Thales


GR

(∼624 BC – ∼546 BC)

geometry

Pythagoras


GR

(∼570 BC – ∼495 BC)

arithmetic;
Pythagorean theorem

Eudoxus of Cnidus


GR

(∼408 BC – ∼355 BC)

geometry;
method of exhaustion
(integral calculus)

Euclid


GR

(∼300 BC)

arithmetic;
number theory;
trigonometry;
Euclidian geometry

Archimedes


GR

(∼287 BC – ∼212 BC)

geometry;
volumes of solids of revolution;
trigonometry;
Archimedean spiral

Eratosthenes


GR

(∼276 BC – ∼195 BC)

sieve of Eratosthenes
(number theory)

Apollonius of Perga


GR

(∼262 BC – ∼190 BC)

conic sections
(geometry);
book "Conics"

Hipparchus


GR

(∼190 BC – ∼120 BC)

trigonometry

Heron of Alexandria


GR

(∼10 – ∼70)

square roots;
algebraic equations;
polynomials of degree 2;
Heron's formula

Diophantus


GR

(between 201 and 215 – between 285 and 299)

algebraic equations;
polynomials of degree 2;
Diophantine equations






Sun Zi


CN

(between 200 and 500)

algebraic equations;
Diophantine equations;
square roots;
Chinese remainder theorem
(number theory);
books

Aryabhata


IN

(476 – 550)

algebraic equations;
polynomials of degree 2;
Diophantine equations;
trigonometry

Brahmagupta


IN

(597 – 668)

algebraic equations;
polynomials of degree 2;
Diophantine equations;
Pell's equation;
arithmetic;
use of 0

alKhwarizmi


Persia

(∼780 – ∼850)

algebraic equations;
polynomials of degree 2;
arithmetic;
HinduArabic numeral system

Bhaskara II


IN

(1114 – 1185)

algebraic equations;
polynomials of degree 2;
Diophantine equations;
Pell's equation

Fibonacci


IT

(∼1170 – ∼1250)

Fibonacci numbers;
HinduArabic numeral system






Del Ferro


IT

(1465 – 1526)

algebraic equations;
polynomials of degree 3

Tartaglia


IT

(1499 – 1557)

algebraic equations;
polynomials of degree 3






Cardano


IT

(1501 – 1576)

algebraic equations;
polynomials of degree 3

Ferrari


IT

(1522 – 1565)

algebraic equations;
polynomials of degree 4

Vičte


FR

(1540 – 1603)

convention of using letters for unknowns in equations

Napier


UK

(1550 – 1617)

logarithm;
decimal point

Faulhaber


DE

(1580 – 1635)

Faulhaber's formula (sums of powers)

Mersenne


FR

(1588 – 1648)

Mersenne primes

Descartes


FR

(1596 – 1650)

Cartesian geometry;
convention of using x, y, z, etc. for unknowns in equations and a, b, c, etc. for knowns






Fermat


FR

(∼1601 – 1665)

Diophantine equations;
Pell's equation;
Fermat's little theorem
(number theory);
Fermat's theorem on sums of two squares
(number theory);
Fermat numbers
(number theory)
Fermat's last theorem
(number theory)

Wallis


UK

(1616 – 1703)

approximation of π;
convention of using symbol ∞
for infinity;
infinitesimal calculus

Pascal


FR

(1623 – 1662)

probability theory;
Pascal's triangle

Newton


UK

(1642 – 1727)

dynamical systems;
infinitesimal calculus;
binomial theorem

Leibniz


DE

(1646 – 1716)

infinitesimal calculus;
convention of using d for differentials
(infinitesimal calculus;);
convention of using an elongated S for integrals
(integral calculus)

Rolle


FR

(1652 – 1719)

Rolle's theorem

Bernoulli, Jacob


CH

(1654 – 1705)

Bernoulli numbers;
constant e;
Bernoulli distribution;
Bernoulli differential equation

L'Hôpital


FR

(1661 – 1704)

L'Hôpital's rule
(infinitesimal calculus)

