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.
Hugh Blackburn was brought up at Killearn House, Stirlingshire, the seventh of eight children of the wealthy Glasgow merchant John Blackburn and his wife Rebecca Leslie Gillies, the daughter of a Church of Scotland minister, and a relative of Colin Maclaurin. His elder brother was the judge Colin Blackburn, Baron Blackburn.
He was educated at Edinburgh Academy and Eton before entering Trinity College, Cambridge in 1840. There he met Thomson, who entered in the same year; he was also a member of the Cambridge Apostles. During this time he invented the Blackburn pendulum. In the Mathematical Tripos examinations of 1845 he graduated fifth wrangler, while Thomson graduated second wrangler.
- A treatise on trigonometry, London, 1855. Part of the Encyclopedia Metropolitana.
- A short sketch of the constitutional history of the University of Glasgow and of Glasgow College in that University : with remarks on the Universities (Scotland) Bill, 1858
- (ed. with William Thomson ) Sir Isaac Newton's Principia, 1871
- Elements of plane trigonometry for the use of the junior class of mathematics in the University of Glasgow, 1871