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 Brook
Taylor was probably one of mathematics most artistically gifted
members. Some say, if the media were to show any interest in Taylor's
accomplishments, his artistic and musical skills would probably
be mentioned first. However, Taylor is remembered more importantly
in the mathematics field for adding a new branch now called the
"calculus of infinite differences", inventing integration
by parts, and discovering the infamous formula known as Taylor's
expansion. Born to an affluent family and a cultured household,
he learned during his adolescence to play the harpsichord and
to paint. Both of these talents, however, found mathematical expression
in later years in the form of his pioneering study of the motion
of vibrating string and his treatise on the mathematical theory
of linear perspective.
Taylor
entered St. John's College, in Cambridge, in 1701, where he prepared
to study law. Despite his chose of study, Taylor's interests in
mathematics soon become his calling. Praised for his Algebraic
skills and his artistic ability by his colleagues, Taylor grew
to be one of the first generation of British and Continental mathematicians
to inherit the algorithms and theories of the new math known as
calculus. Poised with this new analytical pursuit, Taylor was
eager to develop new analytical tools and techniques whose results
could be used throughout new mathematics. However, his work was
often falsely disputed by his peers as being without justification
and merit. An early example of this occurred when Taylor found
a solution to the problem of the center of oscillation which,
sense it went unpublished until 1714, resulted in a priority dispute
with the famed Jonathan Bernoulli. Another case occurred after
Taylor's appointment to Fellow Royal Society with the publication
of Taylor's chief work, Methodu incrementorum directa et inversa
in 1715.
His work added to mathematics the method of increments
or what we refer to as the 'calculus of finite differences'. In
it he also created integration by parts and contained the Taylor's
expansion formula, the importance of which remained unrecognized
until the year of 1772 when Lagrange declared it as the basic
principle of differential calculus. Taylor's work was acclaimed
by the likes of Euler, Maclaurin, and others, but some did not
feel the same praise and admiration. By working several problems
in mechanics already solved by other Continental mathematicians
and by citing no one but Newton in his text, Taylor angered the
leading mathematicians of the continent, Leibniz and Bernoulli,
once again. If Taylor and his advocates were heirs and promoters
of the new calculus, they were also the key to promoting anger,
deception, and favoritism in the dispute over who was the creator
of calculus, Lenbniz or Newton. The fact that Taylor had failed
to cite the work of some of his Continental predecessors was true,
however it was done so by pure honest negligence. Evidence in
Taylor's unpublished papers in London and Cambridge proved, without
a doubt, that Taylor's work was his own. He may have not cited
his work where required, but neither did he claim it as his own.
He simply relied on the work of his peers for help and inspiration.
Taylor's mistake can be characterized as just another example
of the fierce competition and jealousy of this period in mathematical
history.
Despite
Taylor's exceptional genuine mathematical work and his innocence,
the higher-ranking Continental mathematicians continued to hold
bitter anger toward him. In 1721, Taylor's life took a turn for
the worse. He married a woman considered unacceptable by his family,
especially his father, who soon distanced himself from his famed
son. Two years later his wife died at childbirth, and when he
remarried in 1725, his second wife died five years later, also
during childbirth. Although, the surviving daughter helped to
bring Taylor happiness, Taylor died at the age of 46 in 1731,
stricken with grief and failing health.
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