35000 BCE African. First notched tally bones
3100 BCE Sumerian Earliest documented counting and measuring system
2700 BCE Egyptian Earliest fully-developed base 10 number system in use
2600 BCE Sumerian Multiplication tables, geometrical exercises and division problems
2000-1800 BCE Egyptian Earliest papyri showing numeration system and basic arithmetic
1800-1600 BCE Babylonian Clay tablets dealing with fractions, algebra and equations
1650 BCE Egyptian Rhind Papyrus (instruction manual in arithmetic, geometry, unit fractions, etc)
1200 BCE Chinese First decimal numeration system with place value concept
1200-900 BCE Indian Early Vedic mantras invoke powers of ten from a hundred all the way up to a trillion
800-400 BCE Indian “Sulba Sutra” lists several Pythagorean triples and simplified Pythagorean theorem for the sides of a square and a rectangle, quite accurate approximation to √2
650 BCE Chinese Lo Shu order three (3 x 3) “magic square” in which each row, column and diagonal sums to 15
624-546 BCE. Thales. Greek. Early developments in geometry, including work on similar and right triangles
570-495 BCE. Pythagoras. Greek. Expansion of geometry, rigorous approach building from first principles, square and triangular numbers, Pythagoras’ theorem
500 BCE. Hippasus. Greek. Discovered potential existence of irrational numbers while trying to calculate the value of √2
490-430 BCE. Zeno of Elea. Greek. Describes a series of paradoxes concerning infinity and infinitesimals
470-410 BCE Hippocrates of Chios. Greek. First systematic compilation of geometrical knowledge, Lune of Hippocrates
460-370 BCE. Democritus. Greek. Developments in geometry and fractions, volume of a cone
428-348 BCE. Plato. Greek. Platonic solids, statement of the Three Classical Problems, influential teacher and popularizer of mathematics, insistence on rigorous proof and logical methods
410-355 BCE. Eudoxus of Cnidus. Greek. Method for rigorously proving statements about areas and volumes by successive approximations
384-322 BCE. Aristotle. Greek. Development and standardization of logic (although not then considered part of mathematics) and deductive reasoning
300 BCE. Euclid. Greek. Definitive statement of classical (Euclidean) geometry, use of axioms and postulates, many formulas, proofs and theorems including Euclid’s Theorem on infinitude of primes
287-212 BCE. Archimedes. Greek. Formulas for areas of regular shapes, “method of exhaustion” for approximating areas and value of π, comparison of infinities
276-195 BCE Eratosthenes. Greek. “Sieve of Eratosthenes” method for identifying prime numbers
262-190 BCE. Apollonius of Perga. Greek. Work on geometry, especially on cones and conic sections (ellipse, parabola, hyperbola)
200 BCE. Chinese. “Nine Chapters on the Mathematical Art”, including guide to how to solve equations using sophisticated matrix-based methods
190-120 BCE. Hipparchus. Greek. Develop first detailed trigonometry tables
36 BCE. Mayan. Pre-classic Mayans developed the concept of zero by at least this time
10-70 CE Heron (or Hero) of Alexandria. Greek. Heron’s Formula for finding the area of a triangle from its side lengths, Heron’s Method for iteratively computing a square root
90-168 CE. Ptolemy. Greek/Egyptian. Develop even more detailed trigonometry tables
200 CE. Sun Tzu. Chinese. First definitive statement of Chinese Remainder Theorem
200 CE. Indian Refined and perfected decimal place value number system
200-284 CE. Diophantus. Greek. Diophantine Analysis of complex algebraic problems, to find rational solutions to equations with several unknowns
220-280 CE. Liu Hui. Chinese. Solved linear equations using a matrices (similar to Gaussian elimination), leaving roots unevaluated, calculated value of π correct to five decimal places, early forms of integral and differential calculus
400 CE. Indian “Surya Siddhanta” contains roots of modern trigonometry, including first real use of sines, cosines, inverse sines, tangents and secants
476-550 CE. Aryabhata. Indian. Definitions of trigonometric functions, complete and accurate sine and versine tables, solutions to simultaneous quadratic equations, accurate approximation for π (and recognition that π is an irrational number)
598-668 CE. Brahmagupta. Indian. Basic mathematical rules for dealing with zero (+, – and x), negative numbers, negative roots of quadratic equations, solution of quadratic equations with two unknowns
600-680 CE. Bhaskara I. Indian. First to write numbers in Hindu-Arabic decimal system with a circle for zero, remarkably accurate approximation of the sine function
780-850 CE. Muhammad Al-Khwarizmi. Persian. Advocacy of the Hindu numerals 1 – 9 and 0 in Islamic world, foundations of modern algebra, including algebraic methods of “reduction” and “balancing”, solution of polynomial equations up to second degree.
