Mathematicians

Ancient

1. 
   Archimedes of Syracuse287 BCE–212 BCE·Italy

   Greek mathematician, physicist and engineer of Syracuse who computed areas and volumes of curved figures with a rigorous method of exhaustion that anticipated integral calculus by nearly two thousand years, and founded statics and hydrostatics.GeometryAnalysisMathematical physics
2. 
   Euclid of AlexandriaEgypt

   Greek mathematician active in Alexandria around 300 BCE whose textbook the Elements organized geometry and number theory into a chain of definitions, axioms and proofs that shaped mathematics for over two thousand years.GeometryArithmetic and number theoryHistory and philosophy of mathematics
3. 
   Hypatia of AlexandriaEgypt

   Neoplatonist philosopher and mathematician who led a school in Alexandria, is credited with commentaries on Diophantus's Arithmetica and Apollonius's Conics, and is the earliest woman mathematician whose life and work are documented in reasonable detail.Arithmetic and number theoryGeometryHistory and philosophy of mathematics
4. 
   Liu HuiChina

   Chinese mathematician of the Cao Wei state whose 263 CE commentary on The Nine Chapters on the Mathematical Art turned a manual of computational recipes into a text with logical justifications, including a dissection-based proof of the Pythagorean (gou-gu) theorem and a polygon method that approximated pi to four correct decimal digits.GeometryAlgebraHistory and philosophy of mathematics
5. 
   Zu Chongzhi429–501·China

   Chinese mathematician and astronomer who bounded pi between 3.1415926 and 3.1415927 using a polygon method with a 24576-sided figure, and devised the milü fraction 355/113 as an extremely accurate rational approximation.GeometryArithmetic and number theoryHistory and philosophy of mathematics

Medieval

1. 
   Brahmagupta598–668·India

   Indian mathematician and astronomer at the Ujjain observatory who gave the first systematic rules for arithmetic with zero and negative numbers, a general method for solving quadratic equations, and formulas for the area and diagonals of a cyclic quadrilateral.AlgebraArithmetic and number theoryGeometryHistory and philosophy of mathematics
2. 
   Muhammad ibn Musa al-Khwarizmi780–850·Iraq, Uzbekistan, Turkmenistan

   Persian mathematician and astronomer at the House of Wisdom in Baghdad whose treatise on restoring and balancing equations gave algebra its name and its first systematic treatment, and whose book on Indian numerals helped transmit the Hindu-Arabic decimal system to the western mathematical tradition.AlgebraHistory and philosophy of mathematics
3. 
   Omar Khayyam1048–1131·Iran

   Persian mathematician, astronomer and poet who classified cubic equations and solved them geometrically as intersections of conic sections, critiqued Euclid's parallel postulate in a way that foreshadowed non-Euclidean geometry, and reformed the Persian calendar.AlgebraGeometryCombinatorics and discrete mathematicsHistory and philosophy of mathematics
4. 
   Leonardo of Pisa (Fibonacci)1170–1250·Italy

   Italian merchant's son who, after learning Hindu-Arabic arithmetic in North Africa, wrote the Liber Abaci (1202) introducing the Hindu-Arabic decimal numeral system to Latin Europe, and posed the rabbit problem whose solution is the sequence now known as the Fibonacci numbers.Arithmetic and number theoryCombinatorics and discrete mathematicsHistory and philosophy of mathematics

Early modern

1. 
   René Descartes1596–1650·France

   French philosopher and mathematician whose La Géométrie (1637) fused algebra and geometry by representing curves as equations in coordinates, founding what is now called analytic or Cartesian geometry and supplying the notation (x, y, exponents) still used in algebra today.GeometryAlgebra
2. 
   Pierre de Fermat1601–1665·France

   French magistrate and 'prince of amateurs' who founded modern number theory, conjectured what became known as Fermat's Last Theorem, developed methods for finding tangents and extrema that anticipated differential calculus, co-founded probability theory with Pascal, and stated the stationary-time principle in optics.Arithmetic and number theoryAnalysisProbability and statisticsGeometry
3. 
   Blaise Pascal1623–1662·France

   French mathematician, physicist and religious philosopher who at sixteen discovered a key theorem of projective geometry, built one of the first mechanical calculators, co-founded probability theory through his 1654 correspondence with Fermat, and gave a systematic treatment of the arithmetic triangle that bears his name.Probability and statisticsGeometryCombinatorics and discrete mathematics
4. 
   Seki Takakazu1642–1708·Japan

