Brook Taylor
1685-1731
English Mathematician
Two works published by Brook Taylor in 1715 indicate the scope of his interests and accomplishments. The first was Methodus incrementorum directa et inversa, in which he became the first mathematician to discuss the calculus of finite differences. The book also introduced the "Taylor series," concerning the expansion of functions of a single variable in a finite series, for which Taylor became famous. Also in 1715, Taylor published Linear Perspective, which contained the first general treatment of the principle of vanishing points.
Brook Taylor. (Archive Photos. Reproduced with permission.)Born in Edmonton, Middlesex, England, on August 18, 1685, Taylor was the oldest child of John and Olivia Tempest Taylor. The family were members of the minor nobility, and John encouraged his son to take an interest in music and the visual arts. Taylor entered St. John's College, Cambridge, in 1709, and later earned his bachelor of laws degree, which he followed with a doctorate of laws in 1714.
In the meantime, Taylor had been elected to membership in the Royal Society in 1712. He later served as the Society's secretary for four years, and during the period from 1712 to 1724 published 13 articles on a variety of subjects in the Philosophical Transactions of the Royal Society. His first significant paper, a solution to the problem of the center of oscillation, appeared in 1714. Not everyone was impressed with Taylor's work, however: Swiss mathematician Johann Bernoulli (1667-1748), who would remain a lifetime rival, attacked the piece.
In Taylor's watershed year of 1715, his Methodus (its full title means "Direct and Indirect Methods of Incrementation") became the first work to discuss the calculus of finite differences. The book presented the Taylor series, a theorem that provided the first general expression for the expansions of functions of a single variable in finite series. Once again, Taylor was challenged by Bernoulli, who claimed he had discovered the idea first—a claim that turned out to be untrue. (Bernoulli attempted to do much the same thing to his own son, Daniel [1700-1782].) Only in 1772, when Joseph-Louis Lagrange (1736-1813) declared the Taylor series the basic principle of differential calculus, were the implications of Taylor's work fully appreciated.
The Methodus also contained groundbreaking discussions regarding the vibration of strings, and of light rays, concepts that touched—at least obliquely—on the other interests of Taylor, who was said to be a gifted visual artist and musician. His fascination with the visual arts led to Linear Perspective, which he updated in 1719 with New Linear Perspective. He is also reputed to have authored an unpublished manuscript entitled On Musick.
Family matters took much of Taylor's attention during the 1720s, which would turn out to be the last decade of his short life. In 1721, he married a woman of whom his father disapproved, and was estranged from the family. Taylor returned to the fold two years later, when his wife died in childbirth, and in 1725 he married again, this time with the family's approval. His father died in 1729, and Taylor inherited the family estate in Kent. A year later, his second wife died, also in childbirth, and Taylor followed her by another year.
The daughter from the second marriage, Elizabeth, lived. Years after Taylor's death, her son wrote a biography of his grandfather and thus helped ensure that Taylor's achievements gained much wider recognition than they had enjoyed in his lifetime.
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