Everything about Roger Cotes totally explained
Roger Cotes FRS (
July 10,
1682 –
June 5,
1716) was an English
mathematician, known for working closely with
Isaac Newton by proofreading the second edition of his famous book, the
Principia, before publication. He also invented the
quadrature formulas known as
Newton-Cotes formulas and first introduced what is known today as
Euler's formula. He was the first
Plumian Professor at
Cambridge University from 1707 until his death.
Early life
Cotes was born in
Burbage, Leicestershire. His parents were Robert, the
rector of Burbage, and his wife Grace
née Farmer. Roger had an elder brother, Anthony (born 1681) and a younger sister, Susanna (born 1683). At first Roger attended Leicester School where his mathematical talent was recognised. His aunt Hannah had married Rev. John Smith, and Smith took on the role of tutor to encourage Roger's talent. The Smiths' son,
Robert Smith, would become a close associate of Roger Cotes throughout his life. Cotes later studied at
St Paul's School in
London and then at
Trinity College, Cambridge. He
graduated BA in
1702 and
MA in
1706.
Astronomy
Roger Cotes's contributions to modern
computational methods lie heavily in the fields of
astronomy and mathematics. Cotes began his educational career with a focus on
astronomy. He became a
fellow of Trinity College in 1707, and at age 26 he became the first Plumian Professor of Astronomy and Experimental Philosophy. On his appointment to professor, he opened a subscription list in an effort to provide an
observatory for Trinity. Unfortunately, the observatory still was unfinished when Cotes died, and was demolished in 1797. After his death, many of Cotes's mathematical papers were hastily edited by Robert Smith and published in a book,
Harmonia mensurarum.
Cotes's additional works were later published in
Thomas Simpson's
The Doctrine and Application of Fluxions.
Although Cotes's style was somewhat obscure, his systematic approach to
integration and mathematical theory was highly regarded by his peers. Cotes had discovered an important theorem on the nth
roots of unity, foresaw the method of
least squares, and he discovered a method for integrating
rational fractions with
binomial denominators.
He was also praised for his efforts in numerical methods, especially in
interpolation methods and his table construction techniques.
He was regarded as one of the few British mathematicians capable of following the powerful work of Sir Isaac Newton.
Death and assessment
Cotes died from a violent fever in
Cambridge in 1716 at the early age of 33. Isaac Newton remarked, "If he'd lived we'd have known something."
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