# Colin MacLaurin

*13 January 2011*.

**Colin MacLaurin (or Maclaurin)** (February, 1698–14th June, 1746), the Scottish mathematician, was born at Kilmodan, Argyllshire. He published the first systematic exposition of Newton's calculus, written as a reply to Berkeley's attack on its lack of rigorous foundations. Of the more immediate successors of Newton in Great Britain, MacLaurin is possibly the only one who can be placed in competition with the great mathematicians of the continent of Europe at the time.

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## [edit] Early Life and Education

Colin MacLaurin’s father, John MacLaurin, was a clergyman and scholar, who had translated the Psalms into Gaelic; but Colin, never knew him, he died when Colin was just six weeks old. Colin's mother had inherited a small estate in Argyllshire and it was there that Colin spent his early years. In 1707, when Colin was nine years old, his mother died and the task of bringing up Colin and his brother John fell to their uncle Daniel MacLaurin, who was the minister at Kilfinnan on Loch Fyne.

In 1709, Colin became a student at the University of Glasgow at the age of eleven years. There, he showed an exceptional talent for mathematics, and especially for geometry; at the age of 14 he was awarded the degree of MA, for his thesis "On the power of gravity". It is said that by the end of his sixteenth year he had discovered many of the theorems later 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 elected a Fellow of the Royal Society of London, and came to know Sir Isaac Newton.

## [edit] Mathematical Works

In 1719, MacLaurin published his ‘’Geometria organica, sive descriptio linearum curvarum universalis‘’. In it, he developed several of Newton’s theorems, and introduced the method of generating conics which bears his name. In 1721 he wrote a supplement to the *Geometria organica*, which he was eventually published in the ‘’Philosophical Transactions’’ for 1735. This paper is principally based on the following general theorem, which is an 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, etc., 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 in France as tutor and companion to the eldest son of Lord Polwarth, (a diplomatic agent of King George II) ; during this period, he wrote an essay on the percussion of bodies, which won the prize of the French Academy of Sciences for 1724 . However, while they were visiting Montpellier, Polwarth's son became ill and died. Maclaurin returned to Aberdeen to discover that the University was highly displeased that he had been absent from his duties for two years. He was reinstated at Aberdeen, but the following year, on the urgent recommendation of Newton, he was elected professor of mathematics at the University of Edinburgh.

After Newton’s death in 1728, his nephew, John Conduitt, asked MacLaurin for his help in publishing an account of Newton's life and discoveries. This MacLaurin began, but the death of Conduitt interrupted the project.

In 1740 MacLaurin shared 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 the preface, he states that the work was undertaken in response to an attack on the method of fluxions made by George Berkeley in 1734. MacLaurin's intent was to found the doctrine of fluxions (the calculus) on geometry, thereby answering all objections to it as being “founded on false reasoning and full of mystery”.

Part of that work is 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 in connexion with the theory of the tides, the shape of the earth, and other questions, has caused it to be regarded as one of the great problems of mathematical physics. MacLaurin was the first to introduce, in this discussion, the important concept of ‘’surfaces of level’’; namely, surfaces at each of whose points the total force acts in the normal direction. He also gave, 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.

After MacLaurin's death his account of Newton's philosophical discoveries was published by Patrick Murdoch, and also his algebra in 1748.

## [edit] Life and Death

MacLaurin’s last years coincided with the Second Jacobite Rebellion, when Bonnie Prince Charlie attempted to regain the British throne for the deposed House of Stewart. In 1745, when the Jacobite rebels were marching on Edinburgh, Maclaurin took a prominent part in preparing trenches and barricades for its defence. However, the anxiety, fatigue and cold to which he was thus exposed, laid the foundation of the disease to which he afterwards succumbed. When the rebel army occupied Edinburgh, MacLaurin fled to England, to avoid submitting to the Pretender, on the invitation of the 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.

In 1733 MacLaurin married Anne, daughter of Walter Stewart, solicitor-general for Scotland. They had seven children, but only two boys and three girls were to survive him. Not long after his marriage, Maclaurin worked to expand the Medical Society of Edinburgh to include other branches of learning. This Society would, after Maclaurin's death, become the Royal Society of Edinburgh. His eldest son John, born in 1734, became a distinguished advocate, and was appointed one of the judges of the Scottish court of session, with the title of Lord Dreghorn; and he was to become one of the founders of the Royal Society of Edinburgh in 1782 .

## [edit] References

- Ian Tweddle (1998) The prickly genius- Colin MacLaurin (1698-1746)‘’The Mathematical Gazette’’82 Number 495
- ‘’An Account of Sir Isaac Newton's Philosophical Discoveries’’ By Colin MacLaurin (1748) [1]
- ‘’A Treatise of Algebra, in Three Parts. To which is Added, an Appendix ...’’by Colin MacLaurin (1788) [2]

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