Maclaurin biography of michael r

Colin Maclaurin

Scottish mathematician ( – )

Colin Maclaurin (; Scottish Gaelic: Cailean MacLabhruinn;[pronunciation?] February &#;– 14 June )[1] was a Scottish mathematician who made important contributions to geometry and algebra.[2] 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, is named after him.

Owing to changes in orthography since that time (his name was originally rendered as M'Laurine[3]), his surname is alternatively written MacLaurin.[4]

Early life

Maclaurin was born in Kilmodan, 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, he entered university at age

Academic career

At eleven, Maclaurin, a child prodigy at the time, entered the University of Glasgow. He graduated Master of Arts three years later by defending a thesis on the Power of Gravity, and remained at Glasgow to study divinity until he was 19, when he was elected professor of mathematics in a ten-day competition at Marischal College and University in Aberdeen. This record as the world's youngest professor endured until March , when the record was officially given to Alia Sabur.[5]

In the vacations of and , Maclaurin went to London, where he became acquainted with Isaac Newton, Benjamin Hoadly, Samuel Clarke, Martin Folkes, and other philosophers. He was admitted as a member of the Royal Society.

In , 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 Lorraine, he wrote his essay on the percussion of bodies (Demonstration des loix du choc des corps), which gained the prize of the Royal Academy of Sciences in Upon the death of his pupil at Montpellier, Maclaurin returned to Aberdeen.

In , Maclaurin was appointed deputy to the mathematical professor at the University of Edinburgh, James Gregory (brother of David Gregory and nephew of the esteemed James Gregory), upon the recommendation of 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 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 Newton and Gregory, and in special cases to Madhava of Sangamagrama in fourteenth century India.[6] Nevertheless, Maclaurin received credit for his use of the series, and the Taylor series expanded around 0 is sometimes known as the Maclaurin series.[7]

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.[7] Maclaurin corresponded extensively with Clairaut, Maupertuis, and d'Ortous de Mairan.[8][9]

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.[7]

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.[7]

In his Treatise of Algebra (Ch. XII, Sect 86), published in 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.[10][11] This publication preceded by two years Cramer's publication of a generalization of the rule to n unknowns, now commonly known as Cramer's rule.

Personal life

In , 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.[12]

Maclaurin actively opposed the Jacobite rising of 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.[13] 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 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.

The 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 –
  • De Linearum Geometricarum Proprietatibus –
  • Treatise on Fluxions – ( pages in two volumes. The first systematic exposition of Newton's methods.)
  • Treatise of Algebra – (two years after his death.)
  • Account of Newton's Discoveries – Incomplete upon his death and published in [14]
  • Account of Sir Isaac Newton's philosophical discoveries (in French). Paris: Laurent Durand.

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

  • French edition of the Treatise of algebra ()

  • French edition of the Account of Sir Isaac Newton's philosophical discoveries ()

See also

References

  1. ^ Turnbull lectures on Colin Maclaurin (4 February ), Part I
  2. ^Chisholm, Hugh, ed. (). "Maclaurin, Colin"&#;. Encyclopædia Britannica (11th&#;ed.). Cambridge University Press.
  3. ^"Colin Maclaurin: A Biographical Note" by Robin Schlapp (6 December ). (Note that the quotation in [1] has been altered.)
  4. ^"The prickly genius – Colin MacLaurin (–)"(PDF). Archived from the original(PDF) on 29 February Retrieved 20 January
  5. ^David McNeill (1 May ). "University appoints world's youngest professor". The Independent.
  6. ^"Neither Newton nor Leibniz&#;– The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala". MAT . Canisius College. Archived from the original on 6 August Retrieved 9 July
  7. ^ abcdGrabiner, Judith (May ). "Was Newton's Calculus a Dead End? The Continental Influence of Maclaurin's Treatise of Fluxions"(PDF). The American Mathematical Monthly. (5). Mathematical Association of America: – doi/ JSTOR&#;
  8. ^Mills, Stella, ed. (). The collected letters of Colin Maclaurin (–). Nantwich, Cheshire, UK: Shiva. ISBN&#;. LCCN&#;; xx+ pages, letters; correspondents include Newton, Halley, Simson, de Moivre, Voltaire, Sir Hans Sloane & Sir Martin Folkes: CS1 maint: postscript (link)
  9. ^Hankins, Thomas L. (). "Review of The Collected Letters of Colin Maclaurin, edited by Stella Mills". Science. (): 45– doi/science PMID&#;
  10. ^MacLaurin, Colin (). A Treatise of Algebra, in Three Parts. Printed for A. Millar & J. Nourse.
  11. ^Hedman, Bruce (November ). "An Earlier Date for "Cramer's Rule"". Historia Mathematica. 26 (4). Academic Press Elsevier: – doi/hmat
  12. ^Biographical Index of Former Fellows of the Royal Society of Edinburgh –(PDF). The Royal Society of Edinburgh. July ISBN&#;. Archived from the original(PDF) on 4 March Retrieved 24 July
  13. ^Maclaurin, Colin (), "Colin Maclaurin's 'Journal of the Forty-five'", in Hedman, Bruce (ed.), Miscellany XIII of the Scottish History Society Fifth Series volume 14, Edinburgh, Scotland: Lothian Print, pp.&#;–
  14. ^It cannot be in , as the French translation is published in (see online at Gallica).

Sources

  • Anderson, William, The Scottish Nation, Edinburgh, , , p.&#;
  • Ball, W. W. Rouse (). A Short Account of the History of Mathematics (4th&#;ed.). pp.&#;– Retrieved 20 January
  • "Overview of Colin Maclaurin". Gazetteer for Scotland. University of Edinburgh School of GeoSciences. Retrieved 20 January
  • Friedman, Erich. "Colin Maclaurin". Periodic Table of Mathematicians. Stetson University. Archived from the original on 14 February Retrieved 20 January
  • O'Connor, John J.; Robertson, Edmund F., "Colin Maclaurin", MacTutor History of Mathematics Archive, University of St Andrews
  • Sageng, Erik, , "A treatise on fluxions" in Grattan-Guinness, I., ed., Landmark Writings in Western Mathematics. Elsevier: –
  • Tweddle, Ian (November ). "The prickly genius—Colin Maclaurin (–)"(PDF). The Mathematical Gazette. 82 (). Leicester: Mathematical Association: – doi/ JSTOR&#; Archived from the original(PDF) on 31 October Retrieved 20 January

Further reading