Customer Reviews

The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (Sterling Milestones)

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In his previous science book, "Archimedes to Hawking", Cliff Pickover explored the great laws of science and the lives of the physicists and chemists who discovered the laws. In the "Math Book", Pickover takes on the great moments or milestones of mathematics. While the great laws of physics were almost all named by the early twentieth century, scientific milestones continue to be established. Thus, the mathematical milestones of the "Math Book" are documented into the twenty-first century.

The publishers have provided Pickover with a challenging format. Each milestone is described on just one page, and each is accompanied by a full page image on the facing page. These limitations restrict the scope of the presentation for each subject. However, having as many as 250 milestones has allowed Pickover to expand some subject areas into more than one related milestone.

The images are absolutely beautiful. They include paintings, diagrams, photos, and computer-generated art. Among the best are a close-up photo of the game of Go, a map of the Internet as the illustration for the Konigsberg Bridges, the Gray Code using a diagram taken from a US patent, and the Archimedes Spiral as exemplified by a fiddlehead fern.

Many of the milestones cover esoteric theoretical areas of mathematical analysis. This was not my best subject in school. However, because of the latitude provided by having 250 topics to cover, Pickover is able to include more technology-related topics. He has authored many math books, for example, "Wonders of Numbers", "A Passion for Mathematics", "The Mobius Strip", and this year, an updated paperback edition of "The Loom of God." However, he is also a down-to-earth scientist. The topics in this book include such concrete subjects as the bed sheet folding problem, public key cryptography, Rubik's Cube, and my favorite, cicada-generated prime numbers. Not all milestones were charted by humans!

Is every possible milestone included? Even with 250 topics, and yes there are exactly 250, Pickover invites the submission of additional milestones. Before reading the book, I had some expectations of what topics should be covered in the milestones. Upon reading, I found that almost all of my ideas were included.

However, I do have a suggestion for an additional milestone, Legendre Polynomials. These polynomials, well-known to physicists, are used to express the form of atomic wave functions. Thus, they underlie the very fabric of matter. If you can include Bessel Functions, why not have Legendre Polynomials? There must be other milestones to suggest. Perhaps the "Math Book" can become an example of Hilbert's Grand Hotel. Even when the hotel is full, there is always room for another guest.

The Math Book
By Clifford A. Pickover

What a wonderful book. Simply terrific! And, nearly all of the illustrations are
in magnificent full color too. In these pages are told the stories of exactly 250
of some of the greatest events in the history of mathematics, each entry being one
page long with an illustration on the facing page and arranged in chronological
order.

So deep and pervasive is mathematics that mathematical behavior has been
observed in ants in their quest for food, and they appear to have some sort of
counting mechanism which serves as an ant odometer counting the number of steps they take. It must have been an interesting job trimming their little legs or
installing tiny stilts to detect changes in their travel distances. From ant
journeys it's quite a reading journey to the final 2007 entry on Max Tegmark's
speculation that the universe not only can be described in mathematical terms,
but actually is mathematics. In between the ants and the universe we see the spirit of mathematics
persisting in a Nazi concentration camp where Curt Herzstark invented an
ingenious calculating device; so successful was his Curta calculator that it
became a commercial product for about 25 years. There is also a nice story of
Pope Sylvester II who was known as the Number Pope for being a mathematician;
other stories are about dice and games and other chance phenomena, magic squares,and there are some of the most dazzling fractals ever put to paper, especially the
one that accompanies the entry on the Hausdorff dimension. Even the entry on the Austrian logician Kurt Godel is something special; it is the first time I have ever
seen a picture of Godel with his friend Albert Einstein in color.
Not only is this book a fabulous work on the lively history of mathematics,
but one additional number is especially wonderful. The price; its wonderful.

Dennis W. Gordon

Despite already having published more than forty popular science and mathematics books, Cliff Pickover surely outdoes himself with The Math Book!

This is a collection of 250 "milestones" of mathematics throughout history, complete with breathtaking glossy color illustrations for each entry (a first for his books), as well as insightful descriptions that explain the history and the significance of each of these marvels of mathematics. This includes well-known items such as Magic Squares, the Sieve of Eratosthenes, and Fermat's Last Theorem, as well as lesser-known items like Surreal Numbers and Beltrami's Pseudosphere.

As obscure as some of the items might seem to lay readers, the text is thoroughly descriptive and accessible. If you have even the slightest inclination towards mathematics, the entries will immediately draw you in, and won't let go until you've read through them all. The illustrations for each corresponding item include photographs, paintings, and computer-generated images that test the limits of your imagination.

The 250 entries in the book make it an incredibly fascinating stroll through the history of mathematics. The book definitely has bestseller potential, and could easily be one of Pickover's best works.

My wife is a high school math teacher. Almost every week, some smart-ass kid asks her, "what good will math be in my later life?" When will I use it? Why would I need it?

This book answers that question. Now, every article is about 500 words long or so, which means that she can assign them as a reading assignment. It is hard to find good short math articles, and this book contains a whole year's worth.

It is a wonderful book. The articles are clear and understandable. My wife called it "Uncle John's Bathroom Reader" for intelligent people. The article sizes are just the size you need. The only problem is that the hardback book is too nice to leave near the toilet.

