Maclaurin was born in February 1698, in Kilmodan, Scotland, the youngest of the three sons of John Maclaurin, minister of the parish of Kilmodan and a man of profound learning. John, the eldest son, followed in his father’s footsteps and became a noted divine. The father died when Maclaurin was only six weeks old and after the death of his mother nine years later, Maclaurin was cared for by an uncle, Daniel Maclaurin, a minister of Kilfinaan.
In 1709 Maclaurin entered the University of Glasgow where he read divinity for a year. At Glasgow, he became acquainted with Robert Simson, professor of mathematics. Simson, who tried to revive the geometry of the ancients, particularly the Elements of Euclid, stimulated Maclaurin’s interest in this aspect of mathematics. In 1715 Maclaurin defended the thesis "On the Power of Gravity," for which he was awarded a master of arts degree.
In 1717 Maclaurin was appointed a professor of mathematics at Marischal College, Aberdeen, although he was still only in his teens. This appointment marked the beginning of a brilliant mathematical career which was to continue without interruption until the end of his life.
In 1719 Maclaurin visited London, where he was well received in the scientific circles of the capital and where he met Newton. On a second visit he met and formed a lasting friendship with Martin Folkes, who became president of the Royal Society in 1741, Maclaurin was meanwhile actively working on his Geometrica organica, which was published in 1720 with Newton’s imprimatur.
Geometrica organica, sive descripth linearum cwvantm universalis dealt with the general properties of conies and of the higher plane curves. It contained proofs of many important theorems which were to be found, without proof, in Newton’s work, as well as a considerable number of others which Maclaurin had discovered while at the university.
In 1722 Maclaurin left Scotland to serve as companion and tutor to the son of Lord Polwarth, plenipotentiary of Great Britain at Cambrai. They visited Paris, then went on to Lorraine, where Maclaurin, during a period of intense mathematical activity, wrote On the Percussion of Baches. It won him the prize offered by the French Academy of Sciences in 1724.
In the same year, the sudden death of Maelaurin’s pupil caused him to return to Aberdeen. As a result of three years’ absence, however, his chair had been declared vacant, Maclaurin then moved to Edinburgh, where he acted as deputy for the elderly James Gregory. There is no doubt that Maclaurin owed his appointment to a strong recommendation from Newton.
Maclaurin was appointed to the Edinburgh chair when it fell vacant. He assumed its duties in 1725, lecturing on a wide range of topics that included twelve books of Euclid, spherical trigonometry, the conies, the elements of fortification, astronomy, and perspective, as well as a careful exposition of Newton’s Principia.
Maclaurin was elected a fellow of the Royal Society in 1719. He was also influential in persuading the members of the Edinburgh Society for Improving Medical Knowledge to widen its scope. The society’s name was thus changed to the Philosophical Society and Maclaurin became one of its secretaries.
Maclaurin's Treatise of Fluxions (1742) has been described as the earliest logical and systematic publication of the Newtonian methods. It stood as a model of rigor until the appearance of Cauchy’s Cours d’analyse in 1821.
Maclaurin’s advice was sought on many topics, not all of them mathematical. He was a skilled experimentalist, and he devised a variety of mechanical appliances. He made valuable astronomical observations and did actuarial computations for the use of insurance societies. He also took an active part in improving maps of the Orkney and Shetland Islands, with a view to discovering a northeast polar passage from Greenland to the southern seas, and prepared an extensive memorial upon this subject for the government. (Since the government was at that time primarily interested in finding a northwest passage, the matter was dropped.)
When a Highland army marched upon Edinburgh in the uprising of 1745, Maclaurin wholeheartedly organized the defenses of the city. With tireless energy, he planned and supervised the hastily erected fortifications, and, indeed, drove himself to a state of exhaustion from which he never recovered. The city fell to the Jacobites and Maclaurin was forced to flee to England. He reached York and sought refuge with Thomas Herring, the archbishop. He returned Edinburgh once it became clear that the Jacobites were not going to occupy the city, but the rigors he had endured had very severely undermined his health. He died soon after, at the age of forty-eight. Only a few hours before his death he dictated the concluding passage of his work on Newton’s philosophy, in which he affirmed his unwavering belief in future life.
(Volume 2)
1742(Volume 1)
1742Maclaurin, a zealous disciple of Newton, hoped to silence criticism of the latter’s doctrine of "prime and ultimate ratios" which proved something of a stumbling block to even Newton’s staunchest supporters. In the Treatise Maclaurin tried to provide a geometrical framework for the doctrine of fluxions; in this way, he hoped to refute his critics, the most vociferous of whom was George Berkeley, Bishop of Cloyne.
Maclaurin followed Newton in abandoning the view that variable quantities were made up of infinitesimal elements and in approaching the problem from kinematical considerations. Moreover, he consistently followed the Newtonian notation, although the Leibnizian notation was by this time well established on the Continent.
Maclaurin also elaborated many of the principles enunciated by Newton in the Principia in this work, including problems in applied geometry and physics, founded on the geometry of Euclid.
Maclaurin’s persistent defense of the Newtonian methods was not without harmful consequences for the progress of mathematics in Great Britain. National pride induced Englishmen to follow the geometrical methods which Newton had employed in the Principia, and to neglect the analytical methods which were being pursued with such conspicuous success on the Continent As a result, English mathematicians came to think that the calculus was not really necessary. This unfortunate neglect persisted for a century or more. It was said that during the eighteenth century Maclaurin and Matthew Stewart, who succeeded him in the mathematical chair at Edinburgh, were the only prominent mathematicians in Great Britain. Writing toward the end of the century, J. Lalande, in his Life of Condorcet, maintained that in 1764 there was not a single first-rate analyst in the whole of England.
Quotes from others about the person
At the meeting of the university following Maclaurin’s death, his friend, Alexander Munro, professor of anatomy at the University of Glasgow, paid tribute to him: "He was more nobly distinguished from the bulk of mankind by the qualities of the heart: his sincere love of God and men, his universal benevolence and unaffected piety together with a warmth and constancy in his friendship that was in a manner peculiar to himself."
In 1733 Maclaurin married Anne, daughter of Walter Stewart, solicitor general for Scotland. Of their seven children, two sons and three daughters survived him.
