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# Colin Maclaurin

Colin Maclaurin (February 1698 – 14 June 1746) was a Scottish mathematician. 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]

Life and work

Maclaurin was born in Kilmodan, Argyll. His father, Reverend and Minister of Glendaruel John Maclaurin, died when Maclaurin was in infancy, and his mother before he reached nine years of age. He was then educated under the care of his uncle, the Reverend Daniel Maclaurin, minister of Kilfinnan.

At eleven, Maclaurin entered the University of Glasgow. He would graduate MA three years later by defending a thesis on the Power of Gravity, and remain at Glasgow to study divinity until 1717, 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.

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)

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.

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.)

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

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

See also

* Braikenridge–Maclaurin theorem

* Trisectrix of Maclaurin

References

Text document with red question mark.svg

This article includes a list of references or external links, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations where appropriate. (April 2009)

1. ^ "Colin Maclaurin: A Biographical Note" by Robin Schlapp (6 December 1946). (Note that the quotation in [1] has been altered.)

2. ^ http://www.m-a.org.uk/docs/library/2064.pdf

3. ^ http://www-groups.dcs.st-and.ac.uk/~history/Extras/Turnbull_Maclaurin_1.html Turnbull lectures on Colin Maclaurin (4 February 1947), Part I

4. ^ David McNeill (2008-05-01). "University appoints world's youngest professor". The Independent. http://www.independent.co.uk/news/world/asia/university-appoints-child-prodigy-worlds-youngest-professor-818776.html.

5. ^ "Neither Newton nor Leibniz - The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala". MAT 314. Canisius College. http://www.canisius.edu/topos/rajeev.asp. Retrieved 2006-07-09.

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 2008-01-20.

* "Overview of Colin Maclaurin". Gazetteer for Scotland. University of Edinburgh School of GeoSciences. http://www.geo.ed.ac.uk/scotgaz/people/famousfirst829.html. Retrieved 2008-01-20.

* Friedman, Erich. "Colin Maclaurin". Periodic Table of Mathematicians. Stetson University. http://www.stetson.edu/~efriedma/periodictable/html/Mg.html. Retrieved 2008-01-20.

* O'Connor, John J.; Robertson, Edmund F., "Colin Maclaurin", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Maclaurin.html .

* Sageng, Erik, 2005, "A treatise on fluxions" in Grattan-Guinness, I., ed., Landmark Writings in Western Mathematics. Elsevier: 143-58.

* Tweddle, Ian (1998). "The prickly genius—Colin Maclaurin (1698–1746)" (PDF). The Mathematical Gazette (Leicester: Mathematical Association) 82 (495): 373–378. doi:10.2307/3619883. http://www.m-a.org.uk/docs/library/2064.pdf. Retrieved 2008-01-20.

* Grabiner, Judith (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. http://www.jstor.org/stable/2974733. Retrieved 2008-12-22.

Further reading

* Bruce A. Hedman, "Colin Maclaurin's quaint word problems," College Mathematics Journal 31 (2000), 286-288.

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