908-946 CE Ibrahim ibn Sinan. Arabic. Continued Archimedes’ investigations of areas and volumes, tangents to a circle
953-1029 CE. Muhammad Al-Karaji. Persian. First use of proof by mathematical induction, including to prove the binomial theorem
966-1059 CE. Ibn al-Haytham (Alhazen). Persian/Arabic. Derived a formula for the sum of fourth powers using a readily generalizable method, “Alhazen’s problem”, established beginnings of link between algebra and geometry
1048-1131. Omar Khayyam. Persian. Generalized Indian methods for extracting square and cube roots to include fourth, fifth and higher roots, noted existence of different sorts of cubic equations
1114-1185. Bhaskara II. Indian. Established that dividing by zero yields infinity, found solutions to quadratic, cubic and quartic equations (including negative and irrational solutions) and to second order Diophantine equations, introduced some preliminary concepts of calculus
1170-1250. Leonardo of Pisa (Fibonacci). Italian. Fibonacci Sequence of numbers, advocacy of the use of the Hindu-Arabic numeral system in Europe, Fibonacci’s identity (product of two sums of two squares is itself a sum of two squares)
1201-1274. Nasir al-Din al-Tusi. Persian. Developed field of spherical trigonometry, formulated law of sines for plane triangles
1202-1261. Qin Jiushao. Chinese. Solutions to quadratic, cubic and higher power equations using a method of repeated approximations
1238-1298. Yang Hui. Chinese. Culmination of Chinese “magic” squares, circles and triangles, Yang Hui’s Triangle (earlier version of Pascal’s Triangle of binomial co-efficients)
1267-1319 Kamal al-Din al-Farisi. Persian. Applied theory of conic sections to solve optical problems, explored amicable numbers, factorization and combinatorial methods
1350-1425. Madhava. Indian. Use of infinite series of fractions to give an exact formula for π, sine formula and other trigonometric functions, important step towards development of calculus
1323-1382. Nicole Oresme. French. System of rectangular coordinates, such as for a time-speed-distance graph, first to use fractional exponents, also worked on infinite series
1446-1517. Luca Pacioli. Italian. Influential book on arithmetic, geometry and book-keeping, also introduced standard symbols for plus and minus
1499-1557. Niccolò Fontana Tartaglia. Italian. Formula for solving all types of cubic equations, involving first real use of complex numbers (combinations of real and imaginary numbers), Tartaglia’s Triangle (earlier version of Pascal’s Triangle)
1501-1576. Gerolamo Cardano. Italian. Published solution of cubic and quartic equations (by Tartaglia and Ferrari), acknowledged existence of imaginary numbers (based on √-1)
1522-1565. Lodovico Ferrari. Italian. Devised formula for solution of quartic equations
1550-1617. John Napier. British. Invention of natural logarithms, popularized the use of the decimal point, Napier’s Bones tool for lattice multiplication
1588-1648. Marin Mersenne. French. Clearing house for mathematical thought during 17th Century, Mersenne primes (prime numbers that are one less than a power of 2)
1591-1661. Girard Desargues. French Early development of projective geometry and “point at infinity”, perspective theorem
1596-1650. René Descartes. French. Development of Cartesian coordinates and analytic geometry (synthesis of geometry and algebra), also credited with the first use of superscripts for powers or exponents
1598-1647. Bonaventura Cavalieri Italian. “Method of indivisibles” paved way for the later development of infinitesimal calculus
1601-1665. Pierre de Fermat. French. Discovered many new numbers patterns and theorems (including Little Theorem, Two-Square Thereom and Last Theorem), greatly extending knowlege of number theory, also contributed to probability theory
1616-1703. John Wallis. British. Contributed towards development of calculus, originated idea of number line, introduced symbol ∞ for infinity, developed standard notation for powers
1623-1662. B laise Pascal. French. Pioneer (with Fermat) of probability theory, Pascal’s Triangle of binomial coefficients
1643-1727. Isaac Newton. British. Development of infinitesimal calculus (differentiation and integration), laid ground work for almost all of classical mechanics, generalized binomial theorem, infinite power series
1646-1716. Gottfried Leibniz. German. Independently developed infinitesimal calculus (his calculus notation is still used), also practical calculating machine using binary system (forerunner of the computer), solved linear equations using a matrix
1654-1705. Jacob Bernoulli. Swiss Helped to consolidate infinitesimal calculus, developed a technique for solving separable differential equations, added a theory of permutations and combinations to probability theory, Bernoulli Numbers sequence, transcendental curves