Bernoulli, Johann


CH

(1667 – 1748)

infinitesimal calculus

Riccati


IT

(1676 – 1754)

Riccati equation
(differential equation)

Taylor, Brook


UK

(1685 – 1731)

Taylor series;
Taylor's theorem

Goldbach


DE

(1690 – 1764)

Goldbach's conjecture;
Fermat numbers
(number theory)

Stirling


UK

(1692 – 1770)

Stirling numbers
(combinatorics);
Stirling permutations
(combinatorics);
Stirling's approximation
(factorials)

Bernoulli, Nicolaus II


CH

(1695 – 1726)

St. Petersburg paradox
(probability theory)

Maclaurin


UK

(1698 – 1746)

Maclaurin series;
EulerMaclaurin formula
(series
and
integral calculus)






Bernoulli, Daniel


CH

(1700 – 1782)

probability theory

Bayes


UK

(1701 – 1761)

Bayesian probability
(probability theory)

Cramer


CH

(1704 – 1752)

Cramer's rule
(matrix theory)

Euler


CH

(1707 – 1783)

infinitesimal calculus;
Seven Bridges of Königsberg
(graph theory);
number theory;
Euler's totient function;
power series;
EulerMaclaurin formula
(series
and
integral calculus);
transcendental numbers;
concept of mathematical function

Simpson


UK

(1710 – 1761)

Simpson's rule
(integral calculus)

Clairaut


FR

(1713 – 1765)

Clairaut's equation
(differential equation);
Clairaut's relation
(differential geometry)

D'Alembert


FR

(1717 – 1783)

fundamental theorem of algebra;
d'Alembertian

Bézout


FR

(1730 – 1783)

algebraic equations;
Bézout's identity
(number theory)

Vandermonde


FR

(1735 – 1796)

Vandermonde matrix;
Vandermonde determinant;
Vandermonde's identity

Lagrange


IT

(1736 – 1813)

Lagrange's foursquare theorem
(number theory);
calculus of variations;
EulerLagrange equation
(differential equation);
Lagrange multipliers
(mathematical optimization);
Lagrangian

Laplace


FR

(1749 – 1827)

Laplacian;
Laplace transform;
Bayesian probability
(probability theory)

Legendre


FR

(1752 – 1833)

least squares method;
Legendre polynomials;
quadratic reciprocity law;
elliptic functions;
Legendre symbol

Fourier


FR

(1768 – 1830)

Fourier series;
Fourier transform

Germain


FR

(1776 – 1831)

number theory;
Fermat's last theorem
(number theory);
differential equations

Gauss


DE

(1777 – 1855)

fundamental theorem of algebra;
number theory;
quadratic forms;
modular arithmetic;
convention of using ≡ for congruence;
geometry;
Gaussian curvature
(differential geometry);
differential geometry of surfaces;
GaussJordan elimination
(matrix theory)

Poisson


FR

(1781 – 1840)

differential equations;
Poisson's equation;
probability theory;
Poisson distribution

Bolzano


CZ

(1781 – 1848)

foundations of mathematics;
limit of a function;
BolzanoWeierstrass theorem

Bessel


DE

(1784 – 1846)

Bessel functions
(special functions)

Binet


FR

(1786 – 1856)

matrix multiplication;
CauchyBinet formula
(matrix theory);
matrix algebra;
BinetCauchy identity;
Binet's Fibonacci number formula
(number theory);
Binet equation
(differential equation)

Cauchy


FR

(1789 – 1857)

foundations of mathematics;
series;
complex analysis;
infinitesimal calculus;
limit of a function;
Cauchy sequence;
continuity;
CauchySchwarz inequality;
group theory
(abstract algebra)

Lobachevsky


RU

(1792 – 1856)

hyperbolic geometry
(nonEuclidean geometry)

Green


UK

(1793 – 1841)

Green's theorem
(integral calculus)
Green's identities
(integral calculus)

Chasles


FR

(1793 – 1880)

Chasles's relation (geometry);
crossratio
(geometry);
coined the term "homothety"

Bienaymé


FR

(1796 – 1878)

BienayméChebyshev inequality
(probability theory);
Bienaymé formula
(statistics)

