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 was brought up at Killearn House, Stirlingshire, the seventh of eight children of 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 father became wealthy off sugar and slavery in Jamaica, becoming a merchant on his return to Glasgow.

[2] Blackburn was educated at the Edinburgh Academy and Eton before entering Trinity College, Cambridge in 1840.

He entered the Inner Temple in 1847 but was never called to the bar; his name was withdrawn in 1849, the year in which he became a professor of mathematics at the University of Glasgow.