   Japanese samurai-bureaucrat and mathematician, the central figure of wasan (traditional Japanese mathematics), who was the first known person to study determinants systematically, independently discovered the numbers now called Bernoulli numbers, and developed infinite-series methods for computing pi and areas and volumes bounded by curves, entirely independently of contemporary European work by Newton and Leibniz.AlgebraAnalysisArithmetic and number theory
5. 
   Isaac Newton1643–1727·United Kingdom

   English mathematician and physicist, Lucasian Professor at Cambridge, who developed the method of fluxions (differential and integral calculus) independently of Leibniz, generalized the binomial theorem to fractional and negative exponents, and in the Principia Mathematica (1687) unified the laws of motion and universal gravitation.AnalysisMathematical physicsAlgebra
6. 
   Gottfried Wilhelm Leibniz1646–1716·Germany

   German polymath, mathematician, and philosopher who developed differential and integral calculus independently of Isaac Newton, introduced the enduring notation $\int f(x)\,dx$ and $\frac{dy}{dx}$, formulated binary arithmetic, and envisioned a formal symbolic calculus of reasoning.AnalysisFoundations of mathematicsCombinatorics and discrete mathematics
7. CG
   Christian Goldbach1690–1764·Germany, Russia

   Prussian mathematician remembered above all for the conjecture he discussed in a 7 June 1742 letter to Euler: in Goldbach's original formulation, every integer greater than 2 is the sum of three primes; Euler's equivalent modern form says every even integer greater than 2 is the sum of two primes.Arithmetic and number theory

18th century

1. 
   Leonhard Euler1707–1783·Switzerland, Russia, Germany

   Swiss mathematician, the most prolific mathematician in history, who made foundational contributions to analysis, number theory, graph theory and mechanics and introduced much of modern mathematical notation.AnalysisArithmetic and number theoryTopology
2. 
   Joseph-Louis Lagrange1736–1813·Italy, Germany, France

   Italian-born French-Prussian mathematician who transformed mechanics into a branch of mathematical analysis and made foundational contributions to the calculus of variations, number theory and the theory of equations.AnalysisAlgebraMathematical physics
3. 
   Pierre-Simon Laplace1749–1827·France

   French mathematician who transformed probability, celestial mechanics, and differential equations through analysis and mathematical physics.Probability and statisticsArithmetic and number theoryDifferential equations and dynamical systems
4. 
   Joseph Fourier1768–1830·France

   French mathematician and physicist who founded the mathematical theory of heat conduction and showed how periodic phenomena can be decomposed into trigonometric waves.AnalysisDifferential equations and dynamical systemsMathematical physics
5. 
   Sophie Germain1776–1831·France

   Self-taught French mathematician whose work was the most important advance on Fermat's Last Theorem from Euler's 1738 work until Kummer's contributions in the 1840s, and who won the Paris Academy's prize for her pioneering theory of the elasticity of vibrating plates.Arithmetic and number theoryMathematical physics
6. 
   Carl Friedrich Gauss1777–1855·Germany

   German mathematician and astronomer, often called the Prince of Mathematicians, whose Disquisitiones Arithmeticae founded modern number theory and who made fundamental contributions to differential geometry, statistics and geodesy.Arithmetic and number theoryGeometry
7. 
   Augustin-Louis Cauchy1789–1857·France

   French mathematician who put analysis on a rigorous footing, pioneering the modern theory of limits, convergence and complex functions, and produced more mathematical papers than anyone before him.AnalysisAlgebra

19th century

1. 
   Niels Henrik Abel1802–1829·Norway

   Norwegian mathematician who, in his early twenties, proved that the general quintic equation cannot be solved by radicals, and who laid the foundations of the theory of elliptic and abelian functions before dying in poverty at 26.AlgebraAnalysis
2. 
   Peter Gustav Lejeune Dirichlet1805–1859·Germany, France

   German mathematician whose work founded modern analytic number theory, including the first proof that every reduced arithmetic progression contains infinitely many primes.Arithmetic and number theoryAnalysisAlgebra
3. 
   Évariste Galois1811–1832·France

