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SCOTT SIMON, host:

We're going to talk about a book for children right now. Not with our old friend Daniel Pinkwater. We need a little mathematical expertise for this one. The book is called You Can Count On Monsters and it's about prime numbers and prime factorizations.

Thankfully, we have a math whiz, our old friend Keith Devlin on the line. He joins us from Stanford.

Welcome back, Keith.

Mr. KEITH DEVLIN (The Math Guy): Thanks, Scott. It's good to be talking about a math book I can actually enjoy.

SIMON: The book, You Can Count On Monsters, is written by Richard Evan Schwartz, and hes a math professor at Brown University. I'm assuming you guys go to conventions together or something, right?

Mr. DEVLIN: I actually haven't met the author but I was at a convention a couple of weeks ago. I was browsing the book display.

SIMON: Mm-hmm.

Mr. DEVLIN: This one book in the corner just jumped out, I grabbed over, I talked to the publisher and I said, I've got to talk to Scott about this on NPR. This is one of the most amazing math books for kids I have ever seen.

SIMON: Well, help us understand it. Firstly, the illustrations are extraordinary.

Mr. DEVLIN: Oh, yeah, they just jump out. Its beautiful. I mean the author, who is a professor of mathematics at Brown, has this incredible ability to do really good artwork. The kind of artwork that appeals to anyone from the ages of sort of two or three years old all the way to being elderly like myself. Its great colors, it's wonderful, and yet because he knows the mathematics, he very skillfully and subtly embeds mathematical ideas into the drawings. You can tell it's sort of mathematical because his monsters in the book. It's all about monsters.

SIMON: Every number gets a monster.

Mr. DEVLIN: Thats right, and they look vaguely geometrical. And the prime monsters are monsters that can't be broken up into simpler monsters, like the prime numbers, and the composite monsters are made up of simpler monsters. In fact, if you look at each composite monster, part of the fun is figuring out how the artist has embedded all of the prime monsters in it, so the monsters follow the structure of the numbers. It's beautifully done.

SIMON: And whats the best working definition of a prime number?

Mr. DEVLIN: A prime number is a number thats only divisible by itself and one. One itself is excluded, so the examples are 2, 3, 5, 7, 11, 13, 17, 19. Composite numbers, the non-primes, are the ones which can be broken up into a product of smaller numbers, like four, which is 2x2, six, which is 2x3 or 15, which is 3x5.

SIMON: Take a look, Keith. You have the book in front of you?

Mr. DEVLIN: I have the book in front of me.

SIMON: Take a look at 31.

Mr. DEVLIN: The number 31. Okay, lets have a look. Its on six, six, six, six, six...

SIMON: Its just beautifully serpentine.

Mr. DEVLIN: Oh, the serpentine, the snake and you have to find out where there's a 31. And my guess is there's probably 31 corners in there. But I might be wrong. I might have to sit down and count and kids would love to do the counting. Kids love to recognize patterns. They love to count.

SIMON: Yes.

Mr. DEVLIN: And each of these you have to find out where is the 31 in there and its gorgeous. I mean the other nice thing is the diagrams are clearly geometrical, because they have corners and edges, but they have personalities.

SIMON: Yeah.

Mr. DEVLIN: I mean these monsters are fun creatures that you would like to have as pets or I would.

(Soundbite of laughter)

SIMON: No, I would too, particularly 31.

Mr. DEVLIN: Yeah. Yeah.

SIMON: Youngsters can start thumbing through this book at any age and really begin to...

Mr. DEVLIN: I would think at any age, yeah.

SIMON: ...begin to understand at the age of lets say five or six I should think.

Mr. DEVLIN: Yeah. And the parents, I mean parents, even the nonmathematical parents, don't really need to be afraid of this one because the parent can learn as he or she is going along, because there's a little guide at the front and a little bit of information at the back to help you understand what's going on. And it's only counting in multiplication.

SIMON: The illustrations in this book help make a visual association for youngsters so that it's characterized in their heads. It's not just, forgive me saying this to you Keith, it's not just a bunch of numbers. Theyve become kind of real properties of the way they see the world.

Mr. DEVLIN: Oh, indeed. And thats the point. The thing that distinguishes mathematicians is that we at some stage in our development, we develop this understanding that numbers do have personalities, they have structures, they have relationships, we form that but most people don't manage to get it.

What Schwartz has managed to do is use his own skill as an artist to bring out some of the personalities. And the point is that what he brings out through his art is actually structure and the personality that those of us in the business have always seen; we just haven't got the tools and the ability to make it accessible the way Schwartz has managed. Its the skill he has an artist that makes it work.

SIMON: Keith, thanks so much for bringing this to our attention.

Mr. DEVLIN: My pleasure. I'm just delighted to get the word about this wonderful book out there.

SIMON: Our Math Guy, Keith Devlin, speaking from Stanford.

Thanks so much, Keith.

Mr. DEVLIN: Okay. Great. That was fun.

SIMON: And you can see a slide show of the illustrations in "You Can Count On Monsters" on our website, npr.org.

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