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{{Short description|Scottish mathematician (1698 – 1746)}}
{{Use dmy dates|date=February 2020}}
{{Use British English|date=May 2012}}
{{Infobox scientist
| name              = Colin Maclaurin
| image             = Colin Maclaurin (Buchan-Ferguson).jpg
| caption           = Drawing by [[David Erskine, 11th Earl of Buchan|David Steuart Erskine]] {{circa}} 1795, from a portrait by [[James Ferguson (Scottish astronomer)|James Ferguson]]
| birth_date        = February 1698
| birth_place       = [[Kilmodan]], [[Cowal]], [[Argyll]], [[Scotland]]
| death_date        = 14 June 1746 (aged 48)
| death_place       = [[Edinburgh]], [[Scotland]]
| citizenship       = [[Kingdom of Great Britain|Great Britain]]
| nationality       = Scottish
| fields            = [[Mathematician]]
| workplaces        = [[Marischal College]], [[University of Aberdeen]]<br />[[University of Edinburgh]]
| alma_mater        = [[University of Glasgow]]
| doctoral_advisor  = 
| academic_advisors = [[Robert Simson]]
| doctoral_students = 
| notable_students  = [[Robert Adam]]
| known_for         = [[Euler–Maclaurin formula]]<br>[[Maclaurin's inequality]]<br>[[Maclaurin series]]<br>[[Maclaurin spheroid]]<br>[[Maclaurin–Cauchy test]]<br>[[Braikenridge–Maclaurin theorem]]<br>[[Trisectrix of Maclaurin]]
| influences        = 
| influenced        = 
| awards            = Grand Prize of the [[French Academy of Sciences]]
| signature         = 
| footnotes         = 
}}

'''Colin Maclaurin''' ({{IPAc-en|m|ə|ˈ|k|l|ɔː|r|ə|n}}; {{langx|gd|Cailean MacLabhruinn}};{{pronunciation needed|date=September 2024}} February 1698&nbsp;– 14 June 1746)<ref>http://www-groups.dcs.st-and.ac.uk/Extras/Turnbull_Maclaurin_1.html Turnbull lectures on Colin Maclaurin (4 February 1947), Part I</ref> was a Scottish [[mathematician]] who made important contributions to [[geometry]] and [[algebra]].<ref>{{cite EB1911|wstitle=Maclaurin, Colin}}</ref> He is also known for being a [[child prodigy]] and holding the record for being the youngest professor. The Maclaurin series, a special case of the [[Taylor series]], is named after him.

Owing to changes in [[orthography]] since that time (his name was originally rendered as '''M'Laurine'''<ref>[http://www-history.mcs.st-andrews.ac.uk/Extras/Maclaurin_EMS_notes.html "Colin Maclaurin: A Biographical Note" by Robin Schlapp (6 December 1946)]. (Note that the quotation in [http://www-groups.dcs.st-and.ac.uk/Extras/Turnbull_Maclaurin_1.html] has been altered.)</ref>), his surname is alternatively written '''MacLaurin.'''<ref>{{cite web|url=http://www.m-a.org.uk/docs/library/2064.pdf |access-date=20 January 2008 |url-status=dead |archive-url=https://web.archive.org/web/20080229073702/http://www.m-a.org.uk/docs/library/2064.pdf |archive-date=29 February 2008 |title=The prickly genius –  Colin MacLaurin (1698–1746)}}</ref>

==Early life==
{{Unreferenced section|date=January 2023}}
Maclaurin was born in [[Kilmodan]], [[Argyll]]. His father, John Maclaurin, minister of [[Glendaruel]], died when Maclaurin was in infancy, and his mother died before he reached nine years of age. He was then educated under the care of his uncle, Daniel Maclaurin, minister of Kilfinan. A [[child prodigy]], he entered university at age 11.

==Academic career==
At eleven, Maclaurin, a child prodigy at the time, entered the [[University of Glasgow]]. He graduated [[Master of Arts]] three years later by defending a thesis on ''the Power of Gravity,'' and remained at Glasgow to study [[Divinity (academic discipline)|divinity]] until he was 19, when he was elected professor of [[mathematics]] in a ten-day competition at [[Marischal College]] and University in Aberdeen. This record as the world's youngest professor endured until March 2008, when the record was officially given to [[Alia Sabur]].<ref name="theind">{{cite news|url=https://www.independent.co.uk/news/world/asia/university-appoints-child-prodigy-worlds-youngest-professor-818776.html|title=University appoints world's youngest professor|newspaper=The Independent|author=David McNeill|date=1 May 2008}}</ref>

In the vacations of 1719 and 1721, Maclaurin went to London, where he became acquainted with [[Isaac Newton]], [[Benjamin Hoadly (physician)|Benjamin Hoadly]], [[Samuel Clarke]], [[Martin Folkes]], and other philosophers. He was admitted as a member of the [[Royal Society]].

