Customer Reviews

Professor Stewart's Cabinet of Mathematical Curiosities

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I teach middle school and high school math, and I am always on the lookout for challenge problems for my students. This books is full of fun, mathematical challenges for all levels of students: from middle school right on up to the teacher. I also enjoy flipping through to find amusing anecdotes, famous unproven hypotheses, practical explanations of mathematical conventions, and really nerdy jokes. I recommend it for anyone who is passionate about math and wants to help other people become passionate about math as well.

"When I was fourteen years old, I started a notebook. A _math_ notebook." Ian Stewart starts his most recent book this way, and then apologizes for being such a geek. He has written lots of books about serious mathematics, and his new one is serious, too, but it is full of serious fun. _Professor Stewart's Cabinet of Mathematical Curiosities_ (Basic Books) comes from that notebook, and the subsequent notebooks he had to get because more curiosities kept crowding in. He didn't put his school math in the notebooks; he put in all the interesting math that he wasn't taught at school. So in these pages are about two hundred short chapters or essays on what is usually called "recreational math". It's not mathematics you can be tested on, so it's fun. A lot of it does not have to do with numbers; mathematicians may forever be associated with numbers and counting, but it is the logic and the study of patterns that occupies higher math, and a lot of that higher math can be brought down to earth for entertainment purposes, as Stewart has done here repeatedly. For those who like recreational math books, there will be much that is familiar, like the problem of crossing all the bridges of Konigsberg exactly once, or that of the farmer who has to cross the river with a wolf, a goat and a cabbage, but has room in his boat for only two at a time, and none must get eaten by the others en route. If those don't ring a bell, this is a splendid book to start you on wondering about some entertaining mathematical ideas. If you know the old ones, Stewart has included lots of new puzzles, as well as small biographies of quirky mathematicians through history, and little essays on non-puzzle material like fractals or Gödel's proof. He has also, at the back of the book, included the answers, in a section labeled, "Professor Stewart's Cunning Crib Sheet: Wherein the discerning or desperate reader may locate answers to those questions that are currently known to possess them... with occasional supplementary facts for their further edification."

There are rings on the coat of arms of the Borromeo family, three rings that you cannot pull apart but none of which is linked to another. There is a section on famous mathematicians who aren't famous for being mathematicians. Sure, you knew Lewis Carroll, famous for the _Alice_ books, was a mathematician / logician, but did you know Art Garfunkel got his master's in math, and only stopped work on his PhD so he could pursue his singing career? Bram Stoker, author of _Dracula_, had a mathematics degree. Leon Trotsky had his mathematical career ended by exile to Siberia. There is a section on Fermat's famous Last Theorem and how it was proved fifteen years ago by complicated modern methods. Fermat himself could not have used such methods in the proof he said he had, but he did not write it down because he didn't have enough space in the margin in which he was writing notes. Stewart says that there might be a simpler proof, and while he repeatedly encourages readers to branch out on their own from these problems, he warns them about coming up with proofs for this one, and he also hints at the frustrations of being a public mathematician: "If you think you've found it, _please don't send it to me_. I get too many attempted proofs as it is, and so far - well, just don't get me started, OK?" There is a section on dividing a cake fairly. It's easy with two people - one cuts the cake and the other gets to decide which piece to take. How do you extend this to three people? If you have a block of cheese in cube form, how can you cut it so that the cut face is hexagonal? Why in lists of numerical data, like the areas of each of the fifty states, are the numbers far more likely to start with 1 or 2 rather than 8 or 9? And how can this be true whether the numbers represent square miles, square kilometers, acres, or any other measurement? What shape of road would give a smooth ride to a bicycle with square wheels? A person born in 35 BC died after his birthday in 35 AD; how old was he? (Hint: those ancients could do math, but they didn't have the concept of 0.) What number, spelled out in Scrabble tiles, equals its Scrabble score? This delightful book is a real miscellany.

It also has one characteristic those older recreational math books didn't have: internet references. When discussing, for instance, John Horton Conway's fascinating complexity-from-simplicity game Life, Stewart can send the reader to an internet version "which is easy to use and will give hours of pleasure." Some of the references are merely to Wikipedia, but others are to specialty sites, including the extensive Wolfram Mathworld. This would be a wonderful book to give to any young person, especially one who claims not to like math. Stewart may not have a cure for such a condition, but his fine collection of amusements could demonstrate that such abhorrence is at least sometimes misdirected.

I gave it to my husband for his birthday. He says, "Lots of interesting problems old and new, and good information about current developments in mathematics." He teaches mathematics with a problem-solving approach and is especially effective with adults (or near-adults) who are persuaded that they hate math. His worst student review has been, "Well, I still hate math, but Iike THIS math." He now teachers senior citizens in our retirement community.

As a 70 something challenging my brain, I find this melange to be fascinating, challenging, and at times overwhelming, but never dull. I do not think Professor Stewart is as adept as the late Isaac Asimov at explaining to a non-mathematician some of the more arcane mathematical principles with which he deals, but that is a quibble. The book is fun and definitely for the curious.

