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Colin Maclaurin

Colin Maclaurin (1698–1746)
Born February, 1698 (1698-02-16)
Kilmodan, Cowal, Argyllshire, Scotland
Died 14 June 1746 (1746-06-15)
Edinburgh, Scotland
Residence Scotland
Citizenship United Kingdom
Nationality Scottish
Ethnicity 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
Notable awards Académie des Sciences, Grand Prize

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]

Contents

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 Simpsons 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.

See also

References

Sources

Further reading

  • Bruce A. Hedman, "Colin Maclaurin's quaint word problems," College Mathematics Journal 31 (2000), 286-288.
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Colin Maclaurin
File:Maclaurin Colin
Colin Maclaurin (1698–1746)
Born Not recognized as a date. Years must have 4 digits (use leading zeros for years < 1000).
Kilmodan, Cowal, Argyllshire, Scotland
Died Not recognized as a date. Years must have 4 digits (use leading zeros for years < 1000).
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
Notable awards Académie des Sciences, Grand Prize

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]

Contents

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.

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

References

Sources

Further reading

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

1911 encyclopedia

Up to date as of January 14, 2010

From LoveToKnow 1911

COLIN MACLAURIN (1698-1746), Scottish mathematician, was the son of a clergyman, and born at Kilmodan, Argyllshire. In 1709 he entered the university of Glasgow, where he exhibited a decided genius for mathematics, more especially for geometry; it is said that before the end of his sixteenth year he had discovered many of the theorems afterwards published in his Geometria organica. In 1717 he was elected professor of mathematics in Marischal College, Aberdeen, as the result of a competitive examination. Two years later he was admitted F.R.S. and made the acquaintance of Sir Isaac Newton. In 1719 he published his Geometria organica, sive descriptio linearum curvarum universalis. In it Maclaurin developed several theorems due to Newton, and introduced the method of generating conics which bears his name, and showed that many curves of the third and fourth degrees can be described by the intersection of two movable angles. In 1721 he wrote a supplement to the Geometria organica, which he afterwards published, with extensions, in the Philosophical Transactions for 1735. This paper is principally based on the following general theorem, which is a remarkable extension of Pascal's hexagram: "If a polygon move so that each of its sides passes through a fixed point, and if all its summits except one describe curves of the degrees m, n, p, &c., respectively, then the free summit moves on a curve of the degree 2mnp. .. . which reduces to mnp .... when the fixed points all lie on a right line." In 1722 Maclaurin travelled as tutor and companion to the eldest son of Lord Polwarth, and after a short stay in Paris resided for some time in Lorraine, where he wrote an essay on the percussion of bodies, which obtained the prize of the French Academy of Sciences for the year 1724. The following year he was elected professor of mathematics in the university of Edinburgh on the urgent recommendation of Newton. After the death of Newton, in 1728, his nephew, John Conduitt, applied to Maclaurin for his assistance in publishing an. account of Newton's life and discoveries. This Maclaurin gladly undertook, but the death of Conduitt put a stop to the project.

In 1740 Maclaurin divided with Leonhard Euler and Daniel Bernoulli the prize offered by the French Academy of Sciences for an essay on tides. His Treatise on Fluxions was published at Edinburgh in 1742, in two volumes. In the preface he states that the work was undertaken in consequence of the attack on the method of fluxions made by George Berkeley in 1734. Maclaurin's object was to found the doctrine of fluxions on geometrical demonstration, and thus to answer all objections to its method as being founded on false reasoning and full of mystery. The most valuable part of the work is that devoted to physical applications, in which he embodied his essay on the tides. In this he showed that a homogeneous fluid mass revolving uniformly round an axis under the action of gravity ought to assume the form of an ellipsoid of revolution. The importance of this investigation in connexion with the theory of the tides, the figure of the earth, and other kindred questions, has always caused it to be regarded as one of the great problems of mathematical physics. Maclaurin was the first to introduce into mechanics, in this discussion, the important conception of surfaces of level; namely, surfaces at each of whose points the total force acts in the normal direction. He also gave in his Fluxions, for the first time, the correct theory for distinguishing between maxima and minima in general, and pointed out the importance of the distinction in the theory of the multiple points of curves. In 1745, when the rebels were marching on Edinburgh, Maclaurin took a most prominent part in preparing trenches and barricades for its defence. The anxiety, fatigue and cold to which he was thus exposed, affecting a constitution naturally weak, laid the foundation of the disease to which he afterwards succumbed. As soon as the rebel army got possession of Edinburgh Maclaurin fled to England, to avoid making submission to the Pretender. He accepted the invitation of T. Herring, then archbishop of York, with whom he remained until it was safe to return to Edinburgh. He died of dropsy on the 14th of June 1746, at Edinburgh. Maclaurin was married in 1733 to Anne, daughter of Walter Stewart, solicitorgeneral for Scotland. His eldest son John, born in 1734, was distinguished as an advocate, and appointed one of the judges of the Scottish court of session, with the title of Lord Dreghorn. He inherited an attachment to scientific discovery, and was one of the founders of the Royal Society of Edinburgh, in 1782.

After Maclaurin's death his account of Newton's philosophical discoveries was published by Patrick Murdoch, and also his algebra in 1748. As an appendix to the latter appeared his De linearum geometricarum 'proprietatibus generalibus tractatus, a treatise of remarkable elegance. Of the more immediate successors of Newton in Great Britain Maclaurin is probably the only one who can be placed in competition with the great mathematicians of the continent of Europe at the time. (B. W.) M`Lennan, John Ferguson (1827-1881), Scottish ethnologist, was born at Inverness on the 14th of October 1827. He studied at King's college, Aberdeen, where he graduated with distinction in 1849, thence proceeding to Cambridge, where he remained till 1855 without taking a degree. He was called to the Scottish bar in 1857, and in 1871 was appointed parliamentary draughtsman for Scotland. In 1865 he published Primitive Marriage, in which, arguing from the prevalence of the symbolical form of capture in the marriage ceremonies of primitive races, he developed an intelligible picture of the growth of the marriage relation and of systems of kinship (see Family) according to natural laws. In 1866 he wrote in the Fortnightly Review (April and May) an essay on "Kinship in Ancient Greece," in which he proposed to test by early Greek facts the theory of the history of kinship set forth in Primitive Marriage; and three years later appeared a series of essays on "Totemism" in the same periodical for 1869-1870 (the germ of which had been contained in the paper just named), which mark the second great step in his systematic study of early society. A reprint of Primitive Marriage, with "Kinship in Ancient Greece" and some other essays not previously published, appeared in 1876, under the title of Studies in Ancient History. The new essays in this volume were mostly critical, but one of them, in which perhaps his guessing talent is seen at its best, "The Divisions of the Irish Family," is an elaborate discussion of a problem which has long puzzled both Celtic scholars and jurists; and in another, "On the Classificatory System of Relationship," he propounded a new explanation of a series of facts which, he thought, might throw light upon the early history of society, at the same time putting to the test of those facts the theories he had set forth in Primitive Marriage. Papers on "The Levirate and Polyandry," following up the line of his previous investigations (Fortnightly Review, 1877), were the last work he was able to publish. He died of consumption on the 14th of June 1881 at Hayes Common, Kent.

Besides the works already cited, M'Lennan wrote a Life of Thomas Drummond (1867). The vast materials which he had accumulated on kinship were edited by his widow and A. Platt, under the title Studies in Ancient History: Second Series (1896).


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