Timeline of calculus and mathematical analysis

A timeline of calculus and mathematical analysis.

500BC to 1600

5th century BC - The Zeno's paradoxes,
5th century BC - Antiphon attempts to square the circle,
5th century BC - Democritus finds the volume of cone is 1/3 of volume of cylinder,
4th century BC - Eudoxus of Cnidus develops the method of exhaustion,
3rd century BC - Archimedes displays geometric series in The Quadrature of the Parabola,
3rd century - Liu Hui rediscovers the method of exhaustion in order to find the area of a circle,
4th century - The Pappus's centroid theorem,
5th century - Zu Chongzhi established a method that would later be called Cavalieri's principle to find the volume of a sphere,
600 - Liu Zhuo is the first person to use second-order interpolation for computing the positions of the sun and the moon,
665 - Brahmagupta discovers a second order Taylor interpolation for [math]\displaystyle{ \sin (x+\epsilon) }[/math],
862 - The Banu Musa brothers write the "Book on the Measurement of Plane and Spherical Figures",
9th century - Thābit ibn Qurra discusses the quadrature of the parabola and the volume of the paraboloid,
11th century - Ibn al-Haytham derived a formula for the sum of fourth powers which allowed him to calculate the volume of a paraboloid,
12th century - Sharaf al-Din al-Tusi finds the minimum and maximum values of cubic functions,
12th century - Bhāskara II discovers a rule equivalent to Rolle's theorem for [math]\displaystyle{ \sin x }[/math],
14th century - Nicole Oresme proves of the divergence of the harmonic series,
14th century - Madhava discovers the power series expansion for [math]\displaystyle{ \sin x }[/math], [math]\displaystyle{ \cos x }[/math], [math]\displaystyle{ \arctan x }[/math] and [math]\displaystyle{ \pi/4 }[/math],
14th century - Parameshvara discovers a third order Taylor interpolation for [math]\displaystyle{ \sin (x+\epsilon) }[/math],
1501 - Nilakantha Somayaji writes the Tantrasamgraha, which contains the Madhava's discoveries,
1548 - Francesco Maurolico attemptes to calculate the barycenter of various bodies (pyramid, paraboloid, etc.),
1550 - Jyeshtadeva writes the Yuktibhāṣā, a commentary to Nilakantha's Tantrasamgraha,
1560 - Sankara Variar writes the Kriyakramakari,
1565 - Federico Commandino publishes De centro Gravitati,
1588 - Commandino's translation of Pappus' Collectio gets published,
1593 - François Viète discovers the first infinite product in the history of mathematics,

17th century

1606 - Luca Valerio applies methods of Archimedes to find volumes and centres of gravity of solid bodies,
1609 - Johannes Kepler computes the integral [math]\displaystyle{ \int_0^\theta \sin x\ dx = 1-\cos \theta }[/math],
1611 - Thomas Harriot discovers an interpolation formula similar to Newton's interpolation formula,
1615 - Johannes Kepler publishes Nova stereometria doliorum,
1624 - Henry Briggs publishes Arithmetica Logarithmica,
1629 - Pierre de Fermat discovers his method of maxima and minima, precursor of the derivative concept,
1634 - Gilles de Roberval shows that the area under a cycloid is three times the area of its generating circle,
1635 - Bonaventura Cavalieri publishes Geometria Indivisibilibus,
1637 - René Descartes publishes La Géométrie,
1638 - Galileo Galilei publishes Two New Sciences,
1644 - Evangelista Torricelli publishes Opera geometrica,
1644 - Fermat's methods of maxima and minima published by Pierre Hérigone,
1647 - Cavalieri computes the integral [math]\displaystyle{ \int_0^a x^{n}\ dx=\frac{1}{n+1}a^{n+1} }[/math],
1647 - Grégoire de Saint-Vincent discovers that the area under a hyperbola represented a logarithm,
1650 - Pietro Mengoli proves of the divergence of the harmonic series,
1654 - Johannes Hudde discovers the power series expansion for [math]\displaystyle{ \ln(1+x) }[/math],
1656 - John Wallis publishes Arithmetica Infinitorum,
1658 - Christopher Wren shows that the length of a cycloid is four times the diameter of its generating circle,
1659 - Second edition of Van Schooten's Latin translation of Descartes' Geometry with appendices by Hudde and Heuraet,
1665 - Isaac Newton discovers the generalized binomial theorem and develops his version of infinitesimal calculus,
1667 - James Gregory publishes Vera circuli et hyperbolae quadratura,
1668 - Nicholas Mercator publishes Logarithmotechnia,
1668 - James Gregory computes the integral of the secant function,
1670 - Isaac Newton rediscovers the power series expansion for [math]\displaystyle{ \sin x }[/math] and [math]\displaystyle{ \cos x }[/math] (originally discovered by Madhava),
1670 - Isaac Barrow publishes Lectiones Geometricae,
1671 - James Gregory rediscovers the power series expansion for [math]\displaystyle{ \arctan x }[/math] and [math]\displaystyle{ \pi/4 }[/math] (originally discovered by Madhava),
1672 - René-François de Sluse publishes A Method of Drawing Tangents to All Geometrical Curves,
1673 - Gottfried Leibniz also develops his version of infinitesimal calculus,
1675 - Isaac Newton invents a Newton's method for the computation of roots of a function,
1675 - Leibniz uses the modern notation for an integral for the first time,
1677 - Leibniz discovers the rules for differentiating products, quotients, and the function of a function.
1683 - Jacob Bernoulli discovers the number $e$ ,
1684 - Leibniz publishes his first paper on calculus,
1686 - The first appearance in print of the [math]\displaystyle{ \int }[/math] notation for integrals,
1687 - Isaac Newton publishes Philosophiæ Naturalis Principia Mathematica,
1691 - The first proof of Rolle's theorem is given by Michel Rolle,
1691 - Leibniz discovers the technique of separation of variables for ordinary differential equations,
1694 - Johann Bernoulli discovers the L'Hôpital's rule,
1696 - Guillaume de L'Hôpital publishes Analyse des Infiniment Petits, the first calculus textbook,
1696 - Jakob Bernoulli and Johann Bernoulli solve the brachistochrone problem, the first result in the calculus of variations.

