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://wwwgroups.dcs.stand.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 fullydeveloped base 10 number system in use 

2600 BCE 
Sumerian 
Multiplication tables, geometrical exercises and division problems 

20001800 BCE 
Egyptian 
Earliest papyri showing numeration system and basic arithmetic 

18001600 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 

1200900 BCE 
Indian 
Early Vedic mantras invoke powers of ten from a hundred all the way up to a trillion 

800400 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 

624546 BCE 
Thales 
Greek 
Early developments in geometry, including work on similar and right triangles 
570495 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 
490430 BCE 
Zeno of Elea 
Greek 
Describes a series of paradoxes concerning infinity and infinitesimals 
470410 BCE 
Hippocrates of Chios 
Greek 
First systematic compilation of geometrical knowledge, Lune of Hippocrates 
460370 BCE 
Democritus 
Greek 
Developments in geometry and fractions, volume of a cone 
428348 BCE 
Plato 
Greek 
Platonic solids, statement of the Three Classical Problems, influential teacher and popularizer of mathematics, insistence on rigorous proof and logical methods 
410355 BCE 
Eudoxus of Cnidus 
Greek 
Method for rigorously proving statements about areas and volumes by successive approximations 
384322 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 
287212 BCE 
Archimedes 
Greek 
Formulas for areas of regular shapes, “method of exhaustion” for approximating areas and value of π, comparison of infinities 
276195 BCE 
Eratosthenes 
Greek 
“Sieve of Eratosthenes” method for identifying prime numbers 
262190 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 matrixbased methods 

190120 BCE 
Hipparchus 
Greek 
Develop first detailed trigonometry tables 
36 BCE 
Mayan 
Preclassic Mayans developed the concept of zero by at least this time 

1070 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 
90168 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 

200284 CE 
Diophantus 
Greek 
Diophantine Analysis of complex algebraic problems, to find rational solutions to equations with several unknowns 
220280 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 

476550 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) 
598668 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 
600680 CE 
Bhaskara I 
Indian 
First to write numbers in HinduArabic decimal system with a circle for zero, remarkably accurate approximation of the sine function 
780850 CE 
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 CE 
Ibrahim ibn Sinan 
Arabic 
Continued Archimedes’ investigations of areas and volumes, tangents to a circle 
9531029 CE 
Muhammad AlKaraji 
Persian 
First use of proof by mathematical induction, including to prove the binomial theorem 
9661059 CE 
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 
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, 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 
19282014 
Alexander Grothendieck 
French 
Mathematical structuralist, revolutionary advances in algebraic geometry, theory of schemes, contributions to algebraic topology, number theory, category theory, etc 
19282015 
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 
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