at the back of the book.
on February 23, 2002
William Dunham's work is of the highest caliber. He not only knows the techniques of writing and making the best use of language but he also knows the math without question. The book is extremely well-organized with a reasonable number of math examples but not so many as to "clog" the flow of the writing and the stories about the discoverers of the great math sequences. This book is, I think, very much worth the price being asked. Very enjoyable reading and one can even use it for study if necessary, such as when writing a thesis.
After reading this book, one wishes that the cardinality of the English alphabet was much larger. That way, there would have been more letters and hence more chapters. Each of the twenty-five chapters deals with a theme that begins with a letter of the alphabet (X- Y plane is one chapter). Some poetic license is taken here. For example, the K chapter has the title Knighted Newton, but that is just part of the fun.
The author takes an approach that differs from most popular expositions in that there is a good deal of emphasis on the personalities (sometimes cantankerous) of the characters. Mathematicians are often portrayed as brilliant air heads ignorant of the ways of humanity, but here they have all of the human foibles. It is sadly true that intellectual battles are among the most viscous of all. The cross-channel dispute over the origins of calculus lasted for decades and was extremely acrimonious. It took less time for nations to kiss and make up after wars that killed millions of people than it did for the mathematical communities of Britain and France to "resolve" the priority dispute between Newton and Liebniz.
Familial rivalry reached extreme heights (lows) in the Bernoulli family, as at times solving was placed in second position behind squabbling. However, many of the personalities were quite ordinary . Pierre Fermat was in many ways an ordinary member of the French bureaucracy whose life outside mathematics seems to have been quite dull. The most prolific mathematician of all time, Leonhard Euler, was a quite likable father of many children who managed to perform superb mathematics even after going blind.
There is a slithering humorous vein coursing throughout the book, occasionally good but most often a member of the groaner set. The author avoids using the title, "Here's Looking at Eu-Clid," but cannot resist mentioning it later. There is even speculation as to why 50 percent of male mathematicians have beards. Since this reviewer has one, he will offer his own solution. Shaving is boring!
A fascinating collection of essays that touch every facet of the history of mathematics, this is sure to be one of the largest of the crown jewels of popular mathematics.
Published in Journal of Recreational Mathematics, reprinted with permission.
on August 30, 2001
Dunham cites John Locke's opinion of math: "Mathematical proofs, like diamonds, are hard as well as clear" (page 115). The books presents a number of such hard and clear proofs. Dunham's facility as a writer makes this book enjoyable and creates the kind of historical context necessary to appreciate the importance of mathematical achievements. The book is erudite, educational, and enjoyable.
on January 5, 2003
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.
on February 20, 2002
William Dunham has exercised wonderful judgement in a book this thin, making sure that maths, history, biography, and personalities appear in good measure.
There is one chapter for each letter of the alphabet ranging through Arithmetic, Knighted Newton, Mathematical Personality, and culminating in Z ( a chapter on complex or "imaginary" numbers). Even a chapter titled "Where are the women?"! Also, see the chapter on Bertrand Rusell. It will hardly take you an hour or two to read a chapter and you can read almost at random
You need not be intimidated if you do not want to delve deeply into maths. The author has provided just about enough mathematical material in terms of proofs, calculations, diagrams (interspersed with wry humour) The material is not too dense even for the non-technical reader, though you must of course, have the patience to follow a train of thought to its conclusion.
Personally, it represented a return to the wonderful world of maths after a long hiatus, after explorations of such formal (Hall & Knight, SL Loney) and informal (George Gamow, Douglas Hofstafdter, Roger Penrose) scientific writing in my student days.
Some of the pardonable omissions are: 1) I would have liked to see full length chapters on some of my personal favorites such as Gauss, Cauchy, and Hilbert
2) On the utility of prime numbers and number theory, the author seems to have missed out on applications in cryptography
The editing and presentation is excellent. The book is very affordable. Buy two copies, one for your bookshelf, and one for your nephew (niece!)- the budding math prodigy in your family
on November 11, 2000
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.
on April 26, 2002
Most books written by mathematical scholors tend to be boring and straightforward. Dunham, on the other hand, knows how to tell a story along with demonstating the intricate world of mathematics without putting someone to sleep. I thought I wouldn't learn anything too interesting in this book, but surprisingly, I was astounded by many of the facts and anecdotes Dunham presented me with. The best quality of his writing is his train of thought; his logic is not so far out that you aren't able to follow his steps. Everything is laid out like a good road map; it's the Rand McNally of the mathematicians!
on August 5, 2000
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'.
on December 12, 1998
Dunham has done a marvelous job of marching through the alphabet with clever proofs, interesting concepts, and funny moments of mathematics. Throughout the book, he flaunts his wit and guides any realms into the realms of number theory, geometry, algebra, and calculus. If you have any interest whatsoever in math, I would recommend buying this book immediately. Its illustration of the quirkiness of its practitioners and the beauty of its practice are worth the reading.