Mathematics exist before 1900 BC, in great civilizations everywhere, including China, India, Babylon etc. However, the first record of Mathematical manuscripts is found in Egypt, namely, the Moscow Papyrus and the Rhind Papyrus. In the 'Achievement' column below, the notations are as follows:
| AG = Analytic Geometry | Al = Algebra | Ar = Arithmetic |
| As = Astronomy | C = Calculus | DE = Differential Equation |
| FM = Foundation of Mathematics | G = Geometry | GT = Group Theory |
| L = Logic | M = Mechanics | N = Number Theory |
| P = Probability | RM = Recreational Mathematics | S = Statistic |
| ST = Set Theory | T = Topology |
The list here is not exhaustive. The mathematicians listed here are either pioneers in various fields of Mathematics, or those who have contributed to almost all fields, or those who have settled unsolved problems. For a more complete list of mathematicians, click on index of mathematicians.
| Name | Nationality | Year | Achievements |
| ??? | Egyptian | 1900 BC | Moscow Papyrus (25 problems on G) |
| ??? | Egyptian | 1700 BC | Rhind Papyrus (87 problems on Ar, Al, G) |
| Thales | Greek | 634-548 BC | introduced deductive G |
| Pythagoras | Greek | 580-500 BC | G, N, in particular Pythagoras Theorem |
| Zeno of Elea | Greek | 490-425 BC | Zeno paradoxes, G |
| Hippocrates of Chios | Greek | 470-410 BC | Quadrature of Lunes (G) |
| Hippias of Elias | Greek | 460-400BC | G |
| Archytas | Greek | 428-350 BC | Ar, As, G, M |
| Plato | Greek | 427-347 BC | Mathematical Rigor L |
| Eudoxus of Cnidus | Greek | 408-335 BC | Eudoxan Theory of Proportion, Method of Exhaustion, As |
| Aristotle | Greek | 384-322 BC | "Father of Logic" L |
| Euclid | Greek | 325-265 BC | Elements (13 volumes of G, N) |
| ??? | Chinese | 300 BC | Chou-pei Suan-ching ("Arithmetic Classic of the Gnomon and the Circular Paths of Heaven ") Al, Ar, G |
| Archimedes of Syracuse | Greek | 287-212 BC | numerous works on G, M, Hydrostatics |
| Apollonius | Greek | 262-190 BC | Plane Loci (Locus of Points), On Contact (Circles of Apollonius), Conics (8 books on Conic Sections), Porism (G) |
| Chang Tsang | Chinese | 200 BC | Chiu-chang Suan-shu ("Nine Chapters on Mathematics"), which contains 246 problems on Al, N, G |
| Heron of Alexandria | Greek | 10-75 AD | Heron's area of triangle |
| Ptolemy | Greek | 85-165 AD | Almagest, G |
| Diophantus of Alexandria | Greek | 200-284 AD | Arithmetica (13 books on Ar) |
| Pappus | Greek | 290-350 AD | Synagoge (10 books) |
| Sun Tzu | Chinese | 300 AD | Sun Tzu Suan Ching (Mathematical Classic of Sun Tzu) |
| Brahmagupta | Indian | 600-670 | Ar, Al, N, As |
| Mohammmed ibu Musa al-Khwarizmi | Muslim | 780-850 | Hisab al-jabr w'al-muqabala (Al); Ar, As |
| Tabit ibu Korra | Arab | 836-901 | Ar, Al, As |
| Omar Khayyam | Muslim | 1048-1131 | Al, such as solving the General Cubic Equations by Geometric Constructions and Conic Sections |
| Leonardo Fibonacci of Pisa | Italian | 1175-1250 | Liber abaci (Ar, notably Fibonacci Sequence); Liber quadratorum (N) |
| Chu Shih-chieh | Chinese | 1270-1330 | Szu-yuen yu-chien ("The Precious Mirror of the Four Elements"), which deals with modern Al |
| Nicholas Chuquet | French | -1500 | Triparty (Ar, Al) |
| Michael Stifel | German | 1487-1567 | Arithmetica integra (Al) |
| Girolama Cardano | Italian | 1501-1576 | Ars Magna, solving the General Cubic Equation (Al) |
| Ludovico Ferrari | Italian | 1522-1565 | solved the General Quartic Equation, Al |
| Francois Viete | French | 1540-1589 | Isagoge (AG); Canon mathematicus contains highly remarkable contribution to Trigonometry |
