Few equations confront a visitor to the National Museum of Mathematics on Manhattan’s East 26th Street. Instead, museumgoers find children — and adults — riding the Coaster Roller (below), a small platform that offers a surprisingly smooth ride over acorn-shaped balls. (The trick lies in the objects’ diameter, which is the same in every direction.)

This physical, tactile, even rambunctious presentation of math is intentional, says museum cofounder Glen Whitney. Too many people think math is “b...