Printed retail on the book is almost double what Amazon charges for it. I recommend this book to anyone who is remotely interested in mathematics, or who has asked the question about "How has mathematics changed my life"?

It is a wonderful book.

A very nice math stories compendium: all famous mathematicians, theorems, proofs and problems in mankind history. Very well presented, lots of pictures.
Nice to read lying sideways at the bed (all texts are in the left page and all the pictures at the right). No in-depth analysis of anything, just simple explanations.

Clifford Pickover is one of my favorite authors writing about mathematics. His newest book, The Math Book, is a math history book with 250 topics, each of which has a one page essay and a graphic, usually in color on the facing page. The eclectic list of topics chosen include the standard highlights like the Pythagorean Theorum and the Riemann Hypothesis but also games like Hex and Sprouts and even my favorite TV series, Num3ers. The essays are well written and clear and often contain humor, something which is rare in writing about mathematics. Most of the content can be understood by someone with a high school level math background. The illustrations are very well done and are especially helpful in visualizing some of the geometric objects which are described. A few of the essays require additional background in math but there are extensive references to aid in further exploration. Overall, this book is a great way to see that math is everywhere.

This book has three things to say: math is awesome. There are mathematicians whose genius you will never approach. You might as well never even attempt to participate. Unfortunately, it never gets much more detailed than that.

The book's format is largely at fault: it devotes a page or less to each of the items of math history, and devotes the facing page to a large illustration connected (at times tangentially) to the topic at hand. With so little space to work in, Pickover is pressed to explain the simplest overview of any given topic and its significance. He rarely gives examples of the actual math involved, and never attempts to actually convey understanding of it.

From the outside, this book looks like a college textbook. From the inside, it looks like a coffee table book, with thick and glossy pages. However, the quality is inconsistent. Some of the art is beautiful, but other illustrations are badly pixelated.

The biggest problem with this book is that there is simply too little math in it. I expected a Suzuki method introduction to topics in modern math, and instead received something between a history book devoid of detail and a table book with poorly-chosen art.

Beautifully illustrated and beautifully written, this book has something for all ages and all interests; in my case, I have chosen it as a gift for my friend celebrating his 90th birthday and for my granddaughter celebrating her 17th birthday. It is appropriate for both of them because it is not only informative and intellectually stimulating, but it is vastly entertaining. My personal favorite milestone is the perfect magic tesseract, discovered by John Robert Hendricks in 1999. As an admirer of the novel, "A Wrinkle in Time," I was happy to be enlightened about the strictly mathematical definition of a tesseract. The perfect magic tesseract is even more fascinating to contemplate than the simple mathematical tesseract or the fictional one. And just think! This is only one of 250 equally fascinating milestones (see the other reviews). As frugal person, I must comment on what a bargain this beautiful book is. You can't get a cup of coffee for ten cents any more, but you can get a milestone for slightly less! (And how much more stimulating, nourishing, and lasting knowledge of these milestones is!!!)

This heavy book is light.

By "heavy" I mean excellent, profound, important, and yes, the book weighs a lot too, the way many high quality art books do, the ones you place out on a display table, an excellent place for this book also. I do not mean anything ponderous or oppressive; that is one reason I also say this book is light.

By "light" I mean every time you turn a thick glossy page, you are enlightened by a page of lucid text on the left, and a colorful associated image on the right, and another fantastic mathematical discovery that invites entire books to be written. The text is lightweight in a good way; it can be read and understood without a math background, yet considering its brevity, is often surprisingly complete at mentioning major points, along with many pages of notes in the back for further reading. The 250 major mathematical discoveries are in chronological order, starting with prehistory and continuing through to the present.

If you already know about the exquisite beauty of math, buy this book and put it out so as to help enlighten others, or send it as a gift to a child and help save a soul, or pick it up the next time someone wants to talk about intelligent design and you'd rather talk about truly intelligent design.

Isn't it tragic that many humans are blind to the transcendental experience of contemplating how zero is the same as e to the i pi power plus one? Or blind to the beauty of a multidimensional mathematical object known as E8 that just happens to arrange the lowest level building blocks of theoretical physics? Mathematics is so intimately entwined with the real world that some have even considered the extreme possibility that maybe our universe is not just described by math, maybe it IS math. All these points are covered in the book.

This book may help the reader by shining a new light on universal reality. Seeing mathematical beauty is a realistic, repeatable, awe inspiring experience that can be shared by all sentient beings, everywhere, independent of any belief systems. Extraterrestrials will also know these truths to be self-evident.

Based on the associated webpage, I expected a somewhat textbook style of book using illustrations to highlight the concepts. However, this book is approximately 50% illustrations. For every page of text there is a page sized illustration. For some of he pages there is also a small illustration on the page with the text. Now, some of the illustrations actually complement the text, but there are far too many instances of the illustrations being just photographs, paintings or engravings of the historical figures responsible for some of the greatest mathematical discoveries. It's hard to learn anything from a photo of a dead mathematician. Many of the illustrations that do reference the concepts could have been much improved with little effort. This is a good source for terms to look up elsewhere in more depth.