Curiosities is a miscellany of intriguing mathematical games,
puzzles, stories, and factoids. Most items stand by themselves, so you
can dip in at almost any point. A few form short mini-series. I incline
to the view that a miscellany should be miscellaneous, and this one is.
The games and puzzles include some old favourites, which tend to
reappear from time to time, and often cause renewed excitement when
they do—the car and the goats, and the 12-ball weighing puzzle,
both caused a huge stir in the media: one in the USA, the other in the
UK. A lot of the material is new, specially designed for this book.
I’ve striven for variety, so there are logic puzzles, geometric
puzzles, numerical puzzles, probability puzzles, odd items of
mathematical culture, things to do, and things to make.
One of the virtues of knowing a bit of maths is that you can impress
the hell out of your friends. (Be modest about it, though, that’s
my advice. You can also annoy the hell out of your friends.) A good way
to achieve this desirable goal is to be up to speed on the latest
buzzwords. So I’ve scattered some short ‘essays’ here
and there, written in an informal, non-technical style. The essays
explain some of the recent breakthroughs that have featured prominently
in the media. Things like Fermat’s Last Theorem—remember
the TV programme? And the Four Colour Theorem, the Poincaré
Conjecture, Chaos Theory, Fractals, Complexity Science, Penrose
Patterns. Oh, and there are also some unsolved questions, just to show
that maths isn’t all done. Some are recreational, some
serious—like the P=NP? problem, for which a million-dollar prize
is on offer. You may not have heard of the problem, but you need to
know about the prize.
Shorter, snappy sections reveal interesting facts and discoveries about
familiar but fascinating topics: π, prime numbers, Pythagoras’
Theorem, permutations, tilings. Amusing anecdotes about famous
mathematicians add a historical dimension and give us all a chance to
chuckle sympathetically at their endearing foibles…