Maclaurin, who was born at Kilmoden in Scotland, was a child prodigy. He entered Glasgow University at the age of 11 and became professor of mathematics at Marischal College, Aberdeen, at the age of 19.

His chief work was Geometrica organica; sive descriptio linearum curvarum universalis (1720; Organic Geometry, with the Description of the Universal Linear Curves) and in this he proposed several theorems that developed along similar lines to those contained in Isaac Newton's Principia. Maclaurin became a friend of Newton and defended Newton's new theory of calculus against the polemics of the Irish philosopher George Berkeley. Maclaurin was one of the first to treat the theory of maxima and minima properly. He also contributed to the theory of the equilibrium of rotating bodies of fluid. The Maclaurin expansion, which is a special case of the Taylor series, was named for him.

Maclaurin played an important role in organizing the defense of Edinburgh against the Jacobites in 1745 and when they captured the city he was forced to flee to England.