   French mathematician who, before dying at 20 after a duel, determined the precise condition for a polynomial equation to be solvable by radicals and, in doing so, founded what is now called Galois theory and modern group theory.Algebra
4. 
   George Boole1815–1864·Ireland, United Kingdom

   English mathematician and logician who created Boolean algebra, the algebraic foundation of modern digital logic.Foundations of mathematicsAlgebra
5. 
   Arthur Cayley1821–1895·United Kingdom

   English mathematician who helped create abstract group theory and developed matrix theory and invariant theory.AlgebraCombinatorics and discrete mathematicsGeometry
6. 
   Bernhard Riemann1826–1866·Germany

   German mathematician whose 1854 lecture on the hypotheses underlying geometry founded Riemannian geometry, and whose 1859 paper on the prime-counting function posed the Riemann hypothesis, still one of the most important open problems in mathematics.AnalysisGeometryArithmetic and number theory
7. 
   Georg Cantor1845–1918·Russia, Germany

   Russian-born German mathematician who founded set theory, proved that the real numbers are uncountable while the algebraic numbers are countable, and formulated the still-unresolved continuum hypothesis.Foundations of mathematics
8. 
   Ferdinand von Lindemann1852–1939·Germany

   German mathematician who proved in 1882 that π is transcendental, finally settling the ancient problem of squaring the circle with ruler and compass, and who supervised David Hilbert's doctorate.Arithmetic and number theoryAlgebra
9. 
   Henri Poincaré1854–1912·France

   French mathematician and physicist, often called the last universalist, who founded algebraic topology and the qualitative theory of dynamical systems, discovered chaotic behaviour in the three-body problem, and posed the Poincaré conjecture.TopologyDifferential equations and dynamical systemsGeometry
10. 
    David Hilbert1862–1943·Germany

    German mathematician, one of the most influential of the 20th century, who gave modern geometry a rigorous axiomatic foundation, developed Hilbert spaces, and set the agenda for a century of research with his 23 problems of 1900.Foundations of mathematicsGeometryAlgebra
11. 
    Émile Borel1871–1956·France

    French mathematician who helped found measure theory and modern probability, and studied normal numbers and divergent series.AnalysisProbability and statisticsFoundations of mathematics
12. 
    G. H. Hardy1877–1947·United Kingdom

    English mathematician who transformed analytic number theory and produced influential work on inequalities, series, and prime numbers.Arithmetic and number theoryAnalysisCombinatorics and discrete mathematics
13. 
    Emmy Noether1882–1935·Germany, United States

    German mathematician who founded modern abstract algebra through her work on rings and ideals, and proved the theorem, named after her, linking every differentiable one-parameter symmetry of a physical system's action to a conservation law.AlgebraMathematical physics
14. 
    J. E. Littlewood1885–1977·United Kingdom

    English mathematician whose work with Hardy shaped analytic number theory, Fourier analysis, and the theory of differential equations.AnalysisArithmetic and number theoryDifferential equations and dynamical systemsCrafoord Prize in Mathematics
15. 
    George Pólya1887–1985·Hungary, United States

    Hungarian-American mathematician known for work in combinatorics, probability, inequalities, and mathematical problem solving.Combinatorics and discrete mathematicsProbability and statisticsAnalysis
16. 
    Srinivasa Ramanujan1887–1920·India, United Kingdom

    Self-taught Indian mathematician who, with almost no formal training, produced thousands of remarkable results in number theory, infinite series and continued fractions, and co-developed the circle method with G. H. Hardy.Arithmetic and number theory

20th century

1. 
   Andrey Kolmogorov1903–1987·Russia

   Soviet mathematician whose 1933 monograph axiomatized probability theory using measure theory; he also made foundational contributions to Fourier series, topology, turbulence, dynamical systems (KAM theory), and algorithmic complexity.Probability and statisticsAnalysisDifferential equations and dynamical systemsApplied and computational mathematicsWolf Prize in Mathematics
2. 
   John von Neumann1903–1957·Hungary, United States

   Hungarian-American polymath who placed quantum mechanics on a rigorous Hilbert-space footing, founded operator-algebra theory and mathematical game theory, and articulated the stored-program computer architecture.Foundations of mathematicsAlgebraApplied and computational mathematicsMathematical physics
3. 
   Henri Cartan1904–2008·France

