A timeline of calculus and mathematical analysis.
== 1000 to 1500 ==
1020 — Abul Wáfa — Discussed the quadrature
of the parabola and the volume of the paraboloid.
1021 — Ibn al-Haytham completes his Book
of Optics, which formulated and solved “Alhazen's
problem” geometrically, and developed and
proved the earliest general formula for infinitesimal
and integral calculus using mathematical induction.
12th century — Bhāskara II conceives differential
calculus, and also develops Rolle's theorem,
Pell's equation, a proof for the Pythagorean
Theorem, computes π to 5 decimal places,
and calculates the time taken for the earth
to orbit the sun to 9 decimal places
14th century — Madhava is considered the
father of mathematical analysis, who also
worked on the power series for pi and for
sine and cosine functions, and along with
other Kerala school mathematicians, founded
the important concepts of Calculus
14th century — Parameshvara, a Kerala school
mathematician, presents a series form of the
sine function that is equivalent to its Taylor
series expansion, states the mean value theorem
of differential calculus, and is also the
first mathematician to give the radius of
circle with inscribed cyclic quadrilateral
1400 — Madhava discovers the series expansion
for the inverse-tangent function, the infinite
series for arctan and sin, and many methods
for calculating the circumference of the circle,
and uses them to compute π correct to 11
decimal places
== 16th century ==
1501 — Nilakantha Somayaji writes the “Tantra
Samgraha”, which lays the foundation for
a complete system of fluxions (derivatives),
and expands on concepts from his previous
text, the “Aryabhatiya Bhasya”.
1550 — Jyeshtadeva, a Kerala school mathematician,
writes the “Yuktibhāṣā”, the world's
first calculus text, which gives detailed
derivations of many calculus theorems and
formulae.
== 17th century ==
1629 - Pierre de Fermat develops a rudimentary
differential calculus,
1634 - Gilles de Roberval shows that the area
under a cycloid is three times the area of
its generating circle,
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,
1665 - Isaac Newton works on the fundamental
theorem of calculus and develops his version
of infinitesimal calculus,
1671 - James Gregory develops a series expansion
for the inverse-tangent function (originally
discovered by Madhava),
1673 - Gottfried Leibniz also develops his
version of infinitesimal calculus,
1675 - Isaac Newton invents a Newton's method
for the computation of functional roots,
1691 - Gottfried Leibniz discovers the technique
of separation of variables for ordinary differential
equations,
1696 - Guillaume de L'Hôpital states his
rule for the computation of certain limits,
1696 - Jakob Bernoulli and Johann Bernoulli
solve brachistochrone problem, the first result
in the calculus of variations.
== 18th century ==
1712 - Brook Taylor develops Taylor series,
1730 - James Stirling publishes The Differential
Method,
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,
1739 - Leonhard Euler solves the general homogeneous
linear ordinary differential equation with
constant coefficients,
1748 - Maria Gaetana Agnesi discusses analysis
in Instituzioni Analitiche ad Uso della Gioventu
Italiana,
1762 - Joseph Louis Lagrange discovers the
divergence theorem,
== 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,
