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James Stirling (May 1692, Garden, Stirlingshire – 5 December 1770 Edinburgh) was a Scottish mathematician. The Stirling numbers, Stirling permutations, and Stirling's approximation are named after him. He also proved the correctness of Isaac Newton's classification of cubics. Stirling was the third son of Archibald Stirling of Garden, and grandson of Sir Archibald Stirling of Keir (Lord Garden, a lord of session). At 18 years of age he went to Balliol College, Oxford, where, chiefly through the influence of the earl of Mar, he was nominated (1711) one of Bishop Warner's exhibitioners (or Snell exhibitioner) at Balliol. In 1715 he was expelled on account of his correspondence with members of the Keir and Garden families, who were noted Jacobites, and had been accessory to the "Gathering of the Brig o' Turk" in 1708.
From Oxford he made his way to Venice, where he occupied himself as a professor of mathematics. In 1717 appeared his Lineae tertii ordinis Newtonianae, sive . . . (8vo, Oxford). While in Venice, also, he communicated, through Isaac Newton, to the Royal Society a paper entitled "Methodus differentialis Newtoniana illustrata" (Phil. Trans., 1718). Fearing assassination on account of having discovered a trade secret of the glassmakers of Venice, he returned with Newton's help to London about the year 1725. In 1730 his most important work was published, the Methodus differentialis, sive tractatus de summatione et interpolatione serierum infinitarum (4to, London), which, is something more than an expansion of the paper of 1718. In 1735, he communicated to the Royal Society a paper "On the Figure of the Earth, and on the Variation of the Force of Gravity at its Surface."