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* 1668 – [[Nicholas Mercator]] and [[William Brouncker, 2nd Viscount Brouncker|William Brouncker]] discover an [[infinite series]] for the logarithm while attempting to calculate the area under a [[hyperbolic segment]]. |
* 1668 – [[Nicholas Mercator]] and [[William Brouncker, 2nd Viscount Brouncker|William Brouncker]] discover an [[infinite series]] for the logarithm while attempting to calculate the area under a [[hyperbolic segment]]. |
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* 1671 – [[James Gregory (astronomer and mathematician)|James Gregory]] develops a series expansion for the inverse-[[tangent (trigonometric function)|tangent]] function (originally discovered by [[Madhava of Sangamagrama|Madhava]]). |
* 1671 – [[James Gregory (astronomer and mathematician)|James Gregory]] develops a series expansion for the inverse-[[tangent (trigonometric function)|tangent]] function (originally discovered by [[Madhava of Sangamagrama|Madhava]]). |
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* 1671 – James Gregory discovers [[Taylor's |
* 1671 – James Gregory discovers [[Taylor's theorem]]. |
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* 1673 – [[Gottfried Leibniz]] also develops his version of infinitesimal calculus. |
* 1673 – [[Gottfried Leibniz]] also develops his version of infinitesimal calculus. |
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* 1675 – Isaac Newton invents an algorithm for the [[Newton's method|computation of functional roots]]. |
* 1675 – Isaac Newton invents an algorithm for the [[Newton's method|computation of functional roots]]. |
This is a timelineofpure and applied mathematics history. It is divided here into three stages, corresponding to stages in the development of mathematical notation: a "rhetorical" stage in which calculations are described purely by words, a "syncopated" stage in which quantities and common algebraic operations are beginning to be represented by symbolic abbreviations, and finally a "symbolic" stage, in which comprehensive notational systems for formulas are the norm.
Major mathematics areas
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Foundations |
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Algebra |
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Analysis |
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Discrete |
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Geometry |
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Number theory |
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Topology |
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Applied |
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Computational |
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