Brook Taylor was an English mathematician born in 1685 who made significant contributions to calculus and mathematical analysis. He developed Taylor's theorem, which expresses the value of a function as a power series, and is one of the fundamental tools in calculus. Taylor served as the secretary of the Royal Society from 1714 to 1718. He published works on linear perspective and applied his power series to solving numerical equations. Taylor died in 1731, leaving a lasting legacy through Taylor's theorem and its applications in mathematics.

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2. PRESENTATION ON
BIOGRAPHY OF BROOK TAYLOR
BROOK TAYLOR
(1685-1731)

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4. Biodataof Taylor
Brook Taylor was born on 18 August 1685 at Edmonton area of London,England.
Residence:England
Nationality: English
Institution: St John’s college,Cambridge.
Fields: Mathematician
Known for: Taylor’s Theorem
Or, Taylor Series.
Died: 29 December,1731

5. Family Description
Brook Taylor was the son of John Taylor of Bifrons House, Kent,
and Olivia, daughter of Sir Nicholas Tempest, Bart. The family was
fairly well-to-do, and was connected with the minor nobility.
Brook’s grandfather, Nathaniel, had supported Oliver Cromwell.
John Taylor was a stern parent from whom Brook became
estranged in 1721 when he married a woman said to have been
of good family but of no fortune.

6. In 1723 Brook returned home after his wife’s
death in childbirth. He married again in 1725
with his father’s approval, but his second wife
died in childbirth in 1730. The daughter born
at that time survived.

7. EducationalDescription
Taylor’s home life seems to have influenced his work in
several ways. Two of his major scientific contributions deal
with the vibrating string and with perspective drawing. His
father was interested in music and art, and entertained
many musicians in his home. The family archives were said
to contain paintings by Brook, and there is an unpublished
manuscript entitled On Musick among the Taylor materials
at St. John’s College, Cambridge.

8. EducationalDescription
This is not the paper said to have been presented to the
Royal society prior to 1713, but a portion of a projected joint
work by Taylor, Sir Isaac Newton, and Dr. Pepusch, who
apparently was to write on the nonscientific aspects of
music.

9. Taylor was tutored at home before entering St. John’s College in 1701,
where the chief mathematicians were John Machin and John Keill. Taylor
received the LL.B. degree in 1709, was elected to the Royal Society in
1712, and was awarded the LL.D. degree in 1714. He was elected
secretary to the Royal Society in January 1714, but he resigned in
October 1718 because of ill health and perhaps because of a loss of
interest in this rather confining task. He visited France several times both
for the sake of his health and for social reasons.

10. Out of these trips grew a scientific correspondence with
Pierre Rémond de Montmort dealing with infinite series
and Montmort’s work in probability. In this Taylor served on
some occasions as an intermediary between Montmort and
Abraham De Moivre. W. W. Rouse Ball reports that the
problem of the knight’s tour was first solved by Montmort
and De Moivre after it had been suggested by Taylor.

11. Way of Life
The famous Taylor series was printed for the first time in
the Methodus incrementorum directa et inversa (1715), although
there is evidence that Gottfried Wilhelm Leibniz and Isaac
Newton had known the result earlier. The series expresses the
value of a function in the neighborhood of a point in terms of the
derivatives at the point. Taylor derived the series by taking the
limiting case of the general finite difference formula, but he failed
to consider the problem of convergence.

12. He specifically mentioned the case x = 0, which is often
known as Maclaurin's series. Joseph Louis Lagrange was
the first to recognize fully the importance of the Taylor
series, and the first correct proof was given by Augustin
Louis Cauchy.

13. PublishingTheory
In 1717 Taylor applied his series to the solution of numerical
equations, observing that the method could be used to solve
transcendental equations. Other contributions to the calculus
included consideration of change of variable, the first singular
solution of a differential equation, and the derivation of the
differential equation relating to atmospheric refraction. He also
contributed a solution to the problem of the center of oscillation.

14. PublishingTheory
Taylor's theorem is taught in introductory level
calculus courses and it is one of the central
elementary tools in mathematical analysis.
Within pure mathematics it is the starting point of
more advanced asymptotic analysis, and it is
commonly used in more applied fields of numerics as
well as in mathematical physics.

15. PublishingTheory
Taylor's theorem also generalizes to multivariate and vector
valued functions 𝑓: 𝑅 𝑛
→ 𝑅 𝑚
on any dimensions n and m.
This generalization of Taylor's theorem is the basis for the
definition of so-called jets which appear in differential
geometry and partial differential equations.

16. LaterLife
In 1715 Taylor published his Linear
Perspective, followed in 1719 by New Principles of
‘’Linear Perspective’’. These works contained the first
general statement of the principle of vanishing points.
In his later years he became interested in philosophy,
writing” Contemplation philosophical”, which was
printed and circulated privately in 1793.

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