18th century

1711 - Isaac Newton publishes De analysi per aequationes numero terminorum infinitas,
1712 - Brook Taylor develops Taylor series,
1722 - Roger Cotes computes the derivative of sine in his Harmonia Mensurarum,
1730 - James Stirling publishes The Differential Method,
1734 - George Berkeley publishes The Analyst,
1734 - Leonhard Euler introduces the integrating factor technique for solving first-order ordinary differential equations,
1735 - Leonhard Euler solves the Basel problem, relating an infinite series to π,
1736 - Newton's Method of Fluxions posthumously published,
1737 - Thomas Simpson publishes Treatise of Fluxions,
1739 - Leonhard Euler solves the general homogeneous linear ordinary differential equation with constant coefficients,
1742 - Modern definion of logarithm by William Gardiner,
1742 - Colin Maclaurin publishes Treatise on Fluxions,
1748 - Euler publishes Introductio in analysin infinitorum,
1748 - Maria Gaetana Agnesi discusses analysis in Instituzioni Analitiche ad Uso della Gioventu Italiana,
1762 - Joseph Louis Lagrange discovers the divergence theorem,
1797 - Lagrange publishes Théorie des fonctions analytiques,

19th century

1807 - Joseph Fourier announces his discoveries about the trigonometric decomposition of functions,
1811 - Carl Friedrich Gauss discusses the meaning of integrals with complex limits and briefly examines the dependence of such integrals on the chosen path of integration,
1815 - Siméon Denis Poisson carries out integrations along paths in the complex plane,
1817 - Bernard Bolzano presents the intermediate value theorem — a continuous function which is negative at one point and positive at another point must be zero for at least one point in between,
1822 - Augustin-Louis Cauchy presents the Cauchy integral theorem for integration around the boundary of a rectangle in the complex plane,
1825 - Augustin-Louis Cauchy presents the Cauchy integral theorem for general integration paths—he assumes the function being integrated has a continuous derivative, and he introduces the theory of residues in complex analysis,
1825 - André-Marie Ampère discovers Stokes' theorem,
1828 - George Green introduces Green's theorem,
1831 - Mikhail Vasilievich Ostrogradsky rediscovers and gives the first proof of the divergence theorem earlier described by Lagrange, Gauss and Green,
1841 - Karl Weierstrass discovers but does not publish the Laurent expansion theorem,
1843 - Pierre-Alphonse Laurent discovers and presents the Laurent expansion theorem,
1850 - Victor Alexandre Puiseux distinguishes between poles and branch points and introduces the concept of essential singular points,
1850 - George Gabriel Stokes rediscovers and proves Stokes' theorem,
1873 - Georg Frobenius presents his method for finding series solutions to linear differential equations with regular singular points,

20th century

1908 - Josip Plemelj solves the Riemann problem about the existence of a differential equation with a given monodromic group and uses Sokhotsky - Plemelj formulae,
1966 - Abraham Robinson presents non-standard analysis.
1985 - Louis de Branges de Bourcia proves the Bieberbach conjecture,

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