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James Stirling (May 1692[1][2] Garden, Stirlingshire – 5 December 1770 Edinburgh) was a Scottish mathematician. The Stirling numbers and Stirling's approximation are named after him.

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 differentials 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 London he remained for ten years, being most part of the time connected with an academy in Tower Street, and devoting his leisure to mathematics and correspondence with eminent mathematicians. In 1730 his most important work was published, the Methodus differentialis, sive tractatus de summatione et interpolatione serierum infinitarum (4to, London), which, it must be noted, 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."

In the same year he was appointed manager for the Scots Mining Company at Leadhills, where the Scots Mining Company House was built for him in 1736.[3] We are thus prepared to find that his next paper to the Royal Society was concerned, not with pure, but with applied science — "Description of a Machine to blow Fire by the Fall of Water" (Phil. Trans. 1745). His name is also connected with another practical undertaking, since grown to vast dimensions. The accounts of the city of Glasgow for 1752 show that the very first instalment of ten millions sterling spent in making Glasgow a seaport, viz. a sum of £28, 4s. 4d., was for a silver tea-kettle to be presented to "James Stirling, mathematician, for his service, pains, and trouble in surveying the river towards deepening it by locks."

Another edition of the Lineae tertii ordinis was published in Paris in 1797; another edition of the Methodus differentialis in London in 1764; and a translation of the latter into English by Halliday in London in 1749. A considerable collection of literary remains, consisting of papers, letters and two manuscript volumes of a treatise on weights and measures, are still preserved at Garden.

^ Algebraic number theory, Richard A. Mollin
^ Bibmath.net
^ "Scots Mining Company House". Historic Scotland. Retrieved 16 March 2012.

Chisholm, Hugh, ed. (1911). "Stirling, James". Encyclopædia Britannica (11th ed.). Cambridge University Press. This work in turn cites:
WP. Fraser, The Stirlings of Keir, and their Family Papers, (Edinburgh, 1858)
"Modern History of Leadhills," in Gentleman's Magazine (June, 1853)
Brewster, Memoirs of Sir Isaac Newton, ii. 300, 307, 411, 516
J. Nicol, Vital Statistics of Glasgow (1881-1885), p. 70
Glasgow Herald, 5 August 1886

External links

O'Connor, John J.; Robertson, Edmund F., "James Stirling", MacTutor History of Mathematics archive, University of St Andrews.

When k = n or n−1 we saw in the previous section that Vk(Fn) is a principal homogeneous space, and therefore diffeomorphic to the corresponding classical group. These are listed in the table at the right.

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