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Maclaurin published the first systematic exposition of Newton's methods.
Maclaurin was born in Kilmodan where his father was the minister of the parish. The village (population 387 in 1904) is on the river Ruel and the church is at Glendauel. He was a student at Glasgow. He became professor of mathematics at Marischal College, Aberdeen from 1717 to 1725 and then at the University of Edinburgh from 1725 until 1745.
He did notable work in geometry, particularly studying higher plane curves. He wrote an important memoir on the theory of tides.
Maclaurin was elected a Fellow of the Royal Society in 1719 and in 1724 he was awarded a prize by the Académie des Sciences for his work on the impact of bodies. In 1740 he was awarded another prize from the Académie des Sciences for a study of tides. This prize was jointly awarded to Maclaurin, Euler and Daniel Bernoulli.
Maclaurin's first important work was Geometrica Organica... published in 1720.
In 1742 he published his 2 volume Treatise of fluxions , the first systematic exposition of Newton's methods written as a reply to Berkeley's attack on the calculus for its lack of rigorous foundations.
Treatise of fluxions is a major work of 763 pages, much praised by those who read it but of surprisingly little influence and what it had was rather bad in that it encouraged British mathematicians to use geometry rather than the new analysis being developed in Europe.
Maclaurin appealed to the geometrical methods of the ancient Greeks and to Archimedes' method of exhaustion. In Treatise of fluxions Maclaurin uses the special case of Taylor's series now named after him (acknowledging Taylor).
Maclaurin also gave the integral test for the convergence of an infinite series. He investigates in Treatise of fluxions the mutual attraction of two ellipsoids of revolution as an application of the methods.
Maclaurin played an active role in the defence of Edinburgh during the Jacobite rebellion of 1745. When the city fell Maclaurin fled to York and he died the following year in Edinburgh.
Maclaurin's Treatise on algebra was published in 1748, two years after his death. Another work Account of Sir Isaac Newton's discoveries was left incomplete on his death but was published later.
References elsewhere in this archive:
Tell me about Maclaurin series and show me the series for cosine and the series for sine
Tell me about Maclaurin's part in the rise of calculus
Tell me about Maclaurin's work on matrices and determinants
Maclaurin worked on the Cayley's Sextic, on the Lituus and on the Trisectrix of Maclaurin
References:
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