   French mathematician who shaped complex analysis, algebraic topology, and homological algebra through sheaf theory.AlgebraAnalysisTopologyWolf Prize in Mathematics
4. 
   Kurt Gödel1906–1978·Austria, United States

   Austrian-American logician whose incompleteness theorems showed that no consistent, effectively axiomatized system powerful enough for arithmetic can prove all truths about the numbers, or prove its own consistency.Foundations of mathematics
5. 
   Hua Luogeng1910–1985·China

   Self-taught Chinese mathematician who made lasting contributions to analytic number theory (trigonometric sums and Waring's problem), classical groups, and several complex variables, and built modern mathematical research in China.Arithmetic and number theoryAlgebraAnalysis
6. 
   Lothar Collatz1910–1990·Germany

   German mathematician who founded the Hamburg school of applied mathematics and, in 1937, posed the still-unsolved 3n+1 problem now known as the Collatz conjecture.Arithmetic and number theoryApplied and computational mathematics
7. 
   Alan Turing1912–1954·United Kingdom

   British mathematician and logician who defined the abstract computing machine that bears his name, laying the theoretical foundation of computer science, and played a central role in wartime efforts to break German Enigma ciphers.Foundations of mathematicsApplied and computational mathematics
8. 
   Paul Erdős1913–1996·Hungary

   Itinerant Hungarian mathematician who authored more than 1,500 papers with over 500 collaborators, pioneering the probabilistic method in combinatorics, Ramsey theory, extremal graph theory, and an elementary proof of the prime number theorem.Combinatorics and discrete mathematicsArithmetic and number theoryProbability and statisticsWolf Prize in Mathematics
9. 
   Samuel Eilenberg1913–1998·Poland, United States

   Polish-American mathematician who co-founded category theory and established the axiomatic language of homological algebra.AlgebraTopologyFoundations of mathematicsWolf Prize in Mathematics
10. 
    Kiyoshi Itô1915–2008·Japan

    Japanese probabilist who created stochastic integration and stochastic differential equations (Itô calculus and Itô's formula), providing the calculus of Brownian motion used throughout probability, physics, and mathematical finance.Probability and statisticsDifferential equations and dynamical systemsApplied and computational mathematicsWolf Prize in MathematicsKyoto Prize in Basic SciencesCarl Friedrich Gauss Prize
11. 
    Kunihiko Kodaira1915–1997·Japan

    Japanese mathematician — the first Japanese Fields Medallist — who applied harmonic integrals and sheaf cohomology to Kähler manifolds and algebraic varieties, proving the Kodaira vanishing and embedding theorems and classifying compact complex surfaces.GeometryTopologyAnalysisFields MedalWolf Prize in Mathematics
12. 
    Claude Shannon1916–2001·United States

    American mathematician and engineer who founded information theory and formalized the mathematical theory of communication.Foundations of mathematicsApplied and computational mathematicsProbability and statisticsTuring Award
13. 
    Lê Văn Thiêm1918–1991·Vietnam

    Pioneer of modern Vietnamese mathematics: the first Vietnamese to earn a doctorate in mathematics, a contributor to Nevanlinna value-distribution theory in complex analysis, and founding president of the Vietnam Mathematical Society.Analysis
14. 
    Hoàng Tụy1927–2019·Vietnam

    Vietnamese mathematician considered the founding father of deterministic global optimization: his 1964 paper on concave minimization under linear constraints introduced 'Tuy's cut' and launched modern nonconvex global optimization.Applied and computational mathematics
15. RD
    Roy O. Davies1927–2023·United Kingdom

    English mathematician who settled the two-dimensional Kakeya problem in 1971, proving that every Kakeya set in the plane has full Hausdorff dimension.AnalysisGeometry
16. 
    Alexander Grothendieck1928–2014·France, Germany

    German-born mathematician in France who rebuilt algebraic geometry on the language of schemes, sheaves, topoi, and étale cohomology, and transformed homological algebra and category theory.GeometryAlgebraTopologyFoundations of mathematicsFields Medal
17. 
    John Forbes Nash Jr.1928–2015·United States

    American mathematician who established the concept of Nash equilibrium and made major contributions to game theory and differential geometry.Applied and computational mathematicsCombinatorics and discrete mathematicsFoundations of mathematicsAbel Prize
18. 
    Wolfgang Haken1928–2022·Germany, United States