Sarrus


FR

(1798 – 1861)

rule of Sarrus (determinants);
Sarrus numbers
(number theory);






Ostrogradsky


RU

(1801 – 1862)

divergence theorem;
calculus of variations

Abel


NO

(1802 – 1829)

algebraic equations;
polynomials of degree 5;
group theory
(abstract algebra);
Abelian integrals
(integral calculus);
elliptic integrals
(integral calculus)

Bolyai


HU

(1802 – 1860)

nonEuclidian geometry;
complex analysis

Sturm


FR

(1803 – 1855)

Sturm's theorem
(polynomials);
SturmLiouville equation
(differential equation);
SturmLiouville theory (SL theory);
Sturm series
(polynomials)

Jacobi


DE

(1804 – 1851)

elliptic functions;
HamiltonJacobi equation
(differential equation);
Jacobian matrix;
Jacobian (determinant);
Jacobi symbol

Dirichlet


DE

(1805 – 1859)

number theory;
Dirichlet Lfunctions;
Fourier series;
continuity;
Dirichlet integral
(integral calculus)

Hamilton


IE

(1805 – 1865)

Hamiltonian;
quaternions;
hamiltonian paths
(graph theory);
HamiltonJacobi equation
(differential equation)

De Morgan


UK

(1806 – 1871)

De Morgan's laws;
mathematical logic;
mathematical induction

Liouville


FR

(1809 – 1882)

number theory;
complex analysis;
Liouville's theorem;
transcendental numbers;
Liouville numbers;
SturmLiouville theory

Galois


FR

(1811 – 1832)

algebraic equations;
polynomials of any degree;
Galois theory

Laurent


FR

(1813 – 1854)

Laurent series
(complex analysis);
Laurent polynomial

Sylvester


UK

(1814 – 1897)

Sylvester's determinant theorem
(matrix theory);
Sylvester's formula
(matrix theory);
Sylvester equation
(matrix theory);
coined the terms "graph", "discriminant", and "totient"

Weierstrass


DE

(1815 – 1897)

foundations of mathematics;
axiomatization;
limit of a function;
analysis;
Weierstrass factorization theorem
(complex analysis);
BolzanoWeierstrass theorem;
elliptic functions;
calculus of variations

Boole


UK

(1815 – 1864)

Boolean algebra;
mathematical logic

Stokes


UK

(1819 – 1903)

Stokes's theorem
(differential geometry);
Stokes line
(complex analysis)

Chebyshev


RU

(1821 – 1894)

Chebyshev polynomials;
orthogonal polynomials;
BienayméChebyshev inequality
(probability theory);
Chebyshev function
(number theory);
Chebyshev's bias
(number theory);
Chebyshev equation
(differential equation)

Cayley


UK

(1821 – 1895)

group theory
(abstract algebra);
Cayley's theorem
(group theory);
CayleyHamilton theorem
(matrix theory);
Cayley graph
(graph theory);
Cayley's formula
(graph theory)

Hermite


FR

(1822 – 1901)

Hermitian matrices;
Hermite normal form;
Hermite polynomials;
Hermitian forms;
transcendental numbers

Eisenstein


DE

(1823 – 1852)

Eisenstein criterion
(polynomials);
quadratic reciprocity law;
number theory

Kronecker


DE

(1823 – 1891)

Kronecker δ;
Kronecker product
(matrix theory);
Kronecker symbol
(number theory);
algebraic number theory
(abstract algebra)

Brioschi


IT

(1824 – 1897)

elliptic functions;
polynomials of degree 5;
polynomials of degree 6

Riemann


DE

(1826 – 1866)

Riemannian geometry
(nonEuclidean geometry);
Riemann zeta function;
Riemann hypothesis;
Riemann integral
(integral calculus);
real analysis;
differential geometry of surfaces

Dedekind


DE

(1831 – 1916)

foundations of mathematics;
set theory;
ring theory
(abstract algebra);
number theory

Lipschitz


DE

(1832 – 1903)

