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 1972
15. SK
    Sōichi Kakeya1886–1947·Japan

    Japanese mathematician whose work included polynomial root bounds and integral equations. In 1917 he posed the needle-rotation problem that gave rise to Kakeya sets and, later, the modern Kakeya dimension conjecture.AnalysisGeometry
16. 
    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
17. 
    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
18. JD
    Jesse Douglas1897–1965·United States

    American mathematician, one of the first two Fields Medalists (1936), celebrated for the first general solution of the Plateau problem on surfaces of least area spanning a given contour.AnalysisGeometryFields Medal 1936

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 1980
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 1980
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. LA
   Lars Ahlfors1907–1996·Finland, United States

   Finnish-American mathematician, one of the first two Fields Medalists (1936), a founder of geometric function theory through his theory of covering surfaces and later work on quasiconformal mappings and Riemann surfaces.AnalysisFields Medal 1936Wolf Prize in Mathematics 1981
6. 
   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
7. 
   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
8. 
   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
9. 
   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 1983
10. 
    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 1986
11. 
    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 Mathematics 1987Kyoto Prize in Basic Sciences 1998Carl Friedrich Gauss Prize 2006
12. 
    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 Medal 1954Wolf Prize in Mathematics 1984
13. LS
    Laurent Schwartz1915–2002·France

    French mathematician, Fields Medalist 1950, creator of the theory of distributions that gave rigorous foundations to generalized functions and transformed the analysis of partial differential equations.AnalysisDifferential equations and dynamical systemsFields Medal 1950
14. 
    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 1985
15. AS
    Atle Selberg1917–2007·Norway, United States

    Norwegian-American mathematician, Fields Medalist 1950, celebrated for the elementary proof of the prime number theorem, the Selberg sieve, the positive proportion of zeta zeros on the critical line, and the Selberg trace formula.Arithmetic and number theoryAnalysisFields Medal 1950Wolf Prize in Mathematics 1986
16. 
    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
17. RT
    René Thom1923–2002·France

    French mathematician, Fields Medalist 1958, founder of cobordism theory and the Thom space, later creator of catastrophe theory on singularities of smooth maps and its applications to models of sudden change.TopologyDifferential equations and dynamical systemsFields Medal 1958
18. KR
    Klaus Roth1925–2015·United Kingdom, Germany

    German-born British mathematician, Fields Medalist 1958, famous for Roth's theorem giving the best-possible bound on rational approximations to algebraic numbers, and for fundamental work on irregularities of distribution.Arithmetic and number theoryFields Medal 1958
19. JS
    Jean-Pierre Serrefl. 1926·France

    French mathematician, Fields Medalist 1954 (the youngest ever), Abel Prize 2003; reshaped algebraic topology with spectral sequences and algebraic geometry with sheaf methods, then led the modern theory of Galois representations and modular forms.TopologyAlgebraArithmetic and number theoryFields Medal 1954Wolf Prize in Mathematics 2000Abel Prize 2003
20. 
    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
21. 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
22. 
    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 1966
23. 
    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 2015
24. 
    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
25. 
    Michael Atiyah1929–2019·United Kingdom

    British mathematician who created K-theory and the Atiyah–Singer index theorem, linking topology, geometry, and analysis.AlgebraGeometryTopologyFields Medal 1966Abel Prize 2004
26. 
    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 1966
27. HH
    Heisuke Hironakafl. 1931·Japan, United States

    Japanese mathematician who proved the resolution of singularities of algebraic varieties in characteristic zero, a cornerstone of modern algebraic geometry; Fields Medal 1970.AlgebraGeometryFields Medal 1970
28. 
    John Milnorfl. 1931·United States

    American mathematician who transformed differential topology, geometry, and dynamical systems through exotic spheres and classification theory.TopologyGeometryAlgebraFields Medal 1962Abel Prize 2011
29. LH
    Lars Hörmander1931–2012·Sweden

    Swedish mathematician who created the modern theory of linear partial differential equations and founded microlocal analysis; Fields Medal 1962, Wolf Prize 1988.Differential equations and dynamical systemsAnalysisFields Medal 1962Wolf Prize in Mathematics 1988
30. JT
    John G. Thompsonfl. 1932·United States

    American mathematician who, with the Feit–Thompson theorem and the classification of minimal simple groups, laid the foundations of the classification of finite simple groups; Fields Medal 1970, Wolf Prize 1992, Abel Prize 2008.AlgebraFields Medal 1970Wolf Prize in Mathematics 1992Abel Prize 2008
31. 
    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
32. 
    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
33. 
    Michael Artinfl. 1934·Germany, United States

