Colin Maclaurin

Colin Maclaurin

Colin Maclaurin (1698–1746)
Born February, 1698 (1698-02-20)
Kilmodan, Cowal, Argyll, Scotland
Died 14 June 1746 (1746-06-15)
Edinburgh, Scotland
Residence Scotland
Citizenship United Kingdom
Nationality Scottish
Fields Mathematician
Institutions University of Aberdeen
University of Edinburgh
Alma mater University of Glasgow
Academic advisors Robert Simson
Notable students Robert Adam
Known for Euler–Maclaurin formula
Maclaurin's inequality
Maclaurin series
Notable awards Académie des Sciences, Grand Prize

Colin Maclaurin (February 1698 – 14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra. The Maclaurin series, a special case of the Taylor series, are named after him.

Due to changes in orthography since that time (his name was originally rendered as e.g. "M'Laurine"[1]), his surname is alternatively written MacLaurin.[2] In Gaelic the name is "Cailean MacLabhruinn", which is literally 'Colin, the son of Laurence.'[3]


Early life

Maclaurin was born in Kilmodan, Argyll. His father, Reverend and Minister of Glendaruel John Maclaurin, 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, the Reverend Daniel Maclaurin, minister of Kilfinnan.

Academic career

At eleven, Maclaurin entered the University of Glasgow. He graduated MA three years later by defending a thesis on the Power of Gravity, and remain at Glasgow to study divinity until he was 19, when he was elected professor of mathematics in a ten-day competition at the Marischal College in the University of Aberdeen. He would hold the record as the world's youngest professor until March 2008, when the record was officially given to Alia Sabur.[4]

In the vacations of 1719 and 1721, Maclaurin went to London, where he became acquainted with Sir Isaac Newton, Dr. Hoadley, Dr. Samuel Clarke, Martin Folkes, and other eminent philosophers. He was admitted a member of the Royal Society.

In 1722, having provided a substitute for his class at Aberdeen, he traveled on the Continent as tutor to George Hume, the son of Alexander Hume, 2nd Earl of Marchmont. During their time in Lorraine, he wrote his essay on the Percussion of Bodies, which would gain the prize of the 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 Edinburgh, James Gregory (brother of David Gregory and nephew of the esteemed James Gregory), upon the recommendation of Isaac Newton. On November 3 of that year Maclaurin would succeed Gregory, and be credited with raising 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

Though Taylor series were known before Newton and Gregory (Grabiner 1997), and in special cases by Madhava of Sangamagrama in fourteenth century India, Maclaurin attributed Taylor in his work on approximating functions by series.[5] At the time, Maclaurin was unaware and published his work in Methodus incrementorum directa et inversa, Maclaurin series which are Taylor series expanded around 0, and are not attributed to Maclaurin due to the past discoveries, but still receive credit because of his use of them. In particular, he used these series to characterize maxima, minima, and points of inflection for infinitely differentiable functions.

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 spheroids. (Grabiner 1997)

Independently from Euler and using the same methods, Maclaurin discovered the Euler–Maclaurin formula. He used it to sum powers of arithmetic progressions, derive Stirling's formula, and to derive the Newton-Cotes numerical integration formulas which includes Simpson's rule as a special case. (Grabiner 1997)

Maclaurin contributed to the study of elliptic integrals, 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.(Grabiner 1997)

Personal life

In 1733, Maclaurin married Anne Stewart, the daughter of Walter Stewart, the Solicitor General for Scotland, by whom he had seven children.

Maclaurin actively opposed the Jacobite Rebellion of 1745 and superintended the operations necessary for the defence of Edinburgh against the Highland army. Upon entry into the city, however, he fled to York, where he was invited to stay by the Archbishop of York.

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 Jacobite army marched south, but died soon after his return.

He is buried at Greyfriars Kirkyard, Edinburgh.

Mathematician and former MIT President Richard Cockburn Maclaurin is from the same family.

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 on Algebra - 1748 (two years after his death.)
  • Account of Newton's Discoveries - Incomplete upon his death and published in 1750 or 1748 (sources disagree)

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

See also



Further reading

  • Bruce A. Hedman, "Colin Maclaurin's quaint word problems," College Mathematics Journal 31 (2000), 286-288.
  • Bruneau, Olivier (2011). Colin Maclaurin, l'obstination mathématicienne d'un newtonien. Presses Universitaires de Nancy. 

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  • Colin Maclaurin — Naissance février 1698 Kilmodan (Écosse) Décès 14 juin 1746 Édimbourg (Écosse) Nationalité Écosse Champs …   Wikipédia en Français

  • Colin MacLaurin — Naissance Février 1698 Kilmodan (Écosse) Décès 14 juin 1746 Édimbourg (Écosse) …   Wikipédia en Français

  • Colin MacLaurin — (* Februar 1698 in Kilmodan; † 14. Juni 1746 in Edinburgh) war ein schottischer Mathematiker. Maclaurin wurde mit 19 Jahren Professor in Aberdeen und ab 1726 in Edinburgh. Er verfasste 1742 sein wichtigstes Werk A treatise of fluxions und war… …   Deutsch Wikipedia

  • Colin Maclaurin — (* Februar 1698 in Kilmodan, Argyllshire, Schottland; † 14. Juni 1746 in Edinburgh) war ein schottischer Mathematiker. Maclaurin war der Sohn des Pfarrers in dem Dorf Kilmoden am Fluss Ruel. Sein Vater starb, als er sechs Wochen alt war und die… …   Deutsch Wikipedia

  • Colin Maclaurin — Colin Maclaurin. Colin MacLaurin (Kilmodan, febrero de 1698 Edimburgo, 14 de junio de 1746)[1] fue un matemático escocés. Hijo de un ministro de parroquia en Argyll (Esco …   Wikipedia Español

  • Maclaurin — Colin Maclaurin Colin Maclaurin (* Februar 1698 in Kilmodan; † 14. Juni 1746 in Edinburgh) war ein schottischer Mathematiker. Maclaurin wurde mit 19 Jahren Professor in Aberdeen und ab 1726 in Edinburgh. Er verfasste 1742 sein wichtigstes Werk A… …   Deutsch Wikipedia

  • MACLAURIN (C.) — MACLAURIN COLIN (1698 1746) Mathématicien écossais, né à Kilmodan, qui a développé et poursuivi l’œuvre de sir Isaac Newton en analyse, en géométrie et en mécanique. Enfant prodige, Colin Maclaurin entra à l’université de Glasgow à l’âge de onze… …   Encyclopédie Universelle

  • Maclaurin — or MacLaurin (with a capital L ) may refer to:People with the surname Maclaurin: * Colin Maclaurin (1698–1746), Scottish mathematician * Normand MacLaurin (1835–1914), Australian politician and university administrator * Henry Normand MacLaurin… …   Wikipedia

  • Colin (given name) — Colin Pronunciation /ˈkɒlɨn/, occasionally /ˈkoʊlɨn/ Origin Meaning Various meanings including young pup , whelp , cub , victorious people , dark , dove Colin is a male given name. Colin i …   Wikipedia

  • Maclaurin (Mondkrater) — Eigenschaften Breite 1,8° S Länge 68,0° O Durchmesser 50 km Tiefe 1,5 km Selenografische Länge 292° bei Sonnenaufgang Benannt nach Colin Maclaurin …   Deutsch Wikipedia

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