Bailie Hugh Blackburn (; 2 July 1823, Craigflower, Torryburn, Fife – 9 October 1909, Roshven, Inverness-shire) was a Scottish mathematician. A lifelong friend of William Thomson (later Lord Kelvin), and the husband of illustrator Jemima Blackburn, he was professor of mathematics at the University of Glasgow from 1849 to 1879. He succeeded Thomson's father James in the Chair of Mathematics.