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Colin Maclaurin
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Colin Maclaurin (February, 1698 – June 14, 1746) was a Scottish mathematician. Due to changes in orthography since that time (his name was originally rendered as e.g. "M'Laurine"), his surname is alternatively written MacLaurin. In Gaelic the name is "Cailean MacLabhruinn", which is literally 'Colin, the son of Laurence'.
Life and work
He was born in Kilmodan, Argyll. His father, the Reverend John Maclaurin, was the minister of Glendaruel and author of an Irish version of the Psalms.
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Colin Maclaurin (February, 1698 – June 14, 1746) was a Scottish mathematician. Due to changes in orthography since that time (his name was originally rendered as e.g. "M'Laurine"), his surname is alternatively written MacLaurin. In Gaelic the name is "Cailean MacLabhruinn", which is literally 'Colin, the son of Laurence'.
Life and work
He was born in Kilmodan, Argyll. His father, the Reverend John Maclaurin, was the minister of Glendaruel and author of an Irish version of the Psalms. Colin lost his father in infancy, and his mother before he was nine years old, and was educated under the care of his uncle, the Reverend Daniel Maclaurin, minister of Kilfinnan. He entered the University of Glasgow at age eleven, not unusual at the time; but graduating MA by successfully defending a thesis on the Power of Gravity at age 14. After graduation he remained at Glasgow to study divinity for a period, and in 1717, aged nineteen, after a competition which lasted for ten days, he was elected professor of mathematics at Marischal College in the University of Aberdeen. He held the record as the world's youngest professor until March 2008, when the record was officially given to Alia Sabur.
In the vacations of 1719 and 1721 he went to London, where he became acquainted with Sir Isaac Newton, Dr. Hoadley, Dr. Samuel Clarke, and Martin Folkes, and other eminent philosophers, and was admitted a member of the Royal Society.
In 1722, having provided a competent person to attend to his class for a time at Aberdeen, he travelled on the Continent as tutor to George Hume, the son of Alexander Hume, 2nd Earl of Marchmont; and during their time in Lorraine, he wrote his essay on the Percussion of Bodies, which gained the prize of the Royal Academy of Sciences in 1724. Upon the death of his pupil at Montpellier he returned to Aberdeen.
In 1725 he was appointed deputy to the mathematical professor at Edinburgh, James Gregory (brother of David Gregory and nephew of the more famous James Gregory), upon the recommendation of Isaac Newton. Newton was so impressed with his work, he actually offered to pay Maclaurin's salary. On November 3 of that year Maclaurin succeeded Gregory. Maclaurin is credited with raising the character of that university as a school of science.
In his work on approximating functions by series, Maclaurin attributes Taylor. Though Taylor series were known before by Newton and Gregory , and in special cases by Madhava of Sangamagrama in fourteenth century India . But Maclaurin was not aware of this and published it in Methodus incrementorum directa et inversa. Maclaurin series which are Taylor series expanded around 0, were not attributed to Maclaurin because he discovered them, rather are attributed to him 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 also attracted the attention of d'Alembert, A.-C. Clairaut, Euler, Laplace, Legendre, Poisson and Gauss. He showed that an oblate spheroid was a possible equilibrium in Newtons 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 spheriods.
Independently from Euler and using the same methods, he discovered the Euler–Maclaurin formula. He used this formula to sum powers of arithmetic progressions, derive Stirling's formula, and to derive the Newton-Cotes numerical integration formulas which includes Simpsons rule as a special case.
Maclaurin also 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. While ultimately Euler was able to give a more general and elegant approach, he cited the work of d'Alembert and Maclaurin as the source of his investigation.
In 1733, he married Anne Stewart, the daughter of Walter Stewart, the Solicitor General for Scotland, by whom he had seven children.
He actively opposed the Jacobite Rebellion of 1745 and superintended the operations necessary for the defence of Edinburgh against the Highland army, but upon their entry into the city, he had to flee to York, where he was invited by the Archbishop of York to reside with him.
On his journey south, he 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 MIT President Richard Cockburn Maclaurin is from the same family.
See also
Sources
- Anderson, William, The Scottish Nation, Edinburgh, 1867, vol.VII, p.37.
- Sageng, Erik, 2005, "A treatise on fluxions" in Grattan-Guiness, I., ed., Landmark Writings in Western Mathematics. Elsevier: 143-58.
Further reading
- Bruce A. Hedman, "Colin Maclaurin's quaint word problems," College Mathematics Journal 31 (2000), 286-288.
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