Serious Fun May 9, 2009 (6 of 6 found this helpful)
"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 bic
What a disappointment after Flatterland! Nov 13, 2009 (2 of 2 found this helpful)
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