    German-American mathematician who made foundational contributions to algebraic geometry, étale cohomology, and algebra.AlgebraGeometryTopologyWolf Prize in Mathematics 2013
34. 
    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 1966
35. DM
    David Mumfordfl. 1937·United Kingdom, United States

    American-British mathematician who built the moduli theory of curves and abelian varieties via geometric invariant theory, then turned to pattern theory and computer vision; Fields Medal 1974, Shaw Prize 2006.AlgebraGeometryApplied and computational mathematicsFields Medal 1974Shaw Prize in Mathematical Sciences 2006
36. SN
    Sergei Novikov1938–2024·Russia

    Russian mathematician who proved the topological invariance of Pontryagin classes and reshaped manifold topology and soliton theory; Fields Medal 1970, Wolf Prize 2005.TopologyMathematical physicsFields Medal 1970Wolf Prize in Mathematics 2005
37. AB
    Alan Baker1939–2018·United Kingdom

    British mathematician whose effective estimates for linear forms in logarithms revolutionized transcendence theory and made Diophantine equations effectively solvable; Fields Medal 1970.Arithmetic and number theoryFields Medal 1970
38. 
    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 1982
39. DQ
    Daniel Quillen1940–2011·United States

    American mathematician who founded higher algebraic K-theory and reshaped homotopy theory, rational homotopy theory and module theory through concepts such as the plus construction, model categories and the Quillen–Suslin theorem.AlgebraTopologyFields Medal 1978
40. 
    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 2012
41. EB
    Enrico Bombierifl. 1940·Italy, United States

    Italian-American mathematician working in number theory and analysis, known for the Bombieri–Vinogradov theorem on primes in progressions and for work on minimal surfaces; Fields Medal 1974.Arithmetic and number theoryAnalysisGeometryFields Medal 1974
42. PD
    Pierre Delignefl. 1944·Belgium

    Belgian mathematician and a principal architect of modern arithmetic geometry; proved the Weil conjectures and shaped étale cohomology, mixed Hodge theory and the theory of perverse sheaves.AlgebraGeometryArithmetic and number theoryFields Medal 1978Crafoord Prize in Mathematics 1988Wolf Prize in Mathematics 2008Abel Prize 2013
43. GM
    Grigory Margulisfl. 1946·Russia, United States

    Russian-American mathematician who founded the theory of lattices in semisimple Lie groups (arithmeticity, superrigidity) and pioneered the use of ergodic theory and expander graphs across number theory, dynamics and combinatorics.AlgebraDifferential equations and dynamical systemsCombinatorics and discrete mathematicsFields Medal 1978Wolf Prize in Mathematics 2005Abel Prize 2020
44. 
    William Thurston1946–2012·United States

    American mathematician who revolutionized the study of three-dimensional manifolds through geometric structures and the geometrization program.GeometryTopologyAlgebraFields Medal 1982
45. AC
    Alain Connesfl. 1947·France

    French mathematician; classified injective von Neumann algebra factors and founded noncommutative geometry, with applications ranging from foliations and index theory to the Standard Model.AnalysisGeometryMathematical physicsFields Medal 1982Crafoord Prize in Mathematics 2001
46. 
    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
47. 
    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 1978
48. SY
    Shing-Tung Yaufl. 1949·United States, China

    Chinese-American mathematician who proved the Calabi conjecture and the positive mass theorem; a founder of geometric analysis whose work links differential geometry to topology and mathematical physics.GeometryDifferential equations and dynamical systemsMathematical physicsFields Medal 1982Crafoord Prize in Mathematics 1994Wolf Prize in Mathematics 2010Shaw Prize in Mathematical Sciences 2023

Contemporary

1. EW
   Edward Wittenfl. 1951·United States

   American theoretical physicist whose quantum-field-theory methods transformed topology and geometry; the only physicist to win the Fields Medal (1990).Mathematical physicsTopologyAnalysisFields Medal 1990Breakthrough Prize in Mathematics 2012Kyoto Prize in Basic Sciences 2014
2. MF
   Michael Freedmanfl. 1951·United States

   American topologist who proved the four-dimensional Poincaré conjecture and classified simply-connected topological 4-manifolds; awarded the Fields Medal in 1986.TopologyFields Medal 1986
3. SM
   Shigefumi Morifl. 1951·Japan

   Japanese algebraic geometer who founded the minimal model program through the cone theorem and bend-and-break techniques; awarded the Fields Medal in 1990.GeometryAlgebraFields Medal 1990
4. VJ
   Vaughan Jones1952–2020·New Zealand, United States

   New Zealand mathematician who founded subfactor theory and discovered the Jones polynomial knot invariant; awarded the Fields Medal in 1990.AnalysisTopologyFields Medal 1990
5. 
   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 Mathematics 1996Shaw Prize in Mathematical Sciences 2005Abel Prize 2016
6. GF
   Gerd Faltingsfl. 1954·Germany