In 1722, having provided a locum for his class at Aberdeen, he travelled on the Continent as tutor to George Hume, the son of [[Alexander Hume, 2nd Earl of Marchmont]]. During their time in [[Duchy of Lorraine|Lorraine]], he wrote his essay on the percussion of bodies (''Demonstration des loix du choc des corps''), which gained the prize of the [[French Academy of Sciences|Royal Academy of Sciences]] in 1724. Upon the death of his pupil at [[Montpellier]], Maclaurin returned to Aberdeen.

In 1725, Maclaurin was appointed deputy to the mathematical professor at the [[University of Edinburgh]], James Gregory (brother of [[David Gregory (mathematician)|David Gregory]] and nephew of the esteemed [[James Gregory (astronomer and mathematician)|James Gregory]]), upon the recommendation of [[Isaac Newton]]. On 3 November of that year Maclaurin succeeded Gregory, and went on to raise the character of that university as a school of science. Newton was so impressed with Maclaurin that he had offered to pay his salary himself.

==Contributions to mathematics==
[[File:Acta Eruditorum - I monete geometria, 1747 – BEIC 13417751 (cropped).jpg|thumb|Illustration of critique of ''De fluxionibus libri duo'' published in [[Acta Eruditorum]], 1747]]
Maclaurin used [[Taylor series]] to characterize maxima, minima, and points of inflection for infinitely differentiable functions in his ''Treatise of Fluxions''. Maclaurin attributed the series to [[Brook Taylor]], though the series was known before to [[Isaac Newton|Newton]] and [[James Gregory (mathematician)|Gregory]], and in special cases to [[Madhava of Sangamagrama]] in fourteenth century India.<ref>{{cite web
| publisher=Canisius College
| work=MAT 314
| url=http://www.canisius.edu/topos/rajeev.asp
| title=Neither Newton nor Leibniz&nbsp;– The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala
| access-date=9 July 2006
| url-status=dead
| archive-url=https://web.archive.org/web/20060806040307/http://www.canisius.edu/topos/rajeev.asp
| archive-date=6 August 2006
| df=dmy-all
}}</ref>
Nevertheless, Maclaurin received credit for his use of the series, and the Taylor series expanded around 0 is sometimes known as the ''Maclaurin series''.<ref name=Grabiner1997>{{cite journal
  | last=Grabiner
  | first=Judith
  |date=May 1997
  | title=Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions
  | journal=The American Mathematical Monthly
  | volume=104
  | issue=5
  | pages=393–410
  | publisher=Mathematical Association of America
  | format=[[PDF]]
  | doi=10.2307/2974733
  | jstor = 2974733| url=http://scholarship.claremont.edu/pitzer_fac_pub/121
  }}</ref>
[[File:Colin Maclaurin color.jpg|thumb|Colin Maclaurin (1698–1746)]]
Maclaurin also made significant contributions to the gravitation attraction of ellipsoids, a subject that furthermore attracted the attention of d'Alembert, A.-C. Clairaut, Euler, Laplace, Legendre, Poisson and Gauss.  Maclaurin showed that an oblate spheroid was a possible equilibrium in Newton's theory of gravity. The subject continues to be of scientific interest, and Nobel Laureate [[Subramanyan Chandrasekhar]] dedicated a chapter of his book ''Ellipsoidal Figures of Equilibrium'' to [[Maclaurin spheroid]]s.<ref name=Grabiner1997/> Maclaurin corresponded extensively with [[Alexis Clairaut|Clairaut]], [[Pierre Louis Maupertuis|Maupertuis]], and [[Jean-Jacques d'Ortous de Mairan|d'Ortous de Mairan]].<ref>{{cite book|editor=Mills, Stella|isbn=0906812089|lccn=81215733|title=The collected letters of Colin Maclaurin (1698–1746)|location=Nantwich, Cheshire, UK|publisher=Shiva|year=1982|postscript=; xx+496 pages, 218 letters; correspondents include Newton, Halley, [[Robert Simson|Simson]], de Moivre, Voltaire, Sir [[Hans Sloane]] & Sir [[Martin Folkes]] }}</ref><ref>{{cite journal|doi=10.1126/science.218.4567.45|title=Review of ''The Collected Letters of Colin Maclaurin'', edited by Stella Mills|year=1982 |last1=Hankins |first1=Thomas L. |author-link=Thomas L. Hankins|journal=Science |volume=218 |issue=4567 |pages=45–46 |pmid=17776705 }}</ref>

