Colin Maclaurin

Colin Maclaurin
David Steuart Erskine · Public domain · source
Name	Colin Maclaurin
Caption	Portrait of Colin Maclaurin
Birth date	February 1698
Birth place	Kilmodan, Argyll, Scotland
Death date	14 June 1746
Death place	Edinburgh, Scotland
Fields	Mathematics, Physics
Alma mater	University of Glasgow
Doctoral advisor	Robert Simson
Known for	Maclaurin series, Maclaurin's inequality, Maclaurin spheroid
Influences	Isaac Newton
Awards	Royal Society fellowship, Académie des Sciences prize

Colin Maclaurin. He was a preeminent Scottish mathematician and physicist who made foundational contributions to calculus and geometry during the early 18th century. A staunch defender and developer of Isaac Newton's methods, his work bridged the era of Leibniz and Euler, significantly advancing mathematical analysis in Britain. His name is immortalized in the Maclaurin series, a special case of the Taylor series, and his influential textbook, A Treatise of Fluxions, was a standard work for decades.

Early life and education

Born in the parish of Kilmodan in Argyll, he was recognized as a child prodigy, entering the University of Glasgow at the age of eleven. At Glasgow, he studied under the renowned geometer Robert Simson and graduated with a Master of Arts degree in 1713. His early talent in mathematics was evident, and by the age of nineteen, he was appointed professor of mathematics at Marischal College, part of the University of Aberdeen. This remarkable appointment was supported by a strong recommendation from Isaac Newton himself, after Maclaurin sent Newton a paper on the gravitational theory of comets.

Mathematical work

His mathematical contributions were wide-ranging and profound. He produced important work in geometry, including a definitive study of the higher plane curves and a celebrated theorem on the conic sections. In calculus, he was a leading exponent of Newton's method of fluxions, rigorously defending it against criticisms from proponents of Leibnizian calculus, such as George Berkeley in The Analyst. His investigations into the gravitational attraction of ellipsoids led to the concept of the Maclaurin spheroid, a foundational model in celestial mechanics. He also made significant advances in algebra, formulating what is now known as Maclaurin's inequality for symmetric sums.

Maclaurin series

While the general Taylor series was published by Brook Taylor in 1715, he independently discovered and extensively utilized the special case where the series is expanded about zero. This expansion, now universally called the Maclaurin series, was presented in his seminal 1742 work, A Treatise of Fluxions. He employed these series to solve problems in calculus, physics, and astronomy, including evaluating integrals, summing series, and studying the motions of planets. The Maclaurin series became a cornerstone of mathematical analysis, providing a powerful tool for approximating functions and is a fundamental topic taught in courses from Cambridge to the Massachusetts Institute of Technology.

Later life and legacy

In 1725, he moved to Edinburgh to assume the chair of mathematics at the University of Edinburgh, a position created for him upon the recommendation of Isaac Newton and the patronage of James, Duke of Chandos. He was elected a fellow of the Royal Society of London in 1719 and later won a prize from the Académie des Sciences for his work on the tides. During the Jacobite rising of 1745, he was involved in the defense of Edinburgh against the forces of Charles Edward Stuart. The subsequent hardship and exhaustion contributed to his premature death in 1746. His legacy endures through the Maclaurin series, the Maclaurin building at the University of Edinburgh, and his profound influence on subsequent mathematicians like Leonhard Euler and Joseph-Louis Lagrange.

Selected publications

* Geometria Organica (1720) * A Treatise of Fluxions (1742) * A Treatise of Algebra (1748, posthumous) * An Account of Sir Isaac Newton's Philosophical Discoveries (1748, posthumous)

Category:1698 births Category:1746 deaths Category:Scottish mathematicians Category:Scottish physicists Category:Fellows of the Royal Society Category:University of Glasgow alumni Category:University of Edinburgh faculty