 Colin Maclaurin

Colin Maclaurin
Colin Maclaurin (1698–1746)Born February, 1698
Kilmodan, Cowal, Argyll, ScotlandDied 14 June 1746
Edinburgh, ScotlandResidence Scotland Citizenship United Kingdom Nationality Scottish Fields Mathematician Institutions University of Aberdeen
University of EdinburghAlma mater University of Glasgow Academic advisors Robert Simson Notable students Robert Adam Known for Euler–Maclaurin formula
Maclaurin's inequality
Maclaurin seriesNotable 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]}
Contents
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 tenday 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 NewtonCotes 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.
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 HeriotWatt University, Edinburgh.
See also
 Braikenridge–Maclaurin theorem
 Trisectrix of Maclaurin
References
 ^ "Colin Maclaurin: A Biographical Note" by Robin Schlapp (6 December 1946). (Note that the quotation in [1] has been altered.)
 ^ http://www.ma.org.uk/docs/library/2064.pdf
 ^ http://wwwgroups.dcs.stand.ac.uk/~history/Extras/Turnbull_Maclaurin_1.html Turnbull lectures on Colin Maclaurin (4 February 1947), Part I
 ^ David McNeill (20080501). "University appoints world's youngest professor". The Independent. http://www.independent.co.uk/news/world/asia/universityappointschildprodigyworldsyoungestprofessor818776.html.
 ^ "Neither Newton nor Leibniz  The PreHistory of Calculus and Celestial Mechanics in Medieval Kerala". MAT 314. Canisius College. http://www.canisius.edu/topos/rajeev.asp. Retrieved 20060709.
Sources
 Anderson, William, The Scottish Nation, Edinburgh, 1867, vol.VII, p. 37.
 Ball, W. W. Rouse (1908). A Short Account of the History of Mathematics (4th ed.). pp. 384–387. http://www.maths.tcd.ie/pub/HistMath/People/Maclaurin/RouseBall/RB_Maclaurin.html. Retrieved 20080120.
 "Overview of Colin Maclaurin". Gazetteer for Scotland. University of Edinburgh School of GeoSciences. http://www.scottishplaces.info/people/famousfirst829.html. Retrieved 20080120.
 Friedman, Erich. "Colin Maclaurin". Periodic Table of Mathematicians. Stetson University. http://www.stetson.edu/~efriedma/periodictable/html/Mg.html. Retrieved 20080120.
 O'Connor, John J.; Robertson, Edmund F., "Colin Maclaurin", MacTutor History of Mathematics archive, University of St Andrews, http://wwwhistory.mcs.standrews.ac.uk/Biographies/Maclaurin.html.
 Sageng, Erik, 2005, "A treatise on fluxions" in GrattanGuinness, I., ed., Landmark Writings in Western Mathematics. Elsevier: 14358.
 Tweddle, Ian (November 1998). "The prickly genius—Colin Maclaurin (1698–1746)" (PDF). The Mathematical Gazette (Leicester: Mathematical Association) 82 (495): 373–378. doi:10.2307/3619883. JSTOR 3619883. Archived from the original on 20071031. http://web.archive.org/web/20071031133538/http://www.ma.org.uk/docs/library/2064.pdf. Retrieved 20080120.
 Grabiner, Judith (May 1997). "Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions" (PDF). The American Mathematical Monthly (Mathematical Association of America) 104 (5): 393–410. doi:10.2307/2974733. JSTOR 2974733.
Further reading
 Bruce A. Hedman, "Colin Maclaurin's quaint word problems," College Mathematics Journal 31 (2000), 286288.
 Bruneau, Olivier (2011). Colin Maclaurin, l'obstination mathématicienne d'un newtonien. Presses Universitaires de Nancy.
Categories: 1698 births
 1746 deaths
 People from Argyll and Bute
 18thcentury mathematicians
 Burials at Greyfriars Kirkyard
 Alumni of the University of Glasgow
 Academics of the University of Aberdeen
 Deaths from edema
 Fellows of the Royal Society
 Scottish mathematicians
 Members of the Philosophical Society of Edinburgh
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