Lipschitz continuity condition;
DiniLipschitz criterion

Beltrami


IT

(1835 – 1899)

nonEuclidean geometry;
Beltrami–Klein model
(geometry);
Singular value decomposition
(matrix theory)

Jordan, Camille


FR

(1838 – 1922)

group theory
(abstract algebra);
Jordan matrix;
Jordan's totient function;
Jordan curve theorem
(topology

Jordan, Wilhelm


DE

(1842 – 1899)

GaussJordan elimination
(matrix theory)

Lucas


FR

(1842 – 1891)

Diophantine equations;
number theory;
primality tests;
Lucas sequences;
Lucas numbers;
LucasLehmer test;
Mersenne primes

Darboux


FR

(1842 – 1917)

Darboux sums
(integral calculus);
Darboux integral
(integral calculus);
Darboux's formula
(series
and
integral calculus);
EulerPoissonDarboux equation
(differential equations);
differential geometry of surfaces

Lie


NO

(1842 – 1899)

Lie groups
(abstract algebra);
group theory
(abstract algebra)

Cantor


DE

(1845 – 1918)

foundations of mathematics;
axiomatization;
set theory;
transfinite numbers;
cardinal numbers;
ordinal numbers;
transcendental numbers

MittagLeffler


SE

(1846 – 1927)

MittagLeffler function
(special functions);
MittagLeffler star
(complex analysis)
MittagLeffler's theorem
(complex analysis)
MittagLeffler summation
(formal power series)

Klein


DE

(1849 – 1925)

nonEuclidean geometry;
Klein bottle
(geometry);
Erlangen program
(geometry);
Beltrami–Klein model
(geometry);
group theory
(abstract algebra)

Frobenius


DE

(1849 – 1917)

elliptic functions;
differential equations;
Frobenius algebra
(abstract algebra);
Perron–Frobenius theorem

Kovalevskaya


RU

(1850 – 1891)

Cauchy–Kowalevski theorem
(differential equations);
Abelian integrals
(integral calculus)

RicciCurbastro


IT

(1853 – 1925)

tensor calculus;
Ricci flow
(differential geometry);
Ricci curvature
(differential geometry)

Poincaré


FR

(1854 – 1912)

dynamical systems;
Poincaré map
(chaos theory);
topology;
Poincaré conjecture;
fundamental group
(algebraic topology);
Fuchsian groups;
Kleinian groups;
differential equations

Appell


FR

(1855 – 1930)

Appell series;
differential equations;
Appell sequence
(polynomials);
elliptic functions

Markov


RU

(1856 – 1922)

Markov chains;
Markov processes;
stochastic processes

Stieltjes


NL

(1856 – 1894)

RiemannStieltjes integral
(integral calculus);
continued fractions;
orthogonal polynomials

Dudeney


UK

(1857 – 1930)

recreational mathematics

Lyapunov


RU

(1857 – 1918)

differential equations;
Lyapunov exponent
(chaos theory);
central limit theorem
(probability theory)

Peano


IT

(1858 – 1932)

mathematical logic;
foundations of mathematics;
set theory;
Peano axioms
(axiomatization);
Peano existence theorem
(differential equations)

Cesŕro


IT

(1859 – 1906)

differential geometry;
Cesŕro mean
(divergent series)

Hölder


DE

(1859 – 1937)

abstract algebra;
classification of simple groups
(group theory);
Hölder's inequality
(analysis);
Hölder condition
(analysis);
Hölder's theorem
(gamma function)

Hilbert


DE

(1862 – 1943)

foundations of mathematics;
axiomatization;
Hilbert space;
functional analysis;
Hilbert's 23 problems

Thue


NO

(1863 – 1922)

Diophantine equations;
Diophantine approximations;
Thue equation;
ThueSiegelRoth theorem

Painlevé


FR

(1863 – 1933)

differential equations

Minkowski


DE

(1864 – 1909)

Minkowski inequality;
number theory

Hadamard


FR

(1865 – 1963)

prime number theorem
(number theory);
complex analysis;
differential geometry;
calculus of variations;
differential equations

Hausdorff


DE

(1868 – 1942)

