Brook Taylor

Brook Taylor
Brook Taylor (1685-1731)
Born	18 August 1685 Edmonton, Middlesex, England
Died	29 December 1731 (aged 46) London, England
Residence	England
Nationality	English
Fields	Mathematician
Institutions	St John's College, Cambridge
Alma mater	St John's College, Cambridge
Academic advisors	John Machin and John Keill
Known for	Taylor's theorem Taylor series

Brook Taylor FRS (18 August 1685 – 29 December 1731) was an English mathematician who is best known for Taylor's theorem and the Taylor series.

Brook Taylor was born in Edmonton (at that time in Middlesex) to John Taylor of Bifrons House in Patrixbourne, Kent, and Olivia Tempest, daughter of Sir Nicholas Tempest, Bart., of Durham.

He entered St John's College, Cambridge, as a fellow-commoner in 1701, and took degrees of LL.B. and LL.D. in 1709 and 1714, respectively. Having studied mathematics under John Machin and John Keill, in 1708 he obtained a remarkable solution of the problem of the "centre of oscillation," which, however, remained unpublished until May 1714, when his claim to priority was disputed by Johann Bernoulli. Taylor's Methodus Incrementorum Directa et Inversa (1715) added a new branch to higher mathematics, now called the "calculus of finite differences". Among other ingenious applications, he used it to determine the form of movement of a vibrating string, by him first successfully reduced to mechanical principles. The same work contained the celebrated formula known as Taylor's formula, the importance of which remained unrecognized until 1772, when J. L. Lagrange realized its powers and termed it "the main foundation of differential calculus".

In his 1715 essay Linear Perspective, Taylor set forth the true principles of the art in an original and more general form than any of his predecessors; but the work suffered from the brevity and obscurity which affected most of his writings, and needed the elucidation bestowed on it in the treatises of Joshua Kirby (1754) and Daniel Fournier (1761).