Ian Stewart - Professor Stewart’s Hoard of Mathematical Treasures

Professor Stewarts Hoard of Mathematical Treasures

PROFESSOR IAN STEWART is best known for making mathematics accessible and popular. He was awarded the Royal Societys Michael Faraday Medal for furthering the public understanding of science, and became a fellow of the society in 2001. His many popular science books include Does God Play Dice?, Flatterland, Letters to a Young Mathematician, How to Cut a Cake and, with Terry Pratchett, The Science of Discworld. He is the mathematics consultant for the New Scientist and a professor of mathematics at the University of Warwick. He is married and has two sons.

By the Same Author

Professor Stewarts Cabinet of Mathematical Curiosities

Concepts of Modern Mathematics

Game, Set, and Math

Does God Play Dice?

Another Fine Math Youve Got Me Into

Fearful Symmetry (with Martin Golubitsky)

Natures Numbers

From Here to Infinity

The Magical Maze

Lifes Other Secret

Flatterland

What Shape Is a Snowflake?

The Annotated Flatland (with Edwin A. Abbott)

Math Hysteria

The Mayor of Uglyvilles Dilemma

Letters to a Young Mathematician

How to Cut a Cake

Why Beauty Is Truth

Taming the Infinite

with Jack Cohen

The Collapse of Chaos

Figments of Reality

What Does a Martian Look Like?

Wheelers (science fiction)

Heaven (science fiction)

with Terry Pratchett and Jack Cohen

The Science of Discworld

The Science of Discworld II: The Globe

The Science of Discworld III: Darwins Watch

Ian Stewart

This paperback edition published in 2010

First published in Great Britain in 2009 by
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The following figures are reproduced with the permission of the named copyright holders:

(What Seamus Didnt Know); Suppiya Siranan.

(What is the Area of an Ostrich Egg?); Hierakonpolis expedition, leader Rene Friedman, photograph by James Rossiter.

(Mathematical Cats); Dr Sergey P. Kuznetsov, Laboratory of Theoretical Nonlinear Dynamics, SB IRE RAS.

(How to See Inside Things); Brad Petersen.

(Alexanders Horned Sphere);from Topology by John G. Hocking and Gail S. Young, Addison-Wesley, 1961.

).

).

(The Klein Bottle); Konrad Polthier, Free University of Berlin.

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When I was fourteen, I started collecting mathematical curiosities. Ive been doing that for nearly fifty years now, and the collection has outgrown the original notebook. So when my publisher suggested putting together a mathematical miscellany, there was no shortage of material. The result was Professor Stewarts Cabinet of Mathematical Curiosities.

Cabinet was published in 2008, and, as Christmas loomed, it began to defy the law of gravity. Or perhaps to obey the law of levity. Anyway, by Boxing Day it had risen to number 16 in a well-known national bestseller list, and by late January it had peaked at number 6. A mathematics book was sharing company with Stephenie Meyer, Barack Obama, Jamie Oliver and Paul McKenna.

This was, of course, completely impossible: everyone knows that there arent that many people interested in mathematics. Either my relatives were buying a huge number of copies, or the conventional wisdom needed a rethink. So then I got an email from my publisher asking whether there might be any prospect of a sequel, and I thought, My suddenly famous Cabinet is still bursting at the seams with goodies, so why not? Professor Stewarts Hoard of Mathematical Treasures duly emerged from darkened drawers into the bright light of day.

Its just what you need to while away the hours on your desert island. Like its predecessor, you can dip in anywhere. In fact, you could shuffle both books together, and still dip in anywhere. A miscellany, I have said before and stoutly maintain, should be miscellaneous. It need not stick to any fixed logical order. In fact, it shouldnt, if only because there isnt one. If I want to sandwich a puzzle allegedly invented by Euclid between a story about Scandinavian kings playing dice for the ownership of an island and a calculation of how likely it is for monkeys to randomly type the complete works of Shakespeare, then why not?

We live in a world where finding time to work systematically through a long and complicated argument or discussion gets ever more difficult. Thats still the best way to stay properly informed - Im not decrying it. I even try it myself when the world lets me. But when the scholarly method wont work, theres an alternative, one that requires only a few minutes here and there. Apparently quite a lot of you find that to your taste, so here we go again. As one radio interviewer remarked about Cabinet (sympathetically, I believe), I suppose its the ideal toilet book. Now, Avril and I actually go out of our way not to leave books in the loo for visitors to read, because we dont want to have to bang on the door at 1 a.m. to remove a guest who has found War and Peace unexpectedly gripping. And we dont want to risk getting stuck in there ourselves.

But there you go. The interviewer was right. And like its predecessor, Hoard is just the kind of book to take on a train, or a plane, or a beach. Or to sample at random over Boxing Day, in between watching the sports channels and the soaps. Or whatever it is that grabs you.

Hoard is supposed to be fun, not work. It isnt an exam, there is no national curriculum, there are no boxes to tick. You dont need to prepare yourself. Just dive in.

A few items do fit naturally into a coherent sequence, so Ive put those next to each other, and earlier items do sometimes shed light on later ones. So, if you come across terms that arent being explained, then probably I discussed them in an earlier item. Unless I didnt think they needed explanation, or forgot. Thumb quickly through the earlier pages seeking insight. If youre lucky, you may even find it.