Hausdorff space;
topology;
Hausdorff maximal principle
(set theory);
Hausdorff measure
(measure theory)

Cartan


FR

(1869 – 1951)

Cartan matrix;
group theory
(abstract algebra);
Cartan decomposition
(abstract algebra);
Cartan's theorem
(abstract algebra)

Borel


FR

(1871 – 1956)

Borel set
(topology);
measure theory;
probability theory

Zermelo


DE

(1871 – 1953)

mathematical logic;
foundations of mathematics;
axiomatization;
ZermeloFraenkel axioms
(set theory)

Russell


UK

(1872 – 1970)

mathematical logic;
foundations of mathematics;
Russell's paradox

LeviCivita


IT

(1873 – 1941)

tensor calculus;
Hamilton–Jacobi equation

Lebesgue


FR

(1875 – 1941)

Lebesgue integration
(integral calculus);
measure theory

Hardy


UK

(1877 – 1947)

number theory;
mathematical analysis;
Waring's problem;
Hardy–Littlewood conjectures

Fejér


HU

(1880 – 1959)

harmonic analysis;
Fejér kernel
(Fourier series);
Fejér's theorem

Perron


DE

(1880 – 1975)

Perron method
(differential equations);
Perron–Frobenius theorem
(matrix theory);
Perron's formula
(number theory)

Brouwer


NL

(1881 – 1966)

topology;
Brouwer's fixedpoint theorem
(algebraic topology);
simplicial approximation theorem
(algebraic topology);
invariance of domain
(topology)

Littlewood


UK

(1885 – 1977)

number theory;
mathematical analysis;
Diophantine approximation;
Waring's problem;
Hardy–Littlewood conjectures

Weyl


DE

(1885 – 1955)

Riemann surfaces
(topology);
compact groups
(abstract algebra);
Weyl groups
(abstract algebra);
Lie algebras
(abstract algebra);
Weyl law
(eigenvalues);
Weyl's criterion
(Diophantine equations)

Riesz


HU

(1886 – 1969)

divergent series;
partial differential equations

Pólya


HU

(1887 – 1985)

heuristics;
combinatorics;
number theory;
probability theory

Ramanujan


IN

(1887 – 1920)

number theory;
series;
continued fractions;
RamanujanPetersson conjecture

Mordell


UK

(1888 – 1972)

number theory;
Diophantine equations;
Mordell curve;
modular forms;
MordellWeil theorem;
Mordell conjecture

Fraenkel


DE
⇒
IL

(1891 – 1965)

mathematical logic;
foundations of mathematics;
axiomatization;
ZermeloFraenkel axioms
(set theory)

Vinogradov


RU

(1891 – 1983)

analytic number theory

Banach


PL

(1892 – 1945)

Banach space
(functional analysis);
Banach algebra
(functional analysis);
BanachTarski paradox
(topology)

Szegö


HU

(1895 – 1985)

orthogonal polynomials;
Toeplitz matrices

Artin


AT
⇒
US

(1898 – 1962)

Artinian rings
(abstract algebra);
algebraic number theory
(abstract algebra);
Galois theory;
braid theory
(topology)






Van der Waerden


NL

(1903 – 1996)

abstract algebra;
history of mathematics;
book

Kolmogorov


RU

(1903 – 1987)

probability theory;
differential equations;
KAM theorem
(integrable systems);
stochastic processes

Von Neumann


HU
⇒
US

(1903 – 1957)

foundations of mathematics;
measure theory;
ergodic theory

Lehmer


US

(1905 – 1991)

number theory;
primality tests;
LucasLehmer test;
Mersenne primes

Gödel


AT

(1906 – 1978)

mathematical logic;
foundations of mathematics;
Gödel's incompleteness theorems

Weil


FR

(1906 – 1998)

number theory;
algebraic geometry;
MordellWeil theorem;
Weil conjectures;
history of mathematics

Dieudonné


FR

(1906 – 1992)

Dieudonné module
(abstract algebra);
Dieudonné ring
(abstract algebra);
history of mathematics;
books

