Colin Maclaurin | Biography

Colin Maclaurin was one of Europe's foremost mathematicians during the 1700s. He was the first to provide systematic proof of Isaac Newton's theorems. Some of his noted accomplishments include explanations of the properties of conics and the theory of tides. Maclaurin was also a brilliant mathematician in his own right, who solved many problems in geometry and applied physics. Besides being an esteemed mathematician, Maclaurin was a creative inventor who loved to devise mechanical appliances. He was skilled in astronomy, mapmaking and sometimes spent his spare time acting as an actuary for insurance companies.

Maclaurin was born in Kilmodan, Scotland, in 1698, the son of a minister named John Maclaurin, a man of great learning. Unfortunately, his father died when Colin was just six years old. When his mother died nine years later, Maclaurin moved in with his uncle, Daniel Maclaurin.

Maclaurin's eldest brother, John, studied for the ministry and became a noted religious expert. Following his brother's lead, Maclaurin studied divinity at the University of Glasgow for a year. While at Glasgow, he met Robert Simson, professor of mathematics, who inspired Maclaurin's interest in geometry, especially the geometry of ancient mathematicians such as Euclid.

Maclaurin became interested in Newton's theories early on in his career. In 1715, he presented his thesis "On the Power of Gravity," which demonstrated real distinction, even though he was only in his teens when he defended it and earned a master of arts degree. The thesis also won him an appointment as a professor in mathematics at Marischal College in Aberdeen a year later.

In 1719, Maclaurin made two trips to London where he met some of the renowned scientists of the day, including Newton and Martin Folkes, who later became the president of the Royal Society of London. In 1720, Maclaurin published one of his signature works, Geometrica Organica, sive descriptio linearum curvarum universalis, which explained higher plane curves and conics. It proved many of the theories that Newton had proposed as well as solving other important problems in geometry. Maclaurin, for instance, showed that the cubic and the quartic could be represented by rotating these angles around their vertices. Newton had demonstrated similar properties for the conic sections.

In 1722, Maclaurin left Marischal to take on the tutoring of the son of Lord Polwarth, a powerful British diplomat. The two traveled through France, where Maclaurin produced another masterpiece On the Percussion of Bodies. For this work, the French Académie Royale des Sciences presented him with its prize in 1724.

When Polwarth's son died, Maclaurin hoped to reclaim his teaching position at Marischal, but during his three-year absence, it had been declared vacant and filled. When the chair of professor of mathematics at the University of Edinburgh fell vacant in 1725, he was appointed there. The prodigious Maclaurin then began lecturing on some of his favorite topics: the theories of Euclid, conics, astronomy, trigonometry, and Newton's Principia.

Maclaurin moved in Scotland's most inner circles. He was a fellow of the Royal Society and the Philosophical Society, where he acted as secretary. In 1733, he married Anne Stewart, the daughter of the solicitor general in Scotland. They had seven children.

In 1740, Maclaurin attracted international notice when he submitted an essay called "On the Tides" for the Académie Royale des Sciences prize. In the essay, Maclaurin explained the theory of tides, based on Newton's Principia, and defined the tides of the sea as an ellipsoid revolving around an inner point. Maclaurin shared the prize for his theory of tides with the mathematicians Leonhard Euler and Daniel Bernoulli. They all provided proof of Newton's theories about the movement of the ocean. The mathematician Alexis Clairaut was so taken with Maclaurin's success in explaining tides that he began probing the mystery of the Earth's shape with geometry.

Maclaurin's Treatise of Fluxions, published in 1742, was another of his major works. The treatise was written as a reply to George Berkeley's 1734 publication The Analyst, A Letter Addressed to an Infidel Mathematician, in which Berkeley criticized Newton's theory of fluxions as "ghosts of departed quantities." Other mathematicians had also decried Newton's methods for their lack of systematic foundation. In his two-volume work, Maclaurin explained Newton's theories in detail and also solved other great quandaries of mathematics. The book contains descriptions of the infinite series as well as much praised work on the curves of quickest descent.

Though the Treatise of Fluxions was considered noteworthy at the time, it had little influence on international mathematics. The book persuaded British scientists to continue with the geometrical methods of Newton rather than the analytical calculus just being devised in other nations in Europe. As a result, Britain was left far behind in the development of mathematics during the late 1700s.

Maclaurin worked ceaselessly to defend Edinburgh during an attack by Jacobites in the rebellion of 1745. While planning and erecting the defenses of the city, however, he became so exhausted that he fell physically ill. When the city surrendered to the Jacobites, Maclaurin fled to England. A year later he returned to Edinburgh, where he died at age 48.

Until his death in 1746, Maclaurin remained the consummate mathematician and defender of Newtonian theories. A few hours before his death he dictated his last writing on Newton's work, which firmly set forth Maclaurin's belief in life after death. His Treatise on Algebraand An Account of Sir Isaac Newton's Philosophical Discoveries, an incomplete work, were published posthumously.