Colin Maclaurin (1698 - 1746)

The Scottish mathematician Colin Maclaurin, was born in a small village in 1698 to a Presbyterian Minister and his wife. Orphaned by the time he was 9, he went to live with his uncle, also a Minister. Two years later, aged only 11, he went to Glasgow University.

It was at Glasgow that he began to develop his interest in mathematics. He read Euclid, and by the age of 14 had been awarded his Masters degree, for his work On the Power of Gravity, which built on the work of Newton, who was later to become a firm friend.

Maclaurin’s family had intended that he follow tradition and enter the Church, but Maclaurin was unhappy with the state of the Church at the time, and so returned to live with his uncle.

He applied for a post in mathematics and after ten days of gruelling examinations competing against other talented candidates, Maclaurin was appointed professor at Marischal College in Aberdeen University in 1717.

He met Newton on a visit to the Royal Society in London in 1719, and was elected a Fellow the same year.

Nominated by Newton (who even offered to fund him until he succeeded his predecessor), Maclaurin was appointed the deputy to the mathematics professor at the University of Edinburgh in 1725. He settled in Edinburgh, married, and founded the Medical Society of Edinburgh (which became the Royal Society of Edinburgh many years later).

Maclaurin did not devote his entire life to mathematics. He set up an insurance society that helped widows and children of Scottish Ministers and professors. He also worked hard to build Edinburgh’s fortifications when the Jacobites attacked in the Rebellion of 1745, but fled to Newcastle when the city fell.

He returned to Edinburgh when the Jacobites marched on England, but his health had suffered from the bad weather and a fall from his horse - he died a year later.

Maclaurin’s mathematics

He is famous now because he was honoured by giving his name to a particular expansion. His work in this field is not as original or as general as that of Brooke Taylor, but Maclaurin’s name remains alongside that of Taylor. In fact their work may have been preceded by that of an Indian mathematician, Madhava as early as 1400.

The sort of expansions he developed - called either a Maclaurin or a Taylor expansion - were like this one for the inverse tangent function:

\tan^{-1}x=x-{x^3\over{3}}+{x^5\over{5}}-\cdots

He is also known for his work on geometry - here is a curve (rightly) named in his honour:

This curve has the equation y^2(a+x)=x^2(3a-x). You can explore this curve and many more at:

http://www-groups.dcs.st-and.ac.uk/~history/Curves/Trisectrix.html

Maclaurin was jointly awarded a prize with the mathematicians Euler and Daniel Bernoulli from the French Academy of Sciences for their work on the study of tides in 1740.