| Date | Name | Nationality | Major Achievements |
| 35000 BC | | African | First notched tally bones |
| 3100 BC | | Sumerian | Earliest documented counting and measuring system |
| 2700 BC | | Egyptian | Earliest fully-developed base 10 number system in use |
| 2600 BC | | Sumerian | Multiplication tables, geometrical exercises and division problems |
| 2000-1800 BC | | Egyptian | Earliest papyri showing numeration system and basic arithmetic |
| 1800-1600 BC | | Babylonian | Clay tablets dealing with fractions, algebra and equations |
| 1650 BC | | Egyptian | Rhind Papyrus (instruction manual in arithmetic, geometry, unit fractions, etc) |
| 1200 BC | | Chinese | First decimal numeration system with place value concept |
| 1200-900 BC | | Indian | Early Vedic mantras invoke powers of ten from a hundred all the way up to a trillion |
| 800-400 BC | | 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 BC | | Chinese | Lo Shu order three (3 x 3) “magic square” in which each row, column and diagonal sums to 15 |
| 624-546 BC | Thales | Greek | Early developments in geometry, including work on similar and right triangles |
| 570-495 BC | Pythagoras | Greek | Expansion of geometry, rigorous approach building from first principles, square and triangular numbers, Pythagoras’ theorem |
| 500 BC | Hippasus | Greek | Discovered potential existence of irrational numbers while trying to calculate the value of √2 |
| 490-430 BC | Zeno of Elea | Greek | Describes a series of paradoxes concerning infinity and infinitesimals |
| 470-410 BC | Hippocrates of Chios | Greek | First systematic compilation of geometrical knowledge, Lune of Hippocrates |
| 460-370 BC | Democritus | Greek | Developments in geometry and fractions, volume of a cone |
| 428-348 BC | 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 BC | Eudoxus of Cnidus | Greek | Method for rigorously proving statements about areas and volumes by successive approximations |
| 384-322 BC | Aristotle | Greek | Development and standardization of logic (although not then considered part of mathematics) and deductive reasoning |
| 300 BC | 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 BC | Archimedes | Greek | Formulas for areas of regular shapes, “method of exhaustion” for approximating areas and value of π, comparison of infinities |
| 276-195 BC | Eratosthenes | Greek | “Sieve of Eratosthenes” method for identifying prime numbers |
| 262-190 BC | Apollonius of Perga | Greek | Work on geometry, especially on cones and conic sections (ellipse, parabola, hyperbola) |
| 200 BC | | Chinese | “Nine Chapters on the Mathematical Art”, including guide to how to solve equations using sophisticated matrix-based methods |
| 190-120 BC | Hipparchus | Greek | Develop first detailed trigonometry tables |
| 36 BC | | Mayan | Pre-classic Mayans developed the concept of zero by at least this time |
| 10-70 AD | 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 AD | Ptolemy | Greek/Egyptian | Develop even more detailed trigonometry tables |
| 200 AD | Sun Tzu | Chinese | First definitive statement of Chinese Remainder Theorem |
| 200 AD | | Indian | Refined and perfected decimal place value number system |
| 200-284 AD | Diophantus | Greek | Diophantine Analysis of complex algebraic problems, to find rational solutions to equations with several unknowns |
| 220-280 AD | 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 AD | | Indian | “Surya Siddhanta” contains roots of modern trigonometry, including first real use of sines, cosines, inverse sines, tangents and secants |
| 476-550 AD | 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 AD | 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 AD | 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 AD | 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 AD | Ibrahim ibn Sinan | Arabic | Continued Archimedes' investigations of areas and volumes, tangents to a circle |
| 953-1029 AD | Muhammad Al-Karaji | Persian | First use of proof by mathematical induction, including to prove the binomial theorem |
| 966-1059 AD | 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 | Blaise 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 | German | 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- | Alexander Grothendieck | French | Mathematical structuralist, revolutionary advances in algebraic geometry, theory of schemes, contributions to algebraic topology, number theory, category theory, etc |
| 1928- | 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
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