Professor Stewart seemed to have the devil's own time finding a balance that would appeal to fans of popular mathematics. Much of his "Cabinet of Mathematical Curiosities" is positively pedestrian and, frankly, quite boring - riddles we've all heard before; high school geometry; combinatorial curiosities such as the number of ways to shuffle a pack of cards or the number of different sudoku puzzles that exist; school age party tricks based on nothing fancier than public school arithmetic; and, a real yawner for goodness' sake, a dreary listing of constants such as e, the square root of 2 or pi to 50 decimal places ... my, my and ho hum!

At the other end of the scale, Stewart included complex summary essays on cutting edge mathematical topics as advanced and esoteric as the Riemann Hypothesis, fractional dimensions, Zeta functions, the Goldbach conjecture and so on. I don't think of myself as mathematically challenged by any means but (and this is strictly my opinion) I believe many of these essays are pitched at a level that would bewilder a young bright-eyed mathematician fresh off the earning of an undergraduate degree.

It was the merest handful of essays that found that brilliant middle ground that challenged, entertained and educated - Kurt Gödel's Incompleteness Theorem; the Poincaré Conjecture; a discussion of Hilbert's Hotel and the cardinality of infinities put forward by Cantor; Bessel functions and the differences in the "quality" or "timbre" of the sounds generated by the shape of a drum as opposed to merely its pitch. But these successes were precious few and far between.

High expectations dashed on the shores of mediocrity. Not recommended!

Paul Weiss

I'm an engineer by training and love a little mental stimulation. This book is just what I needed to flex my creative brain muscles a little. It's a wonderful mix of logic puzzles, mathematical calculations, interesting anecdotes, and physical modeling activities. I love it!

This is a fun book to make your brain really think. The curiosities are well explained but the problems are still tough. The curiosities are intriguing for the non mathematicians while the problems are hard enough to challenge mathematicians.

Unfortunately this book tries to be a lot of things and fails, unlike many other excellent books by Prof. Stewart. If you want to read good and inspiring biographies of mathematicians there are very good books focused on that topic, if you are into recreational mathematics then you can easily consult excellent volumes e.g. the ones from Martin Gardner and if you want to read mathematical jokes... well, I'm sure you don't need a book for that (do you?). The level of topics discussed vary wildly, from high school algebra to university-level calculus and complex analysis. Even the author himself admits in some pages that the current topic is too technical to describe in a few sentences, so why start to talk about it in the first place? I do not regret having bought and read this book even though I came very close to thinking so.

How do you make people want to study math? It can be a very boring subject with lots of mental arithmetic and obtuse language references and then, when you are almost comfortable with that, the teacher introduces all these weird notations and bizarre concepts that do not seem to relate to anything useful. Well, this book is one of the myriad of such books that attempt to make mathematics more than what you learned in High School. Maybe even fun?

The approach it takes is to tackle any subject at all in a series of short essays or even paragraphs. These subjects can be anything from the typical logic puzzles (the first one is that you meet three people on an alien planet. There are two types: those who only tell the truth, and those who only lie. How do you tell who is who after asking them one question each?) all the way to the uses of fractal geometry and advanced mathematical concepts like the P=NP? problem which has a $1 million dollar prize of you can prove, or disprove it. Along the way are strewn things like brief histories of famout mathematicians and all kinds of additional trivia that can be shoved into a 250 page paperback.

To those who insist on findind the answers to the various puzzles throughout the book, the author includes a 50 page appendix which contains all the answers and more explanations on how to reach them.

This book is suitable for anyone who has gone beyond basic algebra in school and is not so esoteric as to be chock full of too much difficult notations. On the other hand, there are many segments that are thrown in that are either old chestnuts or so advanced as to be incomprehensible to most people. While I understood 98% of the book, the additional 2% made my eyes glaze over which is why I did not give this book all five stars. What was missing for me, to make it into a five star book, was some sort of spark and connectivity around all these different topics that would tie them all together. The only tie in to be found is that it's all related to mathematics, and that was just not sufficient.

Overall, I would give this book to someone with a passing interest in math as a book that can be read in sections and segments when the mood strikes, but not one that you either need to read in one session, nor one that should immediately go on top of your personal reading pile.

I have this book as a paperback and for the kindle (3). I like the book just fine as a paperback, although, (1) it's a little larger than books I like to carry to read on trips, and (2) flipping back and forth from chapters to answers was a bit of a nuisance. I got the kindle version to solve both problems. After all, there would be a link from each chapter to its answers/hints/whatever (and back), right? Wrong. The kindle version just shows you a non-linked word "ANSWER". To get to the relevant answer, sometimes typing in the name of the chapter would work, but often not. The table of contents is not much help either because there are links to each chapter (and back to the contents), but all answers are in one chapter.

I wonder how long it would have taken to add these links. An hour or two? It's like the kindle version was prepared by people who had no idea what a kindle could do. Let me know when the competently prepared kindle version is available for free for suckers like me who paid money for it.