TIMELINE OF MATHEMATICS
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://wwwgroups.dcs.stand.ac.uk/~history/Chronology/full.html.
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 fullydeveloped base 10 number system in use  
2600 BC  Sumerian  Multiplication tables, geometrical exercises and division problems  

Egyptian  Earliest papyri showing numeration system and basic arithmetic  
18001600 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  
1200900 BC  Indian  Early Vedic mantras invoke powers of ten from a hundred all the way up to a trillion  
800400 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  
624546 BC  Thales  Greek  Early developments in geometry, including work on similar and right triangles 
570495 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 
490430 BC  Zeno of Elea  Greek  Describes a series of paradoxes concerning infinity and infinitesimals 
470410 BC  Hippocrates of Chios  Greek  First systematic compilation of geometrical knowledge, Lune of Hippocrates 
460370 BC  Democritus  Greek  Developments in geometry and fractions, volume of a cone 
428348 BC  Plato  Greek  Platonic solids, statement of the Three Classical Problems, influential teacher and popularizer of mathematics, insistence on rigorous proof and logical methods 
410355 BC  Eudoxus of Cnidus  Greek  Method for rigorously proving statements about areas and volumes by successive approximations 
384322 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 
287212 BC  Archimedes  Greek  Formulas for areas of regular shapes, “method of exhaustion” for approximating areas and value of π, comparison of infinities 
276195 BC  Eratosthenes  Greek  “Sieve of Eratosthenes” method for identifying prime numbers 
262190 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 matrixbased methods  
190120 BC  Hipparchus  Greek  Develop first detailed trigonometry tables 
36 BC  Mayan  Preclassic Mayans developed the concept of zero by at least this time  
1070 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 
90168 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  
200284 AD  Diophantus  Greek  Diophantine Analysis of complex algebraic problems, to find rational solutions to equations with several unknowns 
220280 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  
476550 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) 
598668 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 
600680 AD  Bhaskara I  Indian  First to write numbers in HinduArabic decimal system with a circle for zero, remarkably accurate approximation of the sine function 
780850 AD  Muhammad AlKhwarizmi  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 
908946 AD  Ibrahim ibn Sinan  Arabic  Continued Archimedes' investigations of areas and volumes, tangents to a circle 

Muhammad AlKaraji  Persian  First use of proof by mathematical induction, including to prove the binomial theorem 
9661059 AD  Ibn alHaytham (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 
10481131  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 
11141185  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 
11701250  Leonardo of Pisa (Fibonacci)  Italian  Fibonacci Sequence of numbers, advocacy of the use of the HinduArabic numeral system in Europe, Fibonacci's identity (product of two sums of two squares is itself a sum of two squares) 
12011274  Nasir alDin alTusi  Persian  Developed field of spherical trigonometry, formulated law of sines for plane triangles 
12021261  Qin Jiushao  Chinese  Solutions to quadratic, cubic and higher power equations using a method of repeated approximations 
12381298  Yang Hui  Chinese  Culmination of Chinese “magic” squares, circles and triangles, Yang Hui’s Triangle (earlier version of Pascal’s Triangle of binomial coefficients) 
12671319  Kamal alDin alFarisi  Persian  Applied theory of conic sections to solve optical problems, explored amicable numbers, factorization and combinatorial methods 
13501425  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 
13231382  Nicole Oresme  French  System of rectangular coordinates, such as for a timespeeddistance graph, first to use fractional exponents, also worked on infinite series 
14461517  Luca Pacioli  Italian  Influential book on arithmetic, geometry and bookkeeping, also introduced standard symbols for plus and minus 
14991557  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) 
15011576  Gerolamo Cardano  Italian  Published solution of cubic and quartic equations (by Tartaglia and Ferrari), acknowledged existence of imaginary numbers (based on √1) 
15221565  Lodovico Ferrari  Italian  Devised formula for solution of quartic equations 
15501617  John Napier  British  Invention of natural logarithms, popularized the use of the decimal point, Napier’s Bones tool for lattice multiplication 
15881648  Marin Mersenne  French  Clearing house for mathematical thought during 17th Century, Mersenne primes (prime numbers that are one less than a power of 2) 
15911661  Girard Desargues  French  Early development of projective geometry and “point at infinity”, perspective theorem 
15961650  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 
15981647  Bonaventura Cavalieri  Italian  “Method of indivisibles” paved way for the later development of infinitesimal calculus 
16011665  Pierre de Fermat  French  Discovered many new numbers patterns and theorems (including Little Theorem, TwoSquare Thereom and Last Theorem), greatly extending knowlege of number theory, also contributed to probability theory 
16161703  John Wallis  British  Contributed towards development of calculus, originated idea of number line, introduced symbol ∞ for infinity, developed standard notation for powers 
16231662  Blaise Pascal  French  Pioneer (with Fermat) of probability theory, Pascal’s Triangle of binomial coefficients 
16431727  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 
16461716  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 
16541705  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 
16671748  Johann Bernoulli  Swiss  Further developed infinitesimal calculus, including the “calculus of variation”, functions for curve of fastest descent (brachistochrone) and catenary curve 
16671754  Abraham de Moivre  French  De Moivre's formula, development of analytic geometry, first statement of the formula for the normal distribution curve, probability theory 
16901764  Christian Goldbach  German  Goldbach Conjecture, GoldbachEuler Theorem on perfect powers 
17071783  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 
17281777  Johann Lambert  Swiss  Rigorous proof that π is irrational, introduced hyperbolic functions into trigonometry, made conjectures on nonEuclidean space and hyperbolic triangles 
17361813  Joseph Louis Lagrange  Italian/French  Comprehensive treatment of classical and celestial mechanics, calculus of variations, Lagrange’s theorem of finite groups, foursquare theorem, mean value theorem 
17461818  Gaspard Monge  French  Inventor of descriptive geometry, orthographic projection 
17491827  PierreSimon Laplace  French  Celestial mechanics translated geometric study of classical mechanics to one based on calculus, Bayesian interpretation of probability, belief in scientific determinism 
17521833  AdrienMarie Legendre  French  Abstract algebra, mathematical analysis, least squares method for curvefitting and linear regression, quadratic reciprocity law, prime number theorem, elliptic functions 
17681830  Joseph Fourier  French  Studied periodic functions and infinite sums in which the terms are trigonometric functions (Fourier series) 
17771825 

