 # LIST OF IMPORTANT MATHEMATICIANS – TIMELINE

This is a chronological list of some of the most important mathematicians in history and their major achievments, as well as some very early achievements in mathematics for which individual contributions can not be acknowledged.

Where the mathematicians have individual pages in this website, these pages are linked; otherwise more information can usually be obtained from the general page relating to the particular period in history, or from the list of sources used. A more detailed and comprehensive mathematical chronology can be found at http://www-groups.dcs.st-and.ac.uk/~history/Chronology/full.html.

## Math Timeline

 Date Name Nationality Major Achievements 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 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 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 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 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 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 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 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 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 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 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 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 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 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 Italian Published solution of cubic and quartic equations (by Tartaglia and Ferrari), acknowledged existence of imaginary numbers (based on √-1) 1522-1565 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 French Early development of projective geometry and “point at infinity”, perspective theorem 1596-1650 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 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 French Pioneer (with Fermat) of probability theory, Pascal’s Triangle of binomial coefficients 1643-1727 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 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 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 Swiss Further developed infinitesimal calculus, including the “calculus of variation”, functions for curve of fastest descent (brachistochrone) and catenary curve 1667-1754 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 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 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 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 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 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 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 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 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 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 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 British Co-wrote “Principia Mathematica” (attempt to ground mathematics on logic) 1862-1943 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 British Russell’s paradox, co-wrote “Principia Mathematica” (attempt to ground mathematics on logic), theory of types 1877-1947 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 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 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 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 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 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 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- 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