    German-American mathematician who co-proved the four colour theorem with Kenneth Appel (1976) and founded the theory of Haken manifolds in low-dimensional topology.Combinatorics and discrete mathematicsTopology
19. 
    Michael Atiyah1929–2019·United Kingdom

    British mathematician who created K-theory and the Atiyah–Singer index theorem, linking topology, geometry, and analysis.AlgebraGeometryTopologyFields MedalAbel Prize
20. 
    Stephen Smalefl. 1930·United States

    American mathematician who founded modern dynamical-systems theory and proved the higher-dimensional h-cobordism theorem.TopologyAnalysisDifferential equations and dynamical systemsFields Medal
21. 
    John Milnorfl. 1931·United States

    American mathematician who transformed differential topology, geometry, and dynamical systems through exotic spheres and classification theory.TopologyGeometryAlgebraFields MedalAbel Prize
22. 
    Kenneth Appel1932–2013·United States

    American mathematician who, with Wolfgang Haken, proved the four colour theorem in 1976 using an early computer-assisted case analysis.Combinatorics and discrete mathematics
23. 
    Chen Jingrun1933–1996·China

    Chinese number theorist who proved Chen's theorem (announced 1966, full proof 1973): every sufficiently large even integer is the sum of a prime and a product of at most two primes — the closest unconditional result to binary Goldbach's conjecture.Arithmetic and number theory
24. 
    Michael Artinfl. 1934·Germany, United States

    German-American mathematician who made foundational contributions to algebraic geometry, étale cohomology, and algebra.AlgebraGeometryTopologyWolf Prize in Mathematics
25. 
    Paul Cohen1934–2007·United States

    American mathematician who invented the method of forcing in 1963 to prove that the continuum hypothesis and the axiom of choice are independent of Zermelo–Fraenkel set theory, winning the 1966 Fields Medal.Foundations of mathematicsAnalysisFields Medal
26. 
    Stephen Cookfl. 1939·Canada, United States

    American-Canadian computer scientist and mathematician who founded the theory of NP-completeness, formulating the P versus NP question and proving the Cook–Levin theorem.Foundations of mathematicsApplied and computational mathematicsTuring Award
27. 
    Endre Szemerédifl. 1940·Hungary

    Hungarian mathematician who proved that every dense subset of the integers contains arbitrarily long arithmetic progressions.Combinatorics and discrete mathematicsArithmetic and number theoryProbability and statisticsAbel Prize
28. 
    William Thurston1946–2012·United States

    American mathematician who revolutionized the study of three-dimensional manifolds through geometric structures and the geometrization program.GeometryTopologyAlgebraFields Medal
29. 
    Yuri Matiyasevichfl. 1947·Russia

    Russian mathematician and logician who in 1970, at age 22, completed the negative solution to Hilbert's tenth problem by proving what is now called Matiyasevich's theorem.Foundations of mathematicsArithmetic and number theory
30. 
    Charles Feffermanfl. 1949·United States

    American mathematician who made foundational contributions to harmonic analysis, partial differential equations, and several major geometric problems.AnalysisDifferential equations and dynamical systemsTopologyFields Medal

Contemporary

1. 
   Andrew Wilesfl. 1953·United Kingdom

   English number theorist who proved Fermat's Last Theorem in 1994–1995 by establishing the modularity conjecture for semistable elliptic curves.Arithmetic and number theoryWolf Prize in MathematicsShaw Prize in Mathematical SciencesAbel Prize
2. 
   Jean Bourgain1954–2018·Belgium, United States

   Belgian mathematician who transformed harmonic analysis, ergodic theory, combinatorics, and number theory.AnalysisCombinatorics and discrete mathematicsDifferential equations and dynamical systemsFields Medal
3. 
   Preda Mihăilescufl. 1955·Romania, Switzerland

   Romanian-Swiss number theorist who in 2002 proved Catalan's conjecture — that 8 and 9 are the only consecutive perfect powers — 158 years after it was posed.Arithmetic and number theory
4. 
   Yitang Zhangfl. 1955·China, United States

   Chinese-American number theorist who proved in 2013 the first finite bound on gaps between consecutive primes, a landmark step toward the twin prime conjecture.Arithmetic and number theory
5. 
   Noga Alonfl. 1956·Israel, United States

