1089 and All That: A Journey Into Mathematics

I've never before run across another book which covers such a wide range of mathematics in such a short space while making everything so easy to follow and intuitively crystal clear. Though a book like this can't possibly offer a comprehensive presentation of any aspect of mathematics, David Acheson does a perfect job of pleasantly displaying the nature (theorems), beauty (proofs), and power (applications) of the subject - or maybe the beauty is in the theorems and the nature is in the proofs? In any case, Acheson must have been inspired in writing this book, and I'm so delighted with it that I'm pushing my wife (who hasn't touched mathematics in two decades) to read it also! In fact, this is the first book I'd recommend to anyone who shows a budding interest in mathematics and wants to learn more. And even people well-versed in mathematics will enjoy joining Acheson on this brief but wonderful tour, so I highly recommend this book to them also. As a testament to how much I appreciate Acheson's expository skill and style, I've just ordered one of his other books, From Calculus to Chaos: An Introduction to Dynamics. Note: I believe page 126 contains an error, since it seems that p can't both grow exponentially yet be bounded to unity. If I'm right, that doesn't weaken my enthusiastic recommendation for this book, but I wanted to note it in case other readers wondered about this.

This book is simply a delightful little journey into mathematics, not to light to be boring for the working mathematician nor to hard for someone who is not a math head. Many beautiful results are presented in a simple yet marvelous way, ranging from the 1089 number trick through inverted n-linked pendulums and ending with the stunning connection between pi, e and imaginary numbers. In short a delightful read, from an author who obviously loves math and masterly shares this passions with the rest of us. If you find yourself marveling over this book then I can highly recommend picking up Proofs from THE BOOK, which although being quite more math heavy shares many qualities with this book.

This is a delightful short book, not just about mathematics, but actually doing it. Each of the 16 chapters touches on a well-chosen piece of important mathematics. The coverage is broad (in math terms: number theory, algebra, geometry, combinatorics, proof, topology, calculus, differential equations, chaos and catastrophy, and applications as well). The many (black and white) illustrations (including cartoons) make for fast reading, and before you know it, you have finished another chapter. There are numerous connections between chapters.The book has no preface or introduction; you just jump in. (The library copy that I borrowed had lost its dust jacket, and I looked in vain for an explanation of the "purpose" of the book. Why did the author write it? But once I started reading, that question quickly turned out to be irrelevant.) The single page of references for further reading is well chosen. The index spans almost four pages. The typography and layout are beyond reproach. The writing style is concise, informative, precise, inviting, and certainly not dry (reflective and historic tidbits are interspersed).Some minor comments. (1) The (algebraic) explanation of the 1089 number trick does not mention the role of the requirement (which is mentioned) that the first and last digit of the starting number need to differ 2 or more. (2) The reader needs the ability to deal with formulae involving variables, including raising to a power, and ellipses (... to denote infinite series). I don't think this is a limitation for the seriously interested reader. (3) The book is somewhat biased towards "continuous" mathematics, rather than "discrete" mathematics. This is easily explained by the author's background, and again I didn't find it a limitation. My background is more in "discrete" than "continuous" math. I did learn a few new things from the book, such as Malfatti's circles-in-triangle problem, Kakeya's unsolvable needle-turning problem, and the upside-down pendulum theorem. (These may seem strange to you to include in a short math book, but they serve their purpose well.)In such a short book it is very difficult to please everyone. The author has done a wonderful job. Everyone should know at least this much (about) mathematics.