| John Napier | Scottish | 1550-1617 | founded Logarithm; concept of Binary System |
| Galileo Galilei | Italian | 1564-1642 | Dialogues Concerning Two New Sciences, As, M |
| Johannes Kepler | German | 1571-1630 | Kepler's 3 Laws of Planetary Motion, As |
| Girard Desargues | French | 1591-1661 | founded Projective G |
| Ren� Descartes | French | 1596-1650 | La G�om�trie, which includes invention of Cartesian Plane (3 books on AG) |
| Pierre de Fermat | French | 1601-1665 | AG, C, N, P; proposed Fermat's Last Theorem |
| John Wallis | English | 1616-1703 | Tractatus de sectioibus conicas (Conics); Arithmetica infinitorum (Infinite Series); Al |
| Blaise Pascal | French | 1623-1662 | G, P, C; first calculator; Pascal's Law of Pressure; first clear exposition of Mathematical Induction |
| Isaac Barrow | English | 1630-1677 | Lectiones Opticae (1669), Lectiones Geometricae (1670) and Lectiones Mathematicae (1683) |
| James Gregory | Scottish | 1638-1675 | C |
| Isaac Newton | English | 1642-1727 | Principia, Opticks (Optics), General Binomial Theorem, approximation of roots, founded C and Newtonian M, AG, Al |
| Gottfried Wilhelm Leibniz | French | 1646-1716 | Symbolic L, co-founded C |
| Jacob Bernoulli | Swiss | 1654-1705 | C |
| Johann Bernoulli | Swiss | 1667-1748 | C |
| Daniel Bernoulli | Swiss | 1700-1782 | Bernoulli's Principle |
| Leonhard Euler | Swiss | 1707-1783 | contribution in almost all fields of Mathematics |
| Jean d'Alembert | French | 1717-1783 | As, C, M |
| Edward Waring | English | 1734-1798 | N, including Waring's Theorem; Infinite Series |
| Joseph Louis Lagrange | French | 1736-1813 | GT, DE, M, N, C, Al |
| Pierre-Simon de Laplace | French | 1749-1827 | Laplace Transform, Laplacian |
| Joseph Fourier | French | 1768-1830 | On the Propagation of Heat in Solid Bodies, Fourier Series and Transform |
| Carl Friedrich Gauss | German | 1777-1855 | "Prince of Mathematics"; contribution in almost all fields of Mathematics |
| Sim�on Poisson | French | 1781-1840 | Poisson Distribution (S), As, Electromagnetism |
| Bernard Bolzano | Czech | 1781-1848 | L, Infinite Series |
| Augustin-Louis Cauchy | French | 1789-1857 | Complex Analysis, DE, GT |
| Augustus M�bius | German | 1790-1868 | idea of 4th dimension, M�bius strip (T) |
| George Peacock | English | 1791-1858 | Treatise on Algebra, Principle of Permanence of Equivalent Forms |
| Nikolai Lobachevsky | Russian | 1793-1856 | co-founded Hyperbolic G with Gauss and Bolyai |
| Niels Henrik Abel | Norwegian | 1802-1829 | proved that General Polynomial Equation of Degree > 4 does not have radical solution, GT |
| J�nos Bolyai | Austrian | 1802-1860 | Hyperbolic G |
| Lejeune Dirichlet | German | 1805-1859 | C |
| William Rowan Hamilton | Irish | 1805-1865 | Quaternion, Hamiltonian cycle |
| Augustus de Morgan | English | 1806-1871 | De Morgan's Law, ST, L |
| Benjamin Peirce | American | 1809-1880 | Multiplication Table of 162 different Als |
| Joseph Liouville | French | 1809-1882 | Electromagnetism, N, DE, Transcendental Numbers |
| �variste Galois | French | 1811-1832 | Galois Theory |
| George Boole | American | 1815-1864 | The Investigation of the Laws of Thought, in which he formalized L and the Calculus of Propositions; Boolean Al; first to study Lattices |
| Karl Weierstrass | German | 1815-1897 | 7 great volumes on Analysis, Elliptic Functions, C of Variation, Contour Integral, Power Series |