   German mathematician who proved the Mordell conjecture on finiteness of rational points and founded the quantitative tools — heights, arithmetic intersection theory, p-adic Hodge theory — of modern arithmetic geometry.Arithmetic and number theoryAlgebraGeometryFields Medal 1986Shaw Prize in Mathematical Sciences 2015
7. 
   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 1994
8. VD
   Vladimir Drinfeldfl. 1954·Ukraine, United States

   Ukrainian-born mathematician who founded the theory of quantum groups and proved the $GL_2$ Langlands conjecture over function fields; Fields Medal 1990, Wolf Prize 2018, Shaw Prize 2023.AlgebraGeometryArithmetic and number theoryFields Medal 1990Wolf Prize in Mathematics 2018Shaw Prize in Mathematical Sciences 2023
9. EZ
   Efim Zelmanovfl. 1955·Russia, United States

   Russian-American algebraist who solved the restricted Burnside problem on groups of finite exponent and transformed the theory of Jordan and Lie algebras.AlgebraCombinatorics and discrete mathematicsFields Medal 1994
10. 
    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
11. 
    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
12. 
    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 2022
13. PL
    Pierre-Louis Lionsfl. 1956·France

    French analyst who created viscosity-solution theory and the concentration-compactness method, and proved existence for the Boltzmann equation; Fields Medal 1994.Differential equations and dynamical systemsAnalysisApplied and computational mathematicsFields Medal 1994
14. JY
    Jean-Christophe Yoccoz1957–2016·France

    French mathematician who solved the linearization problem for circle diffeomorphisms and proved local connectivity results for the Mandelbrot set; Fields Medal 1994.Differential equations and dynamical systemsAnalysisGeometryFields Medal 1994
15. SD
    Simon Donaldsonfl. 1957·United Kingdom

    British mathematician who founded smooth four-manifold theory through gauge-theoretic Donaldson invariants, and later resolved the existence of constant scalar curvature Kähler metrics on toric Fano manifolds.TopologyGeometryDifferential equations and dynamical systemsFields Medal 1986Crafoord Prize in Mathematics 1994Shaw Prize in Mathematical Sciences 2009Breakthrough Prize in Mathematics 2015Wolf Prize in Mathematics 2020
16. 
    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
17. CM
    Curtis McMullenfl. 1958·United States

    American mathematician who unified complex dynamics, hyperbolic 3-manifold geometry and renormalization theory, and proved Kra's theta conjecture on Riemann surfaces.Differential equations and dynamical systemsTopologyAnalysisFields Medal 1998
18. 
    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
19. RB
    Richard Borcherdsfl. 1959·United Kingdom

    British mathematician who invented vertex operator algebras and generalized Kac–Moody algebras and used them to prove the Conway–Norton monstrous moonshine conjecture.AlgebraMathematical physicsFields Medal 1998
20. TG
    Timothy Gowersfl. 1963·United Kingdom

    British mathematician who united Banach space theory and combinatorics, proving the Gowers dichotomy for Banach spaces and a quantitative new proof of Szemerédi's theorem.AnalysisCombinatorics and discrete mathematicsFields Medal 1998
21. MK
    Maxim Kontsevichfl. 1964·Russia, France

    Russian-French mathematician whose work on deformation quantization, Gromov–Witten invariants and homological mirror symmetry built bridges between geometry and quantum physics.GeometryMathematical physicsAlgebraFields Medal 1998Crafoord Prize in Mathematics 2008Shaw Prize in Mathematical Sciences 2012Breakthrough Prize in Mathematics 2015
22. 
    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 2006
23. LL
    Laurent Lafforguefl. 1966·France

    French mathematician who proved the Langlands correspondence for the general linear groups over function fields, the deepest completed case of the Langlands program.Arithmetic and number theoryAlgebraAnalysisClay Research Award 2000Fields Medal 2002
24. VV
    Vladimir Voevodsky1966–2017·Russia, United States

    Russian-American mathematician who created motivic homotopy theory, proved the Milnor conjecture, and later initiated univalent foundations for mathematics.AlgebraTopologyFoundations of mathematicsFields Medal 2002
25. WW
    Wendelin Wernerfl. 1968·France, Germany

    German-born French probabilist who, with Lawler and Schramm, rigorously described the conformally invariant scaling limits of planar random curves, receiving the Fields Medal in 2006.Probability and statisticsMathematical physicsFields Medal 2006
26. AO
    Andrei Okounkovfl. 1969·Russia, United States

