Timeline of Mathematical History¶

Key milestones in the development of mathematics, from ancient times to the modern era.

Ancient Mathematics¶

Period	Mathematician(s)	Contribution
c. 2000 BCE	Babylonians	Base-60 number system, quadratic equations, Pythagorean triples
c. 1650 BCE	Egyptians (Rhind Papyrus)	Practical arithmetic, geometry for surveying, unit fractions
c. 570–495 BCE	Pythagoras	Pythagorean theorem, number theory, musical ratios
c. 500 BCE	Indian mathematicians	Concept of zero, decimal place-value system
c. 400 BCE	Zeno of Elea	Zeno's paradoxes (Achilles and the tortoise)
c. 300 BCE	Euclid	Elements — axiomatic geometry, number theory, proof methods
c. 287–212 BCE	Archimedes	Method of exhaustion, area/volume formulas, lever principle
c. 200–284 CE	Diophantus	Arithmetica — solving equations in integers

Period	Mathematician(s)	Contribution
c. 598–668 CE	Brahmagupta	Rules for zero, negative numbers, quadratic equations
c. 780–850 CE	Al-Khwārizmī	Al-Jabr — systematic algebra, Hindu-Arabic numerals
c. 1048–1131	Omar Khayyam	Geometric solutions for cubic equations
c. 1170–1250	Fibonacci	Liber Abaci — popularized Hindu-Arabic numerals in Europe
c. 1501–1576	Cardano, Tartaglia, Ferrari	Solutions for cubic and quartic equations (Ars Magna)

Period	Mathematician(s)	Contribution
1540–1603	François Viète	Symbolic algebra using letters for unknowns
1596–1650	René Descartes	Analytic geometry, Cartesian coordinates
1607–1665	Pierre de Fermat	Number theory, Fermat's Last Theorem, probability
1623–1662	Blaise Pascal	Probability theory, Pascal's triangle
1643–1727	Isaac Newton	Calculus (fluxions), laws of motion, universal gravitation
1646–1716	Gottfried Wilhelm Leibniz	Calculus notation (dy/dx, ∫), binary arithmetic
1707–1783	Leonhard Euler	Euler's formula, graph theory, number theory, notation (π, e, i, Σ, f(x))

Period	Mathematician(s)	Contribution
1777–1855	Carl Friedrich Gauss	Number theory (Disquisitiones Arithmeticae), statistics, differential geometry
1792–1856	Nikolai Lobachevsky	Hyperbolic (non-Euclidean) geometry
1802–1860	János Bolyai	Hyperbolic geometry (independent of Lobachevsky)
1811–1832	Évariste Galois	Group theory, solvability of polynomials
1815–1864	George Boole	Boolean algebra, foundations of logic
1815–1897	Karl Weierstrass	Rigorous ε-δ definitions, calculus foundations
1821–1895	Augustin-Louis Cauchy	Complex analysis, convergence, rigorous calculus
1826–1866	Bernhard Riemann	Riemann integral, Riemann zeta function, Riemannian geometry
1845–1918	Georg Cantor	Set theory, cardinality, transfinite numbers
1848–1925	Gottlob Frege	Predicate logic, foundations of arithmetic
1854–1912	Henri Poincaré	Algebraic topology, dynamical systems, Poincaré conjecture
1868–1942	Felix Hausdorff	Axiomatic topology, Hausdorff spaces

Period	Mathematician(s)	Contribution
1862–1943	David Hilbert	Hilbert's problems (1900), formalist program
1872–1970	Bertrand Russell	Principia Mathematica, Russell's paradox
1875–1941	Henri Lebesgue	Measure theory, Lebesgue integral
1881–1966	L. E. J. Brouwer	Fixed-point theorem, intuitionism
1903–1957	John von Neumann	Game theory, computer architecture, quantum mechanics
1906–1978	Kurt Gödel	Incompleteness theorems (1931)
1912–1954	Alan Turing	Turing machines, computability, Enigma code-breaking
1915–1998	Paul Erdős	Graph theory, combinatorics, probabilistic method
1931–present	John Milnor	Differential topology, exotic spheres (Fields Medal)
1953–present	Andrew Wiles	Proof of Fermat's Last Theorem (1994)
1966–present	Grigori Perelman	Proof of Poincaré conjecture (2003)