James Stirling (mathematician)

2025-08-23T16:52:44Z

2003:C3:6717:2500:2C2E:40FB:3E21:5C59: /* Biography */

{{Short description|Scottish mathematician}}
{{Use dmy dates|date=September 2021}}
{{Use British English|date=April 2012}}
{{Infobox scientist
| name = James Stirling
| birth_date = 11 May<ref>Monument to the Stirlings of Garden, Dunblane Cathedral</ref> [[Old Style and New Style dates|O.S.]] 1692<ref>[https://books.google.com/books?id=_fU8k16vbsMC&dq=James+Stirling+may+1692&pg=PA378 ''Algebraic number theory''] by Richard A. Mollin</ref><ref>[http://www.bibmath.net/bios/index.php3?action=affiche&quoi=stirling Bibmath.net] {{webarchive|url=https://web.archive.org/web/20090910075329/http://www.bibmath.net/bios/index.php3?action=affiche&quoi=stirling |date=10 September 2009 }}</ref>
| birth_place = Garden, [[Stirlingshire]]
| death_date = 5 December 1770 (aged 78)
| death_place = [[Edinburgh]], [[Scotland]]
| resting_place = [[Greyfriars Kirkyard]]
| nationality = Scottish
| fields = {{unbulleted list
| {{hlist | [[Mathematics]] }}
}}
| known_for = {{unbulleted list
| [[Stirling's approximation]] | [[Stirling number]]s
}}
}}
'''James Stirling''' (11 May<ref>Monument to the Stirlings of Garden, Dunblane Cathedral</ref> [[Old Style and New Style dates|O.S.]] 1692,<ref>[https://books.google.com/books?id=_fU8k16vbsMC&dq=James+Stirling+may+1692&pg=PA378 ''Algebraic number theory''] by Richard A. Mollin</ref><ref>[http://www.bibmath.net/bios/index.php3?action=affiche&quoi=stirling Bibmath.net] {{webarchive|url=https://web.archive.org/web/20090910075329/http://www.bibmath.net/bios/index.php3?action=affiche&quoi=stirling |date=10 September 2009 }}</ref> Garden, [[Stirlingshire]] – 5 December 1770, [[Edinburgh]]) was a [[Scotland|Scottish]] [[mathematician]]. He was nicknamed "'''The Venetian'''".

The [[Stirling number]]s, [[Stirling permutation]]s, and [[Stirling's approximation]] are named after him. He also proved the correctness of [[Isaac Newton]]'s classification of [[cubic plane curve]]s.<ref>''Conics and Cubics'', Richard Bix, 2nd edition, Springer Verlag UTM, 2006.</ref>

==Biography==
[[File:Grave of James Stirling (1692-1770), general view.jpg|thumb|265px|Stirling's grave in [[Greyfriars Kirkyard]], Edinburgh, general view. It is the small plate between the two large tablets.]]
[[File:Grave of James Stirling (1692-1770), detail.jpg|thumb|265px|Stirling's grave in [[Greyfriars Kirkyard]], Edinburgh, detail]]
[[File:Plaque to the Stirlings of Garden, Dunblane Cathedral.jpg|thumb|265px|Plaque to the Stirlings of Garden, [[Dunblane Cathedral]]]]
Stirling was born on 11 May 1692<ref>Monument to the Stirlings of Garden, Dunblane Cathedral</ref> [[Old Style and New Style dates|O.S.]] at Garden House near Stirling, the third son of Archibald Stirling (1651−1715) and Anna Hamilton, and grandson of [[Archibald Stirling, Lord Garden]], (1617−1668).<ref>{{Cite journal |last=Maritz |first=Pieter |date=2011-09-01 |title=James Stirling: Mathematician and Mine Manager |url=https://doi.org/10.1007/s00283-010-9193-0 |journal=The Mathematical Intelligencer |language=en |volume=33 |issue=3 |pages=141–147 |doi=10.1007/s00283-010-9193-0 |issn=1866-7414|url-access=subscription }}</ref>

At 18 years of age he went to [[Balliol College, Oxford]], where, chiefly through the influence of the [[John Erskine, Earl of Mar (1675–1732)|Earl of Mar]], he was nominated in 1711 to be one of Bishop Warner's exhibitioners (or [[Snell exhibitioner]]) at Balliol. In 1715 he was expelled on account of his correspondence with his cousins, who were members of the Keir and Garden families, who were noted [[Jacobitism|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 [[glassmaker]]s of Venice, he returned with [[Isaac Newton|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 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.<ref>{{Historic Environment Scotland|num=LB732|desc=Scots Mining Company House...|cat=A|access-date=27 March 2019}}</ref> His next paper to the Royal Society was concerned, not with pure but with applied sciences; specifically, a [[trompe]], i.e., a water-powered air compressor that was used by a Scottish lead mine.<ref>{{cite journal|last1=Stirling|first1=James|title=A description of a machine to blow fire by the fall of water|journal=Philosophical Transactions of the Royal Society of London|date=1744|volume=43|issue=475|pages=315–317|doi=10.1098/rstl.1744.0069|doi-access=free}}</ref> 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 million [[Pound sterling|sterling]] spent in making Glasgow a seaport (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.

==Notes==
{{reflist}}

==See also==
*[[Stirling polynomials]]
*[[Stirling transform]]

==References==
[[File:Stirling - Methodus differentialis, sive Tractatus de summatione et interpolatione serierum infinitarum, 1764 - 739821.tif |thumb|''Methodus differentialis'', 1764]]
*{{EB1911|wstitle=Stirling, James}} 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==
* {{MacTutor Biography|id=Stirling|title=James Stirling}}

{{Authority control}}

{{DEFAULTSORT:Stirling, James}}
[[Category:1692 births]]
[[Category:1770 deaths]]
[[Category:18th-century Scottish mathematicians]]
[[Category:People from Stirling (council area)]]
[[Category:Clan Stirling|James]]
[[Category:Combinatorialists]]
[[Category:Alumni of the University of Glasgow]]
[[Category:Alumni of Balliol College, Oxford]]
[[Category:Fellows of the Royal Society]]
[[Category:Scottish expatriates in Italy]]
[[Category:Scottish Jacobites]]
[[Category:Scottish surveyors]]
[[Category:British technology writers]]

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James Stirling (mathematician)