Hardy argued that mathematics exists as a separate reality and that discoveries about math are merely observations of that reality through the use of thought. He used analytic geometry (which he called “real” geometry) as an example. Analytic geometry uses graphs—formally, Cartesian coordinate systems—to study geometric forms. It’s the type of geometry most familiar to the public, the one used by engineers when they calculate orbits or build bridges. The lines, circles, triangles, and other geometric elements are drawn on a graph, and their lengths are precisely determined by the graph’s coordinates, usually the horizontal X, or abscissa, line and the vertical Y, or ordinate, line.

Although analytic geometry is highly useful in the real world, Hardy pointed out that its theorems are entirely independent of physical reality. As an example, he noted that if a drawing of a triangle is badly executed or distorted in some way, the principles that underlie the drawing remain unchanged.

Played with balls and bats, cricket is an English game that has become popular the world over. Vaguely similar to baseball, cricket includes a bowler who tries to knock the top off one of a “wicket” defended by a batter who tries to hit the ball deep into the outfield and score “runs” by running between his wicket and another one 20 meters away.