Customer Reviews

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

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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.

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.

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'.

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. Dunham's picture of a Venn diagram--a rectangle with two large circles that do not overlap and a small circle completely inside of one of the large ones--is absolutely wrong and misses the genius of Venn's contribution. Dunham is right that other mathematicians, e.g. Euler, had drawn diagrams such as the one he pictures, but those are not what Venn did. The point of Venn's diagrams is that they reflect the Boolean understanding of the hypothetical nature of a universal statement. Thus a statement like "All frogs are amphibians," is drawn with two overlapping circles, and the area that represents frogs outside of the "amphibian" circle is shaded out, meaning we know it is not populated, but leaving it open whether there is a population in the overlap area. This technique makes a huge difference in the understanding of logical relationships; it is a revolution after some two thousand years of Aristotelian assumptions. Dunham can do no better than belittle it.
Thus, I come back to my original thought. These are two entries in the area with which I am familiar, and they are both just plain wrong. How much credence can I give the other entries when I try to learn from them?

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

Although I enjoyed this book, particularly the historical accounts of mathematical figures, I was disappointed with the lack of mathematical depth with which the subjects were treated. If you want an equally good book with more depth buy Journey Through Genius by the same author.

This book is filled with enormously entertaining anecdotes about math and mathematicians, and it includes lots of very cute proofs. I've studied a lot of math (I have a PhD in physics), but I found much in this book that was fresh, nontrivial, and always enjoyable. It may be misleading to think of this as a "popular" math book.

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.

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.

Excellent book that gives us a synopsis of the history of maths from early days. The only criticism I found (and no doubt other readers and the author) is that by virtue of the title, we are limited to one piece as per each letter of the alphabet. I personally would have liked to see the Z chapter written on Zero.

That apart, quite an entertaining read and highly recommended. Dunham should write some more.