   Israeli mathematician who developed probabilistic and algebraic methods across combinatorics, number theory, and theoretical computer science.Combinatorics and discrete mathematicsProbability and statisticsArithmetic and number theoryWolf Prize in Mathematics
6. 
   Yann Brenierfl. 1957·France

   French mathematician who established the polar-factorization approach to optimal transport and its links with fluid mechanics.AnalysisApplied and computational mathematicsDifferential equations and dynamical systems
7. 
   Thomas Halesfl. 1958·United States

   American mathematician who proved the Kepler conjecture on sphere packing in 1998 and later led the Flyspeck project, a full formal, computer-verified version of the proof.Geometry
8. 
   Grigori Perelmanfl. 1966·Russia

   Russian mathematician who proved the Poincaré and geometrization conjectures in 2002–2003 using Ricci flow with surgery, then declined both the Fields Medal (2006) and the Clay Millennium Prize (2010).GeometryTopologyFields Medal
9. 
   Ngô Bảo Châufl. 1972·Vietnam, France

   Vietnamese-French mathematician who proved the Fundamental Lemma of the Langlands programme in 2008, becoming the first Vietnamese citizen to receive the Fields Medal (2010).Arithmetic and number theoryAlgebraClay Research AwardFields Medal
10. 
    Cédric Villanifl. 1973·France

    French mathematician who proved major regularity and convergence results for the Boltzmann equation and developed modern optimal-transport methods.AnalysisDifferential equations and dynamical systemsApplied and computational mathematicsFields Medal
11. 
    Larry Guthfl. 1973·United States

    American mathematician whose polynomial partitioning method transformed incidence geometry and harmonic analysis.AnalysisGeometryCombinatorics and discrete mathematics
12. 
    Terence Taofl. 1975·Australia, United States

    Australian-American mathematician working across harmonic analysis, partial differential equations, combinatorics and number theory, known for the Green–Tao theorem and for prolific collaborative research on primes.AnalysisArithmetic and number theoryCombinatorics and discrete mathematicsFields MedalCrafoord Prize in MathematicsBreakthrough Prize in Mathematics
13. 
    Ciprian Demeterfl. 1976·Romania, United States

    Romanian-American mathematician known for decoupling theory and its applications to harmonic analysis and analytic number theory.AnalysisCombinatorics and discrete mathematicsDifferential equations and dynamical systems
14. HH
    Harald Helfgottfl. 1977·Peru, France, Germany

    Peruvian mathematician who proved the ternary (weak) Goldbach conjecture unconditionally in 2013, ending a 250-year-old problem.Arithmetic and number theoryCombinatorics and discrete mathematics
15. 
    Maryam Mirzakhani1977–2017·Iran, United States

    Iranian mathematician who worked on the geometry and dynamics of Riemann surfaces and moduli spaces, becoming in 2014 the first woman and first Iranian to win the Fields Medal.GeometryTopologyClay Research AwardFields Medal
16. 
    Maryna Viazovskafl. 1984·Ukraine, Switzerland

    Ukrainian mathematician who solved the sphere-packing problem in dimensions 8 and 24 using modular forms and interpolation.Arithmetic and number theoryAnalysisGeometryFields Medal
17. JZ
    Joshua Zahlfl. 1986·United States, Canada, China

    American mathematician working in harmonic analysis and combinatorics who, with Hong Wang, proved the three-dimensional Kakeya set conjecture in 2025.AnalysisCombinatorics and discrete mathematicsClay Research Award
18. 
    James Maynardfl. 1987·United Kingdom

    English number theorist who gave a simpler, more flexible proof of bounded gaps between primes (2013) and, with Dimitris Koukoulopoulos, resolved the Duffin–Schaeffer conjecture (2019); awarded the Fields Medal in 2022.Arithmetic and number theoryFields Medal
19. 
    Peter Scholzefl. 1987·Germany

    German mathematician who created perfectoid spaces and transformed modern arithmetic geometry.Arithmetic and number theoryAlgebraGeometryFields Medal
20. HW
    Hong Wangfl. 1991·China, United States, France

    Chinese mathematician who, with Joshua Zahl, proved the three-dimensional Kakeya set conjecture in 2025; awarded the 2026 Fields Medal.AnalysisGeometryFields Medal