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, nonEuclidean geometry, Gaussian curvature 
17891857  AugustinLouis 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) 
17901868  August Ferdinand Möbius  German  Möbius strip (a twodimensional surface with only one side), Möbius configuration, Möbius transformations, Möbius transform (number theory), Möbius function, Möbius inversion formula 
17911858  George Peacock  British  Inventor of symbolic algebra (early attempt to place algebra on a strictly logical basis) 
17911871  Charles Babbage  British  Designed a "difference engine" that could automatically perform computations based on instructions stored on cards or tape, forerunner of programmable computer. 
17921856  Nikolai Lobachevsky  Russian  Developed theory of hyperbolic geometry and curved spaces independendly of Bolyai 
18021829  Niels Henrik Abel  Norwegian  Proved impossibility of solving quintic equations, group theory, abelian groups, abelian categories, abelian variety 
18021860  János Bolyai  Hungarian  Explored hyperbolic geometry and curved spaces independently of Lobachevsky 
18041851  Carl Jacobi  German  Important contributions to analysis, theory of periodic and elliptic functions, determinants and matrices 
18051865  William Hamilton  Irish  Theory of quaternions (first example of a noncommutative algebra) 
18111832  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 
18151864  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 
18151897  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 
18211895  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 
18261866  Bernhard Riemann  German  NonEuclidean elliptic geometry, Riemann surfaces, Riemannian geometry (differential geometry in multiple dimensions), complex manifold theory, zeta function, Riemann Hypothesis 
18311916  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) 
18341923  John Venn  British  Introduced Venn diagrams into set theory (now a ubiquitous tool in probability, logic and statistics) 
18421899  Marius Sophus Lie  Norwegian  Applied algebra to geometric theory of differential equations, continuous symmetry, Lie groups of transformations 
18451918  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”) 
18481925  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 
18491925  Felix Klein  German  Klein bottle (a onesided closed surface in fourdimensional space), Erlangen Program to classify geometries by their underlying symmetry groups, work on group theory and function theory 
18541912  Henri Poincaré  French  Partial solution to “three body problem”, foundations of modern chaos theory, extended theory of mathematical topology, Poincaré conjecture 
18581932  Giuseppe Peano  Italian  Peano axioms for natural numbers, developer of mathematical logic and set theory notation, contributed to modern method of mathematical induction 
18611947  Alfred North Whitehead  British  Cowrote “Principia Mathematica” (attempt to ground mathematics on logic) 
18621943  David Hilbert  German  23 “Hilbert problems”, finiteness theorem, “Entscheidungsproblem“ (decision problem), Hilbert space, developed modern axiomatic approach to mathematics, formalism 
18641909  Hermann Minkowski  German  Geometry of numbers (geometrical method in multidimensional space for solving number theory problems), Minkowski spacetime 
18721970  Bertrand Russell  British  Russell’s paradox, cowrote “Principia Mathematica” (attempt to ground mathematics on logic), theory of types 
18771947  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 
18781929  Pierre Fatou  French  Pioneer in field of complex analytic dynamics, investigated iterative and recursive processes 
18811966  L.E.J. Brouwer  Dutch  Proved several theorems marking breakthroughs in topology (including fixed point theorem and topological invariance of dimension) 
18871920  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 
18931978  Gaston Julia  French  Developed complex dynamics, Julia set formula 
19031957  John von Neumann 
Hungarian/ American 
Pioneer of game theory, design model for modern computer architecture, work in quantum and nuclear physics 
19061978  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 
19061998  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 
19121954  Alan Turing  British  Breaking of the German enigma code, Turing machine (logical forerunner of computer), Turing test of artificial intelligence 
19131996  Paul Erdös  Hungarian  Set and solved many problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory and probability theory 
19172008  Edward Lorenz  American  Pioneer in modern chaos theory, Lorenz attractor, fractals, Lorenz oscillator, coined term “butterfly effect” 
19191985  Julia Robinson  American  Work on decision problems and Hilbert's tenth problem, Robinson hypothesis 
19242010  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 
19342007  Paul Cohen  American  Proved that continuum hypothesis could be both true and not true (i.e. independent from ZermeloFraenkel 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 TaniyamaShimura 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 