Erdélyi


HU

(1908 – 1977)

special functions;
orthogonal polynomials;
hypergeometric functions

Sobolev


RU

(1908 – 1989)

theory of distributions;
Sobolev space
(analysis)

Turán


HU

(1910 – 1976)

number theory;
graph theory

Erdös


HU

(1913 – 1996)

graph theory;
number theory;
Prime Number Theorem;
probability theory

Gelfand


RU

(1913 – 2009)

group theory;
representation theory;
functional analysis

Gardner


US

(1914 – 2010)

recreational mathematics

Schwartz


FR

(1915 – 2002)

theory of distributions

Ito


JP

(1915 – 2008)

probability theory;
stochastic differential equations;
Ito's lemma

Iwasawa


JP

(1917 – 1998)

Iwasawa decomposition
(abstract algebra)
Iwasawa algebra
(abstract algebra)
Iwasawa theory
(abstract algebra)

Thom


FR

(1923 – 2002)

topology;
catastrophe theory;
singularity theory

Zeeman


UK

(1925 – )

geometric topology;
Poincaré conjecture for n=5;
catastrophe theory;
singularity theory

Serre


FR

(1926 – )

algebraic geometry;
algebraic number theory
(abstract algebra)

Lang


US

(1927 – 2005)

abstract algebra;
Diophantine geometry;
modular forms;
books

Taniyama


JP

(1927 – 1958)

Fermat's last theorem
(number theory);
TaniyamaShimura conjecture
(topology
and
number theory)

Grothendieck


DE
⇒
stateless
⇒
FR

(1928 – 2014)

algebraic geometry;
algebraic number theory
(abstract algebra)

Shimura


JP

(1930 – 2019)

Fermat's last theorem
(number theory);
TaniyamaShimura conjecture
(topology
and
number theory)

Smale


US

(1930 – )

geometric topology;
hcobordism;
Poincaré conjecture for n≥5

Stallings


US

(1935 – 2008)

geometric group theory;
Stallings theorem about ends of groups
(group theory);
geometric topology;
Poincaré conjecture for n=6;

Langlands


CA

(1936 – )

abstract algebra;
Langlands program
(algebra
and
analysis)

Manin


RU

(1937 – )

algebraic geometry;
arithmetic topology;
Diophantine geometry;
GaussManin connection

Arnold


RU

(1937 – 2010)

differential equations;
dynamical systems;
KAM theorem
(integrable systems);
catastrophe theory;
mathematical physics

Mazur


US

(1937 – )

geometric topology;
arithmetic topology;
Diophantine geometry

Hamilton, Richard


US

(1943 – )

differential geometry;
Ricci flow
(differential geometry)

Stewart


UK

(1945 – )

recreational mathematics

Thurston


US

(1946 – 2012)

manifolds;
(topology);
foliation theory;
(topology);
Thurston's geometrization conjecture
(geometric topology)

Matiyasevich


RU

(1947 – )

Hilbert's tenth problem;
Diophantine equations

Ribet


US

(1948 – )

Fermat's last theorem
(number theory);
modular forms;
TaniyamaShimura conjecture
(topology
and
number theory)

Freedman


US

(1951 – )

geometric topology;
Poincaré conjecture for n=4;

Wiles


UK

(1953 – )

Fermat's last theorem
(number theory);
TaniyamaShimura conjecture
(topology
and
number theory)

Faltings


DE

(1954 – )

number theory;
Mordell conjecture

Lions


FR

(1956 – )

nonlinear partial differential equations

Yoccoz


FR

(1957 – 2016)

dynamical systems

Taylor, Richard


UK

(1962 – )

Fermat's last theorem
(number theory);
TaniyamaShimura conjecture
(topology
and
number theory);
Langlands program
(algebra
and
analysis)

Perelman


RU

(1966 – )

geometric topology;
Poincaré conjecture for n=3;
Thurston's geometrization conjecture
(geometric topology)

Tao


AU
⇒
US

(1975 – )

GreenTao theorem
(number theory);
circular law
(probability theory);
HardyLittlewood prime tuples conjecture;
prime gaps
(number theory)
