So You Want To Be A Mathematician

This book opens with a trick and then makes good on it. Before we're told what a mathematician is, we're handed a certainty nobody could count their way to: somewhere in New York, two people have exactly the same number of hairs. Buckets, pigeons, one "very annoyed pigeon," and a child understands the pigeonhole principle and, more importantly, why proof beats checking. Linda Soules never lets that thesis go. The circle-and-dots puzzle where the pattern 2, 4, 8, 16 breaks at 31 sends the reader to a pencil to be fooled personally, and the book returns to it later, in "Honest Self-Checking."

What earns the top mark is how much real mathematics this book trusts a ten-year-old with. Euclid's infinitude-of-primes argument is laid out in full, with 30,031 = 59 × 509 as the worked example. Homer Simpson's wrong Fermat equation is dismantled with nothing but digit sums and divisibility by 3. The cake-cutting joke in "A Day in the Life" turns out to be a real research problem with dates attached. Nothing is condescended to, and nearly every page ends in something a kid can do.

The human stories are chosen with care. Noether teaching under a male colleague's name, Ramanujan wiping his slate with his elbow, June Huh the high-school dropout who became a Fields medalist, and the live goose Mazur owed Per Enflo all show mathematics as a human, stubborn, funny enterprise. The author's closing note ties it together: a proof doesn't care who wrote it. For a ten-year-old who has been told they're not a "math person," that is a generous thing to say, and the book has earned it.