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Stirling studied infinite series, summation, interpolation and quadrature
Stirling matriculated at Balliol College Oxford in 1710. However he lost his scholarships because he was a Jacobite supporter and corresponded with Jacobites while at Oxford. In 1717 Stirling published his first work Lineae Tertii Ordinis Neutonianae which extends Newton's theory of plane curves of degree 3. In the same year he went to Venice to take up a chair of mathematics but the appointment somehow fell through. He certainly submitted a paper to the Royal Society of London in 1719 from Venice. In 1721 he attended the University of Padua.
In 1722 Stirling returned to Glasgow and in 1725 he travelled to London where he was to remain for 10 years. While in London he was elected to the Royal Society in 1726 and published his most important work Methodus Differentialis in 1730. This book is a treatise on infinite series, summation, interpolation and quadrature. The asymptotic formula for n! for which Stirling is best known appears as Example 2 to Proposition 28 of Methodus Differentialis .
In 1735 he returned to Scotland where he became manager of the 'Scotch mining company, Leadhills' at a salary of £120 per year. In 1745 Stirling published a paper on the ventilation of mine shafts.
In 1746 he was elected to membership of the Royal Academy of Berlin. In the same year Maclaurin died and Stirling was offered his chair at Edinburgh but he declined the offer. In 1753 he resigned from the Royal Society of London as he was in debt to the Society and could no longer afford the annual subscriptions. It cost him £20 to resign.
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