Brook Taylor Essay, Research Paper

Brook Taylor

Mathematician

Biographical Sketch

4/2/01

Shannon Pringle

Born: August 18, 1685; Edmonton, Middlesex, England.

Died: December 29, 1731; Somerset House, London, England.

Brook Taylor was born into a fairly wealthy family on the fringes of nobility. His father, John Taylor, was the son of Nathaniel Taylor – a member of Oliver Cromwell’s Assembly. His mother, Olivia Tempest, was the daughter of Sir John Tempest.

Taylor was brought up in a household where his father ruled as a strict disciplinarian, yet he was a man of culture with interests in painting and music. Therefore, Taylor grew up not only to be an accomplished musician and painter, but he applied his mathematical skills to both these areas later in his life.

Since Taylor’s family was well off, they could afford to have private tutors for their son, and in fact this home education was all that he enjoyed before entering St. John’s College – Cambridge on April 3, 1703. By this time he had a good grounding in classics and mathematics. At Cambridge, Taylor became highly involved with mathematics. He graduated with an L.L.B in 1709, but by this time he had already written his first important mathematics paper in 1708. (It was not published until 1714)

In 1712, Taylor was elected to the Royal Society. It was an election based more on the expertise, which Machin, Keill, and others knew that Taylor had, rather than on his published results. For example, Taylor wrote to Machin in 1712 providing a solution to a problem concerning Kepler’s second law of planetary motion. Also in 1712, Taylor was appointed to the committee set up to adjudicate on whether the claim of Newton or of Leibniz to have invented the calculus was correct.

The year 1714 also marks the time in which Taylor was elected Secretary to the Royal Society. It was a position that Taylor held from January 14 of that year until October 21, 1718 when he resigned, partly for health reasons and his lack of interest in the rather demanding position. That time period marks what must be his most mathematically productive time. Two books, which appeared in 1715, Methodus incrementorum directa et inversa and Linear Perspective are extremely important in the history of mathematics.

Taylor made several visits to France. These were made partly for health reasons and partly to visit friends he had made there. He met Pierre Remond de Montmort and corresponded with him on various mathematical topics after his return. In particular, they discussed infinite series and probability. Taylor also corresponded with de Moivre on probability and at times there was a three-way discussion going on between them.

Between 1712 and 1724, Taylor published 13 articles on topics as diverse as describing experiments in capillary action, magnetism and thermometers. He gave an account of an experiment to discover the law of magnetic attraction (1715) and an improved method for approximating the roots of an equation by giving a new method for computing logarithms (1717).

Taylor added to mathematics a new branch now called the “calculus of finite differences”, invented integration by parts, and discovered the celebrated series known as Taylor’s expansion. These ideas appear in his first book mentioned previously. Other important ideas, which are contained in said book, are singular solutions to differential equations, a change of variables formula, and a way of relating the derivative of a function to the derivative of the inverse function. Also contained is a discussion on vibrating strings, an interest which almost certainly comes from his early love of music.

Taylor also devised the basic principles of perspective in Linear Perspective (1715). The main theorem in this work was that the projection of a straight line not parallel to the plane of the picture passes through its intersection and its vanishing point.

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