Playfair was professor of mathematics and later professor of natural philosophy at Edinburgh University. He is best known for his book Illustrations of the Huttonian Theory of the Earth (1802), which was a summary of the work of James Hutton. It was through this that Hutton's principal of uniformitarianism, later taken up by Charles Lyell, first reached a wide audience.
In 1795 Playfair created an alternative formulation of Euclid's parallel postulate called Playfair's axiom.