Matthew Stewart attended school on the Isle of Bute, then in 1734 he began to work under Simson at the University of Glasgow. In 1741 he began to work under Maclaurin at the University of Edinburgh. During this time he continued to correspond with Simson, who was by now a friend rather than a teacher, on Greek geometry.
Stewart was licensed to preach at Dunoon in 1744, then one year later he became a minister at Roseneath, Dumbartonshire. He resigned when appointed to Maclaurin's chair at Edinburgh in 1747. Maclaurin had left to serve the troops in the Jacobite rebellion of 1745.
Stewart's fame is based on General Theorems (1746), described by Playfair as
among the most beautiful, as well as most general, propositions known in the whole compass of geometry.
In 1756 Stewart wrote on Kepler's second law of planetary motion using geometrical methods.
In 1761 Stewart wrote Tracts Physical and Mathematical describing planetary motion and the perturbation of one planet on another and, two years later, he wrote the supplement The Distance of the Sun from the Earth determined by the Theory of Gravity. This work achieved the rather inaccurate result of 119 million miles (the correct value is approximately 93 million miles). His geometrical methods required too many simplifications to get a better result and this work was criticised by John Landen in 1771.
Stewart was elected a Fellow of the Royal Society in 1764. In 1772 his health began to deteriorate and his duties as professor at Edinburgh were taken over by his son Dugald.