| Arthur Cayley | English | 1821-1895 | Linear Al, Graph Theory, G, GT, invented Matrices and Theory of Algebraic Invariants with JJ Sylvester |
| Charles Hermite | French | 1822-1901 | proved e is transcendental, DE, Hermitian matrices |
| Bernhard Riemann | German | 1826-1866 | Elliptic G, Riemann surfaces, Riemann Hypothesis (N) |
| Richard Dedekind | German | 1831-1916 | Dedekind Cut, FM |
| Leopold Kronecker | German | 1832-1892 | Higher Al, N, Elliptic Function |
| Charles Lutwidge Dodgson (Lewis Carroll) | English | 1832-1898 | RM |
| John Venn | English | 1834-1923 | Venn Diagram, ST, L |
| Camille Jordon | French | 1838-1922 | GT, Cours d'Analyse which contains Jordon Curve Theorem (T) |
| Charles Peirce | American | 1839-1924 | showed only 3 of the 162 Als require unique division, namely Real Nos., Complex Nos. and Quaternions |
| Sam Loyd | American | 1841-1911 | one of two greatest mathematician in RM |
| Edouard Lucas | French | 1842-1891 | R�cr�ations math�matiques (4 volumes of RM), Lucas Sequence, Primality Tests |
| Georg Cantor | German | 1845-1918 | Cantor's ST, Transfinites |
| Henry Ernest Dudeney | English | 1847-1930 | one of two greatest mathematician in RM |
| Gottlob Frege | German | 1848-1925 | "Father of Mathematical Logic", The Foundations of Arithmetic (1884), The Basic Laws of Arithmetic (L) |
| Felix Klein | German | 1849-1925 | Projective G, Klein Bottle (T) |
| Ferdinand von Lindemann | German | 1852-1939 | proved π is transcendental using Hermite's result on e |
| Hendrik Lorentz | Dutch | 1853-1928 | Lorentz Force, Lorentz Transformation |
| Henri Poincar� | French | 1854-1912 | Analysis Situs, Combinatorial T, Analytic Functions of several variables, various applications of Mathematics to physical systems, Chaos Theory |
| Guiseppe Peano | Italian | 1858-1932 | Peano Axioms, Peano space-filling curves, Linear DE |
| Alfred North Whitehead | English | 1861-1947 | published Principia Mathematica (with Russell), FM, ST, L |
| David Hilbert | German | 1862-1942 | FM, ST, L, C of Variation |
| Jacques Hadamard | French | 1865-1963 | proved Prime Number Theorem (N); Complex Function Theory; various fields of Mathematics |
| Bertrand Russell | Welsh | 1872-1970 | Russell's Paradox, published Principia Mathematica (with Whitehead), FM, ST, L |
| Godfrey Harold Hardy | English | 1877-1947 | Theory of Series, Riemann Zeta Function, Inequalities and Theory of Functions |
| Albert Einstein | German | 1879-1955 | Special and General Relativity |
| Luitzen Brouwer | Dutch | 1881-1961 | Brouwer's Fixed Point Theorems, T |
| Hermann Weyl | German | 1885-1955 | his Die Idee der Riemannschen Fl�che (1913) united analysis, geometry and topology; applied GT to Quantum M |
| John Edensor Littlewood | English | 1885-1977 | Theory of Series, Riemann Zeta Function, Inequalities and Theory of Functions, Non-linear DE |
| Srinivasa Ramanujan | Indian | 1887-1920 | Elliptic Function, Continued Fractions, Infinite Series, Analytical N |
| John von Neumann | Hungarian | 1903-1957 | Quantum M; pioneered Game Theory; one of the pioneers of Computer Science |
| Kurt G�del | Austrian | 1906-1978 | his 2 Incompleteness Theorems, shook the reigning FM; L |
| Alan Turing | English | 1912-1954 | Turing machine, Halting Theorem, GT, P |
| Paul Erd�s | Hungarian | 1913-1996 | more than 1500 papers on Combinatorics, Graph Theory, and N |
| Ren� Thom | French | 1923- | pioneered Catastrophe Theory |
| Benoit Mandelbrot | Polish | 1924- | pioneered Fractal G |
| Paul Cohen | American | 1934- | L, DE |
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