[2] Smith was born in Maybole, Scotland, where his father, William, was a merchant.
[1][3] He studied at the University of Glasgow beginning in 1736, entered Balliol College, Oxford in 1744 with the support of the Snell Exhibition, and earned a B.A.
[1][3] He then studied under Nathan Alcock in St Mary Hall, earning his doctorate in 1757.
[1][4] Alcock left Oxford for Bath in the same year, and Smith took his place.
[2][5] Despite not being a mathematician, he held the Savilian chair of geometry from 1766 until his death in 1797.