1667-1748. Johann Bernoulli. Swiss. Further developed infinitesimal calculus, including the “calculus of variation”, functions for curve of fastest descent (brachistochrone) and catenary curve
1667-1754. Abraham de Moivre. French. De Moivre’s formula, development of analytic geometry, first statement of the formula for the normal distribution curve, probability theory
1690-1764 Christian Goldbach. German. Goldbach Conjecture, Goldbach-Euler Theorem on perfect powers
1707-1783 Leonhard Euler. Swiss. Made important contributions in almost all fields and found unexpected links between different fields, proved numerous theorems, pioneered new methods, standardized mathematical notation and wrote many influential textbooks
1728-1777. Johann Lambert. Swiss. Rigorous proof that π is irrational, introduced hyperbolic functions into trigonometry, made conjectures on non-Euclidean space and hyperbolic triangles
1736-1813. Joseph Louis Lagrange. Italian/French. Comprehensive treatment of classical and celestial mechanics, calculus of variations, Lagrange’s theorem of finite groups, four-square theorem, mean value theorem
1746-1818. Gaspard Monge. French. Inventor of descriptive geometry, orthographic projection
1749-1827. Pierre-Simon Laplace. French. Celestial mechanics translated geometric study of classical mechanics to one based on calculus, Bayesian interpretation of probability, belief in scientific determinism
1752-1833. Adrien-Marie Legendre. French. Abstract algebra, mathematical analysis, least squares method for curve-fitting and linear regression, quadratic reciprocity law, prime number theorem, elliptic functions
1768-1830. Joseph Fourier. French. Studied periodic functions and infinite sums in which the terms are trigonometric functions (Fourier series)
1777-1825. Carl Friedrich Gauss. G erman. Pattern in occurrence of prime numbers, construction of heptadecagon, Fundamental Theorem of Algebra, exposition of complex numbers, least squares approximation method, Gaussian distribution, Gaussian function, Gaussian error curve, non-Euclidean geometry, Gaussian curvature
1789-1857. Augustin-Louis Cauchy. French. Early pioneer of mathematical analysis, reformulated and proved theorems of calculus in a rigorous manner, Cauchy’s theorem (a fundamental theorem of group theory)
1790-1868. August Ferdinand Möbius. German. Möbius strip (a two-dimensional surface with only one side), Möbius configuration, Möbius transformations, Möbius transform (number theory), Möbius function, Möbius inversion formula
1791-1858. George Peacock. British. Inventor of symbolic algebra (early attempt to place algebra on a strictly logical basis)
1791-1871. Charles Babbage. British. Designed a “difference engine” that could automatically perform computations based on instructions stored on cards or tape, forerunner of programmable computer.
1792-1856 Nikolai Lobachevsky Russian. Developed theory of hyperbolic geometry and curved spaces independendly of Bolyai
1802-1829. Niels Henrik Abel. Norwegian. Proved impossibility of solving quintic equations, group theory, abelian groups, abelian categories, abelian variety
1802-1860. János Bolyai. Hungarian. Explored hyperbolic geometry and curved spaces independently of Lobachevsky
1804-1851. Carl Jacobi. German. Important contributions to analysis, theory of periodic and elliptic functions, determinants and matrices
1805-1865. William Hamilton. Irish. Theory of quaternions (first example of a non-commutative algebra)
1811-1832. Évariste Galois. French. Proved that there is no general algebraic method for solving polynomial equations of degree greater than four, laid groundwork for abstract algebra, Galois theory, group theory, ring theory, etc
1815-1864. George Boole. British. Devised Boolean algebra (using operators AND, OR and NOT), starting point of modern mathematical logic, led to the development of computer science
1815-1897. Karl Weierstrass. German. Discovered a continuous function with no derivative, advancements in calculus of variations, reformulated calculus in a more rigorous fashion, pioneer in development of mathematical analysis
1821-1895 Arthur Cayley. British. Pioneer of modern group theory, matrix algebra, theory of higher singularities, theory of invariants, higher dimensional geometry, extended Hamilton’s quaternions to create octonions
1826-1866. Bernhard Riemann. German. Non-Euclidean elliptic geometry, Riemann surfaces, Riemannian geometry (differential geometry in multiple dimensions), complex manifold theory, zeta function, Riemann Hypothesis
1831-1916.Richard Dedekind. German. Defined some important concepts of set theory such as similar sets and infinite sets, proposed Dedekind cut (now a standard definition of the real numbers)
1834-1923. John Venn British. Introduced Venn diagrams into set theory (now a ubiquitous tool in probability, logic and statistics)
1842-1899 Marius Sophus Lie. Norwegian. Applied algebra to geometric theory of differential equations, continuous symmetry, Lie groups of transformations
