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Gregory
James Gregory, a Scottish mathematician and astronomer, discovers the Binomial series. that was unrecognized as his discovery. "A Concise History of Mathematics"
Dirk J. Struik -
Gregory Derives Tanget Series
In 1671, James Gregory discoveres the inverse tangent series that Leibniz is later given credit for. "The History of Mathematics: An Introduction"
David M. Burton -
Gregory's Unrecognized Discovery
James Gregory discovers the series later named as the Taylor Series. http://mathworld.wolfram.com/TaylorSeries.html "A Concise History of Mathematics"
Dirk J. Struik, page 114 -
Leibniz Derives?
Gottfried Leibniz finds the alternating series for π/4 which he is most famous for. Too bad Gregory discovered it in 1671 and was, again, unrecognized for it. -
Taylor's Theorem Devised
Brook Taylor devises his theorem during this year --approximately 40 years after Gregory devised the same theorem. His theorem states that any function satisfying certain conditions can be written as a Taylor Series. It is actually also known that Jean Bernoulli, a Swiss mathematician, had discovered this same series sometime before both Gregory and Taylor. The picture to the left is a general example of a Taylor series. http://mathworld.wolfram.com/TaylorSeries.html -
Taylor's Theorem is Published
Taylor publishes his famous Taylor Theorem in his "Methodus incrementorum directa et inversa". The Taylor series is established as a power series centered at C (where C is a constant). "A History of Mathematics"
Carl B. Boyer, page 469 -
Stirling Publishes MacLaurin Series
James Stirling, a Scottish mathematician, publishes the Maclaurin series in his work "Methodus differentialis" --over ten years before the series' namesake does. "A History of Mathematics"
Carl B. Boyer, page 469 -
Maclaurin Series
Colin Maclaurin publishes his book "Treatise of Fluxions" in which a general version of the Taylor series is stated that is more commonly known as the Maclaurin series. The Maclaurin series is simply the Taylor series centered at zero. The Maclaurin series is also a power series. "A History of Mathematics"
Carl B. Boyer, page 469 -
Recognition
Euler applies the Taylor series to problems in differential calculus. "Mathematics: From the Birth of Numbers"
Jan Gullberg -
Lagrange's Remainder
J.L. Lagrange derives a remainder theorem of a Taylor series. (The date above is an approximation for the actual date is unknown.) http://mathworld.wolfram.com/CauchyRemainder.html -
Importance of Taylor's Theorem
Lagrange proclaims Taylor's Theorem is the basic principle of differential calculus. This is first moment when people recoginzed the theorem as being an important contribution to other mathematics. This is when a direct connection between series and other branches of mathematics occurred. -
Cauchy's Remainder
Augustin-Louis Cauchy went even further with the Taylor series to develop a formula for finding the remainder of the remaining terms of a Taylor series after expanding after a certain point. The formula is to the left. http://mathworld.wolfram.com/TaylorSeries.html (Date above is an approximate time of discovery) -
Today's Uses
Taylor Series can be used to approximate numbers such as e, ln 2, and pi (and other transcendental numbers). The Taylor series, as previously mentioned, is also very important to many fundamental calculus applications in today's classroom. "Calculus with Analytic Geometry"
Third Edition
Robert Ellis, Denny Gulick
