Colin Maclaurin
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Colin Maclaurin (; gd, Cailean MacLabhruinn; February 1698 – 14 June 1746) was a
Scottish Scottish usually refers to something of, from, or related to Scotland, including: *Scottish Gaelic, a Celtic Goidelic language of the Indo-European language family native to Scotland *Scottish English *Scottish national identity, the Scottish iden ...
mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained ( ...

mathematician
who made important contributions to
geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ...

geometry
and
algebra Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad areas of mathematics, together with number theory, geometry and mathematical analysis, analysis. In its most ge ...

algebra
. 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 In , the Taylor series of a is an of terms that are expressed in terms of the function's s at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor's series are named after ...
, is named after him. Owing to changes in
orthography An orthography is a set of for a , including norms of , ation, , , , and . Most transnational languages in the modern period have a system of , and for most such languages a standard orthography has been developed, often based on a of the la ...
since that time (his name was originally rendered as “M‘Laurine”), his surname is alternatively written MacLaurin.


Early life

Maclaurin was born in Kilmodan,
Argyll Argyll (; archaically Argyle, in Scottish Gaelic language, modern Gaelic, ), sometimes called Argyllshire, is a Counties of Scotland, historic county and registration county of western Scotland. Argyll is of ancient origin, and corresponds to ...

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 A child prodigy is defined in psychology research literature as a person under the age of ten who produces meaningful output in some domain to the level of an adult expert. The term ''wunderkind'' (from German ''Wunderkind''; literally "wonder ...
, he entered university at age 11.


Academic career

At eleven, Maclaurin, a child prodigy at the time, entered the
University of Glasgow , image_name = University_of_Glasgow_Coat_of_Arms.jpg , image_size = 150px , latin_name = Universitas Glasguensis , motto = la, Via, Veritas, Vita ''Via et veritas et vita'' (, ) is a Latin language, Latin phrase meaning "the way and the t ...

University of Glasgow
. He graduated
master of arts A Master of Arts ( la, Magister Artium or ''Artium Magister''; abbreviated MA or AM) is the holder of a master's degree A master's degree (from Latin ) is an academic degree awarded by University, universities or colleges upon completion of a co ...
three years later by defending a thesis on ''the Power of Gravity,'' and remained at Glasgow to study
divinity Divinity or the divine are things that are either related to, devoted to, or proceeding from a deity A deity or god is a supernatural being considered divinity, divine or sacred. The ''Oxford Dictionary of English'' defines deity as "a God (m ...
until he was 19, when he was elected professor of
mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no general consensus abo ...
in a ten-day competition at the
Marischal College Marischal College is a large granite building on Broad Street in the centre of Aberdeen in north-east Scotland, and since 2011 has acted as the headquarters of Aberdeen City Council. However, the building was constructed for and is on long-term l ...
in the
University of Aberdeen , mottoeng = The fear of the Lord is the beginning of wisdom , established = , type = Public In public relations and communication science, publics are groups of individual people, and the public (a.k.a. the general public) is the t ...
. This record as the world's youngest professor endured until March 2008, when the record was officially given to Alia Sabur. In the vacations of 1719 and 1721, Maclaurin went to London, where he became acquainted with
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of s ...

Isaac Newton
, Benjamin Hoadly, Samuel Clarke, Martin Folkes, and other philosophers. He was admitted 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 Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of s ...

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

Maclaurin used
Taylor series In , the Taylor series of a is an of terms that are expressed in terms of the function's s at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor's series are named after ...
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. Nevertheless, Maclaurin received credit for his use of the series, and the Taylor series expanded around 0 is sometimes known as the ''Maclaurin series''. 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. 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. 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. 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. 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

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 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. 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. When the Highland army entered 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 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. 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 1748It cannot be in 1750, as the French translation is published in 1749
see online at Gallica
.
* Colin Maclaurin was the name used for the new Mathematics and Actuarial Mathematics and Statistics Building at Heriot-Watt University, Edinburgh. 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)


See also

*Braikenridge–Maclaurin theorem *Trisectrix of Maclaurin *Cayley's sextic *Cramer's paradox *Hesse configuration *Sinusoidal spiral


References


Sources

* Anderson, William, ''The Scottish Nation'', Edinburgh, 1867, vol.VII, p. 37. * * * * *Sageng, Erik, 2005, "A treatise on fluxions" in Ivor Grattan-Guinness, Grattan-Guinness, 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. * * {{DEFAULTSORT:Maclaurin, Colin 1698 births 1746 deaths 18th-century Scottish mathematicians Burials at Greyfriars Kirkyard Alumni of the University of Glasgow Academics of the University of Edinburgh Academics of the University of Aberdeen Deaths from edema Fellows of the Royal Society Scottish mathematicians Members of the Philosophical Society of Edinburgh People from Glendaruel