While we’re on the subject of books, here’s a book for the smaller mathematicians in your life. The ones who can’t necessarily spell “mathematician”.

The book is You Can Count on Monsters by Richard Evan Schwartz (ISBN 1568815786), and it’s a picture book about prime number decompositions. It’s much more colorful than you’re picturing, I promise.

One thing that makes this book so nice is that it doesn’t beat you over the head with anything. There are some very basic remarks about primes and multiplication at the beginning and some slightly deeper remarks at the very end, but the vast bulk of the pages have no text at all.

Each number from 1 to 100 gets a double page. On the left is the the number and a configuration of that many dots (usually clustered into spirals or some such in an interesting way). On the right is a whimsical (and strangely compelling) drawing of a monster. For a prime number, the monster is some simple monster which smoehow embodies the nature of the number (the right number of teeth, or legs, or whatever). For a composite number, the monster is in some way a conglomeration of the corresponding prime monsters. (So the 70-monster incorporates the natures of the 2-, 5-, and 7-monsters.)

There’s plenty to stare at, plenty of patterns sitting right near the surface, and plenty more lurking underneath to be discovered over time. An artistically-inclined child might try to invent prime monsters larger than 100, or to draw some composite monster. (I’ll confess that when I bought the book, I entertained myself for quite some time trying to draw the 1001 monster.) It’s just fun to look at, and it provides lots of interesting avenues for mathematical conversation with “grown-up” mathematicians.

Speaking as a number theorist, I love the way this book conveys the essential predictable/chaotic dual nature of prime numbers. There are always more monsters, but you’re never quite sure when you’ll meet the next one.

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You should post the drawing!

That’s a good point. Will do this weekend.