Independently from [[Euler]] and using the same methods, Maclaurin discovered the [[Euler–Maclaurin formula]].  He used it to sum powers of [[arithmetic progression]]s, derive [[Stirling's formula]], and to derive the Newton–Cotes numerical integration formulas which includes [[Simpson's rule]] as a special case.<ref name=Grabiner1997/>

Maclaurin contributed to the study of [[elliptic integral]]s, reducing many intractable integrals to problems of finding arcs for hyperbolas.  His work was continued by d'Alembert and Euler, who gave a more concise approach.<ref name=Grabiner1997/>

In his ''Treatise of Algebra'' (Ch. XII, Sect 86), published in 1748 two years after his death, Maclaurin proved a rule for solving square linear systems in the cases of 2 and 3 unknowns, and discussed the case of 4 unknowns.<ref>{{cite book
  | last = MacLaurin
  | first = Colin
  | title = A Treatise of Algebra, in Three Parts.
  | url = https://archive.org/details/atreatisealgebr03maclgoog
  | year = 1748
| publisher = Printed for A. Millar & J. Nourse
 }}</ref><ref>{{cite journal
  | last=Hedman
  | first=Bruce
  |date=November 1999
  | title=An Earlier Date for "Cramer's Rule"
  | journal=Historia Mathematica
  | volume=26
  | issue=4
  | pages=365–368
  | publisher=Academic Press Elsevier
  | doi=10.1006/hmat.1999.2247
  | doi-access=free
  }}</ref> This publication preceded by two years [[Gabriel Cramer|Cramer]]'s publication of a generalization of the rule to ''n'' unknowns, now commonly known as [[Cramer's rule]].

==Personal life==
[[File:The grave of Colin Maclaurin, Greyfriars Kirkyard.jpg|thumb|left|260px|The grave of Colin Maclaurin, Greyfriars Kirkyard]]
[[File:Colin MacLaurin Road, Edinburgh.JPG|thumb|Colin MacLaurin Road, Edinburgh]]
In 1733, Maclaurin married Anne Stewart, the daughter of Walter Stewart, the [[Solicitor General for Scotland]], by whom he had seven children. His eldest son [[John Maclaurin, Lord Dreghorn|John Maclaurin]] studied law, was a [[Senator of the College of Justice]], and became Lord Dreghorn; he was also joint founder of the [[Royal Society of Edinburgh]].<ref>{{cite book|title=Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002|date=July 2006|publisher=The Royal Society of Edinburgh|isbn=0-902-198-84-X|url=https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp2.pdf|access-date=24 July 2017|archive-url=https://web.archive.org/web/20160304074135/https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp2.pdf|archive-date=4 March 2016|url-status=dead}}</ref>

Maclaurin actively opposed the [[Jacobite rising of 1745]] and superintended the operations necessary for the defence of Edinburgh against the Highland army. Maclaurin compiled a diary of his exertions against the Jacobites, both within and without the city.<ref>{{Citation| last=Maclaurin | first=Colin | chapter=Colin Maclaurin's 'Journal of the Forty-five'| editor-last=Hedman| editor-first=Bruce | title=Miscellany XIII of the Scottish History Society Fifth Series volume 14| publisher=Lothian Print| place=Edinburgh, Scotland| date= 2004 |pages= 312–322}}</ref> When the Highland army entered the city, however, he fled to [[York]], where he was invited to stay by the [[Archbishop of York]].

[[File:Maclaurin grave.jpg|upright|thumb|right|Memorial, Greyfriars Kirkyard, Edinburgh]]

On his journey south, Maclaurin fell from his horse, and the fatigue, anxiety, and cold to which he was exposed on that occasion laid the foundations of [[dropsy]]. He returned to Edinburgh after the [[Jacobitism|Jacobite]] army marched south, but died soon after his return.

He is buried at [[Greyfriars Kirkyard]], [[Edinburgh]]. The simple table stone is inscribed simply "C. M. Nat MDCXCVIII Ob MDCCXLVI" and stands close to the south-west corner of the church but is supplemented by a more wordy memorial on the outer wall of the church.

The mathematician and former [[MIT]] President [[Richard Cockburn Maclaurin]] was from the same family.

The Maclaurin Society (MacSoc), the Mathematics and Statistics Society at Glasgow University, is named in his honour.

Colin MacLaurin Road within Edinburgh University's [[King's Buildings]] complex is named in his honour.

