Professor Stewart’s Cabinet of Mathematical Curiosities by Ian Stewart (PDF)

Description

Knowing that the most exciting math is not taught in school, Professor Ian Stewart has spent years filling his cabinet with intriguing mathematical games, puzzles, stories, and factoids intended for the adventurous mind. This book reveals the most exhilarating oddities from Professor Stewart’s legendary cabinet.Inside, you will find hidden gems of logic, geometry, and probability-like how to extract a cherry from a cocktail glass (harder than you think), a pop-up dodecahedron, and the real reason why you can’t divide anything by zero. Scattered among these are keys to Fermat’s last theorem, the Poincaréonjecture, chaos theory, and the P=NP problem (you’ll win a million dollars if you solve it). You never know what enigmas you’ll find in the Stewart cabinet, but they’re sure to be clever, mind-expanding, and delightfully fun.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐”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.

⭐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.

⭐I purchased this book to place in my bathroom for myself and guests to read in that “Crude, I forgot my smart phone” moment on the John. I personally have a bachelor’s degree in math and had high hopes that this book would give a glimpse into many of the fun neat things I learned during my time in school. Although the book does indeed touch on many of the deeply interesting but still accessible topics of higher level math, I found that half of the books just seemed like word problems or brain teasers. These are not inherently bad and I’m sure those with a non math background will really find the book fun and interesting. But on a personal level I am just not a huge fan of the book.

⭐This has been my “coffee table” book that I like to just dip into occasionally, when I have spare 5-10 minutes. This is because it’s full of lots of little bits, with no overall narrative. It’s not quite a school exercise book, but it does have quite a lot of puzzles for you to think through, some of which require some scribbling with some pen & paper or plugging numbers into a calculator. As well as these, there are lots of little vignettes of mathematical thought which inform but require less input from the reader.So my initial advice for any readers of this would be get a notepad and some pens and keep them nearby. Fans of recreational mathematics will find much that is familiar here, as some problems recur in just about every such ‘popular’ level book on maths, such as the problem of the bridges of Konigsberg or lots of factoids about pi.That may sound like damning with faint praise, but there is a depth of mathematics on display here that is rather splendid. Many of the ideas are really quite profound, yet the way they are presented makes them quite accessible. A non mathematician might disagree with me, but it may be interesting to find out from others if there are areas where they get stuck.There is a general trend for the puzzles to get a little bit more difficult later on in the book. So we are given some treats that will be unfamiliar even to those who did maths at A-level. We deal with topics ranging from geometry, number theory, topology and even some complexity is thrown in at the end.I probably ought to add that for any sections that ask questions there are answers provided at the back of the book. Most are pretty good, though if the book does have any weaknesses, it is here, where some of the answers are given with not enough explanation. Though for recreational mathematics, one of the litmus tests has to be how well the solution to the Monty Hall problem is described and this one is very fair.There is a follow-up book that Ian Stewart wrote, in the same vein but with a different set of problems. Given the quality of this work, I will be reading that as well, so you can look forward to seeing another review like this when I get around to it.

⭐Really enjoyed reading through these curiousities and problems. This is a book I will dip into again over the years. My only issue is that I would like the problems and puzzles to be grouped into easy, hard amd harder etc. The wonderful Martin Gardmer books are also an eclectic mix like this. It makes it difficult when trying to find a lovely teaser for younger children or if ta teen wants to look through the book themselves – it can all seem quite daunting – though I guess teens are not exactly the target market

⭐This book is great, but I would say many of the “curiosities”almost need you to be taking your own notes in order to grapple with the subject matter. Basically, this isn’t a book to take on holiday with you, or read on the train. More like an evening read, taken at a slower pace, concentrating hard on what’s being discussed.I think overall I enjoyed it though.

⭐Superb little book with lots of mathematical puzzles. Great fun!

⭐Having been afraid of maths since school and apart from having excellent mental arithmetic skills, had no interest in the topic. This book has changed this. Much to like in here and some mysteries de-mystified. A good fun bit of reading

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