1845-1918. Georg Cantor. German. Creator of set theory, rigorous treatment of the notion of infinity and transfinite numbers, Cantor’s theorem (which implies the existence of an “infinity of infinities”)
1848-1925. Gottlob Frege. German. One of the founders of modern logic, first rigorous treatment of the ideas of functions and variables in logic, major contributor to study of the foundations of mathematics
1849-1925. Felix Klein. German. Klein bottle (a one-sided closed surface in four-dimensional space), Erlangen Program to classify geometries by their underlying symmetry groups, work on group theory and function theory
1854-1912. Henri Poincaré French. Partial solution to “three body problem”, foundations of modern chaos theory, extended theory of mathematical topology, Poincaré conjecture
1858-1932. Giuseppe Peano. Italian. Peano axioms for natural numbers, developer of mathematical logic and set theory notation, contributed to modern method of mathematical induction
1861-1947. Alfred North Whitehead. British. Co-wrote “Principia Mathematica” (attempt to ground mathematics on logic)
1862-1943 David Hilbert. German. 23 “Hilbert problems”, finiteness theorem, “Entscheidungsproblem“ (decision problem), Hilbert space, developed modern axiomatic approach to mathematics, formalism
1864-1909 Hermann Minkowski. German. Geometry of numbers (geometrical method in multi-dimensional space for solving number theory problems), Minkowski space-time
1872-1970. Bertrand Russell. British. Russell’s paradox, co-wrote “Principia Mathematica” (attempt to ground mathematics on logic), theory of types
1877-1947. G.H. Hardy. British. Progress toward solving Riemann hypothesis (proved infinitely many zeroes on the critical line), encouraged new tradition of pure mathematics in Britain, taxicab numbers
1878-1929 Pierre Fatou. French. Pioneer in field of complex analytic dynamics, investigated iterative and recursive processes
1881-1966 L.E.J. Brouwer Dutch Proved several theorems marking breakthroughs in topology (including fixed point theorem and topological invariance of dimension)
1887-1920 Srinivasa Ramanujan Indian Proved over 3,000 theorems, identities and equations, including on highly composite numbers, partition function and its asymptotics, and mock theta functions
1893-1978 Gaston Julia French Developed complex dynamics, Julia set formula
1903-1957 John von Neumann Hungarian/American Pioneer of game theory, design model for modern computer architecture, work in quantum and nuclear physics
1906-1978. Kurt Gödel. Austria. Incompleteness theorems (there can be solutions to mathematical problems which are true but which can never be proved), Gödel numbering, logic and set theory
1906-1998. André Weil. French. Theorems allowed connections between algebraic geometry and number theory, Weil conjectures (partial proof of Riemann hypothesis for local zeta functions), founding member of influential Bourbaki group
1912-1954. Alan Turing. British. Breaking of the German enigma code, Turing machine (logical forerunner of computer), Turing test of artificial intelligence
1913-1996. Paul Erdös. Hungarian. Set and solved many problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory and probability theory
1917-2008 Edward Lorenz. American. Pioneer in modern chaos theory, Lorenz attractor, fractals, Lorenz oscillator, coined term “butterfly effect”
1919-1985. Julia Robinson. American. Work on decision problems and Hilbert’s tenth problem, Robinson hypothesis
1924-2010. Benoît Mandelbrot. French. Mandelbrot set fractal, computer plottings of Mandelbrot and Julia sets
1928-2014. Alexander Grothendieck. French. Mathematical structuralist, revolutionary advances in algebraic geometry, theory of schemes, contributions to algebraic topology, number theory, category theory, etc
1928-2015. John Nash. American. Work in game theory, differential geometry and partial differential equations, provided insight into complex systems in daily life such as economics, computing and military
1934-2007. Paul Cohen. American. Proved that continuum hypothesis could be both true and not true (i.e. independent from Zermelo-Fraenkel set theory)
1937- John Horton Conway. British. Important contributions to game theory, group theory, number theory, geometry and (especially) recreational mathematics, notably with the invention of the cellular automaton called the “Game of Life”
1947- Yuri Matiyasevich. Russian. Final proof that Hilbert’s tenth problem is impossible (there is no general method for determining whether Diophantine equations have a solution)
1953- Andrew Wiles British Finally proved Fermat’s Last Theorem for all numbers (by proving the Taniyama-Shimura conjecture for semistable elliptic curves)
1966- Grigori Perelman Russian Finally proved Poincaré Conjecture (by proving Thurston’s geometrization conjecture), contributions to Riemannian geometry and geometric topology