==Notable works==
Some of his important works are:

*''Geometria Organica'' – 1720
*''De Linearum Geometricarum Proprietatibus'' – 1720
*''Treatise on Fluxions'' – 1742 (763 pages in two volumes. The first systematic exposition of Newton's methods.)
*''Treatise of Algebra'' – 1748 (two years after his death.)
*''Account of Newton's Discoveries'' – Incomplete upon his death and published in 1748<ref>It cannot be in 1750, as the French translation is published in 1749 ([https://gallica.bnf.fr/ark:/12148/bpt6k1042623z/ see online at Gallica]).</ref>
* {{Cite book|title=Account of Sir Isaac Newton's philosophical discoveries|volume=|publisher=Laurent Durand|location=Paris|year=1749|language=fr|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=743185}}

Colin Maclaurin was the name used for the new Mathematics and Actuarial Mathematics and Statistics Building at [[Heriot-Watt University]], Edinburgh.

<gallery>
File:MacLaurin - Treatise of algebra, 1753 - 1429142.jpg|French edition of the ''Treatise of algebra'' (1748)
File:MacLaurin, Colin – Account of Sir Isaac Newton's philosophical discoveries, 1749 – BEIC 743185.jpg|French edition of the ''Account of Sir Isaac Newton's philosophical discoveries'' (1749)
</gallery>

==See also==
*[[Braikenridge–Maclaurin theorem]]
*[[Trisectrix of Maclaurin]]
*[[Cayley's sextic]]
*[[Cramer's paradox]]
*[[Hesse configuration]]
*[[Sinusoidal spiral]]

==References==

{{Reflist}}

==Sources==
* Anderson, William, ''The Scottish Nation'', Edinburgh, 1867, vol.VII, p.&nbsp;37.
* {{cite book
  | last = Ball
  | first = W. W. Rouse
  | author-link = W. W. Rouse Ball
  | title = A Short Account of the History of Mathematics
  | url = http://www.maths.tcd.ie/pub/HistMath/People/Maclaurin/RouseBall/RB_Maclaurin.html
  | access-date = 20 January 2008
  | edition = 4th
  | year = 1908
  | pages = 384–387 }}
* {{cite web
  | url = http://www.scottish-places.info/people/famousfirst829.html
   | title = Overview of Colin Maclaurin
  | access-date = 20 January 2008
  | work = [[Gazetteer for Scotland]]
  | publisher = [[University of Edinburgh]] School of GeoSciences }}
* {{cite web
  | url = http://www.stetson.edu/~efriedma/periodictable/html/Mg.html
  | title = Colin Maclaurin
  | access-date = 20 January 2008
  | last = Friedman
  | first = Erich
  | work = Periodic Table of Mathematicians
  | publisher = [[Stetson University]]
  | archive-url = https://web.archive.org/web/20080214180732/http://www.stetson.edu/~efriedma/periodictable/html/Mg.html
  | archive-date = 14 February 2008
  | url-status = dead
  }}
* {{MacTutor Biography|id=Maclaurin}}
*Sageng, Erik, 2005, "A treatise on fluxions" in [[Ivor Grattan-Guinness|Grattan-Guinness, I.]], ed., ''Landmark Writings in Western Mathematics''. Elsevier: 143–58.
* {{cite journal
  | last = Tweddle
  | first = Ian
  |date=November 1998
  | title = The prickly genius—Colin Maclaurin (1698–1746)
  | journal = The Mathematical Gazette
  | volume = 82
  | issue = 495
  | pages = 373–378
  | publisher = [[Mathematical Association]]
  | location = [[Leicester]]
  | url = http://www.m-a.org.uk/docs/library/2064.pdf
  | access-date = 20 January 2008
  | doi = 10.2307/3619883
  | jstor = 3619883 |archive-url = https://web.archive.org/web/20071031133538/http://www.m-a.org.uk/docs/library/2064.pdf <!-- Bot retrieved archive --> |archive-date = 31 October 2007}}

==Further reading==
{{Wikiquote}}
{{Commons and category}}
*Bruce A. Hedman, "Colin Maclaurin's quaint word problems," College Mathematics Journal 31 (2000), 286–288.
* {{cite book
  | last=Bruneau
  | first=Olivier
  | year=2011
  | title=Colin Maclaurin, l'obstination mathématicienne d'un newtonien
  | publisher=Presses Universitaires de Nancy}}
* {{cite ODNB|id=17643|title=MacLaurin, Colin|orig-year=2004|year=2006|last=Sageng|first=Erik}}

{{Authority control}}

{{DEFAULTSORT:Maclaurin, Colin}}
[[Category:1698 births]]
[[Category:1746 deaths]]
[[Category:18th-century Scottish mathematicians]]
[[Category:Burials at Greyfriars Kirkyard]]
[[Category:Alumni of the University of Glasgow]]
[[Category:Academics of the University of Edinburgh]]
[[Category:Academics of the University of Aberdeen]]
[[Category:Deaths from edema]]
[[Category:Fellows of the Royal Society]]
[[Category:Members of the Philosophical Society of Edinburgh]]
[[Category:People from Glendaruel]]