    Russian-American mathematician who uncovered deep links between probability, representation theory and algebraic geometry, receiving the Fields Medal in 2006.AlgebraGeometryProbability and statisticsFields Medal 2006
27. EL
    Elon Lindenstraussfl. 1970·Israel, United States

    Israeli mathematician whose measure-rigidity results in ergodic theory gave the strongest progress on Littlewood's conjecture and resolved quantum unique ergodicity on arithmetic surfaces; Fields Medal 2010.Differential equations and dynamical systemsArithmetic and number theoryAnalysisFields Medal 2010
28. SS
    Stanislav Smirnovfl. 1970·Russia, Switzerland

    Russian-Swiss mathematician who proved conformal invariance of critical percolation and the planar Ising model, laying rigorous foundations for two-dimensional statistical physics; Fields Medal 2010.Probability and statisticsMathematical physicsClay Research Award 2001Fields Medal 2010
29. 
    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 Award 2004Fields Medal 2010
30. 
    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 2010
31. 
    Larry Guthfl. 1973·United States

    American mathematician whose polynomial partitioning method transformed incidence geometry and harmonic analysis.AnalysisGeometryCombinatorics and discrete mathematics
32. MB
    Manjul Bhargavafl. 1974·Canada, United States, India

    Canadian-American number theorist who generalized Gauss's composition law and used the geometry of numbers to count rings and bound the average rank of elliptic curves; Fields Medal 2014.Arithmetic and number theoryAlgebraFields Medal 2014
33. MH
    Martin Hairerfl. 1975·United Kingdom, Austria

    Austrian-British mathematician who created the theory of regularity structures, giving rigorous meaning to singular stochastic PDEs such as the KPZ equation; Fields Medal 2014 and Breakthrough Prize 2021.Probability and statisticsDifferential equations and dynamical systemsFields Medal 2014Breakthrough Prize in Mathematics 2021
34. 
    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 Medal 2006Crafoord Prize in Mathematics 2012Breakthrough Prize in Mathematics 2015
35. 
    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
36. 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
37. 
    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 Award 2014Fields Medal 2014
38. CB
    Caucher Birkarfl. 1978·United Kingdom, Iran

    Kurdish-British algebraic geometer at the University of Cambridge, specialist of birational geometry and the minimal model program; Fields Medalist 2018.AlgebraGeometryFields Medal 2018
39. AA
    Artur Avilafl. 1979·Brazil, France

    Brazilian-French mathematician who unified one-dimensional dynamics and Teichmüller dynamics through renormalization, and solved the Ten Martini problem; Fields Medal 2014.Differential equations and dynamical systemsAnalysisFields Medal 2014
40. AV
    Akshay Venkateshfl. 1981·Australia, United States

    Australian-American number theorist at the Institute for Advanced Study, known for uniting analytic number theory, homogeneous dynamics and representation theory; Fields Medalist 2018.Arithmetic and number theoryAnalysisAlgebraFields Medal 2018
41. JH
    June Huhfl. 1983·United States, South Korea

    American-South Korean mathematician at Princeton University who created a Hodge theory for matroids; Fields Medalist 2022.Combinatorics and discrete mathematicsAlgebraGeometryFields Medal 2022
42. AF
    Alessio Figallifl. 1984·Italy

    Italian mathematician at ETH Zurich working on optimal transport, partial differential equations and the calculus of variations; Fields Medalist 2018.AnalysisDifferential equations and dynamical systemsFields Medal 2018
43. 
    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 2022
44. HD
    Hugo Duminil-Copinfl. 1985·France

    French probabilist at IHÉS and the University of Geneva, known for rigorous results on phase transitions in lattice models; Fields Medalist 2022.Probability and statisticsMathematical physicsFields Medal 2022
45. 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 2026
46. 
    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 2022
47. 
    Peter Scholzefl. 1987·Germany

    German mathematician who created perfectoid spaces and transformed modern arithmetic geometry.Arithmetic and number theoryAlgebraGeometryFields Medal 2018
48. JT
    Jacob Tsimermanfl. 1988·Canada

    Canadian arithmetic geometer at the University of Toronto who turned o-minimality into a core tool of Diophantine geometry; Fields Medalist 2026.Arithmetic and number theoryGeometryFields Medal 2026
49. JP
    John Pardonfl. 1989·United States

    American geometer and topologist, permanent member of the Simons Center for Geometry and Physics at Stony Brook; Fields Medalist 2026.GeometryTopologyClay Research Award 2022Fields Medal 2026
50. YD
    Yu Dengfl. 1989·China, United States

    Chinese mathematician at the University of Chicago working on nonlinear dispersive PDEs and kinetic theory; Fields Medalist 2026.Differential equations and dynamical systemsProbability and statisticsMathematical physicsClay Research Award 2026Fields Medal 2026
51. 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 2026