List of geometers

Short description: None

"Geometer" redirects here. For the moth family, see geometer moth.

"Geometrician" redirects here. For the moth, see Grammodes stolida.

One of the oldest surviving fragments of Euclid's Elements, found at Oxyrhynchus and dated to c. 100 AD (P. Oxy. 29). The diagram accompanies Book II, Proposition 5.[1] Geometry

Projecting a sphere to a plane.

* Outline
* History

Branches

* Euclidean
* Non-Euclidean
* Elliptic
* Spherical
* Hyperbolic
* Non-Archimedean geometry
* Projective
* Affine
* Synthetic
* Analytic
* Algebraic
* Arithmetic
* Diophantine
* Differential
* Riemannian
* Symplectic
* Discrete differential
* Complex
* Finite
* Discrete/Combinatorial
* Digital
* Convex
* Computational
* Fractal
* Incidence

* Concepts
* Features

Dimension

* Straightedge and compass constructions

* Angle
* Curve
* Diagonal
* Orthogonality (Perpendicular)
* Parallel
* Vertex

* Congruence
* Similarity
* Symmetry

Zero-dimensional

* Point

One-dimensional

* Line
* segment
* ray
* Length

Two-dimensional

* Plane
* Area
* Polygon

Triangle

* Altitude
* Hypotenuse
* Pythagorean theorem

Parallelogram

* Square
* Rectangle
* Rhombus
* Rhomboid

Quadrilateral

* Trapezoid
* Kite

Circle

* Diameter
* Circumference
* Area

Three-dimensional

* Volume

* Cube
* cuboid
* Cylinder
* Pyramid
* Sphere

Four- / other-dimensional

* Tesseract
* Hypersphere

Geometers

by name

* Aida
* Aryabhata
* Ahmes
* Alhazen
* Apollonius
* Archimedes
* Atiyah
* Baudhayana
* Bolyai
* Brahmagupta
* Cartan
* Coxeter
* Descartes
* Euclid
* Euler
* Gauss
* Gromov
* Hilbert
* Jyeṣṭhadeva
* Kātyāyana
* Khayyám
* Klein
* Lobachevsky
* Manava
* Minkowski
* Minggatu
* Pascal
* Pythagoras
* Parameshvara
* Poincaré
* Riemann
* Sakabe
* Sijzi
* al-Tusi
* Veblen
* Virasena
* Yang Hui
* al-Yasamin
* Zhang
* List of geometers

by period

|  BCE

* Ahmes
* Baudhayana
* Manava
* Pythagoras
* Euclid
* Archimedes
* Apollonius

1–1400s

* Zhang
* Kātyāyana
* Aryabhata
* Brahmagupta
* Virasena
* Alhazen
* Sijzi
* Khayyám
* al-Yasamin
* al-Tusi
* Yang Hui
* Parameshvara

1400s–1700s

* Jyeṣṭhadeva
* Descartes
* Pascal
* Minggatu
* Euler
* Sakabe
* Aida

1700s–1900s

* Gauss
* Lobachevsky
* Bolyai
* Riemann
* Klein
* Poincaré
* Hilbert
* Minkowski
* Cartan
* Veblen
* Coxeter

Present day

* Atiyah
* Gromov

* v
* t
* e

A geometer or geometrician is a mathematician who specializes in geometry.[2][3]

Some notable geometers and their main fields of work, chronologically listed, are:

## Contents

* 1 1000 BCE to 1 BCE
* 2 1–1300 AD
* 3 1301–1800 AD
* 4 1801–1900 AD
* 5 1901–present
* 6 Geometers in art
* 7 See also
* 8 References

## 1000 BCE to 1 BCE

* Baudhayana (fl. c. 800 BC) – Euclidean geometry
* Manava (c. 750 BC–690 BC) – Euclidean geometry
* Thales of Miletus (c. 624 BC – c. 546 BC) – Euclidean geometry
* Pythagoras (c. 570 BC – c. 495 BC) – Euclidean geometry, Pythagorean theorem
* Zeno of Elea (c. 490 BC – c. 430 BC) – Euclidean geometry
* Hippocrates of Chios (born c. 470 – 410 BC) – first systematically organized Stoicheia – Elements (geometry textbook)
* Mozi (c. 468 BC – c. 391 BC)
* Plato (427–347 BC)
* Theaetetus (c. 417 BC – 369 BC)
* Autolycus of Pitane (360–c. 290 BC) – astronomy, spherical geometry
* Euclid (fl. 300 BC) – Elements, Euclidean geometry (sometimes called the "father of geometry")
* Apollonius of Perga (c. 262 BC – c. 190 BC) – Euclidean geometry, conic sections
* Archimedes (c. 287 BC – c. 212 BC) – Euclidean geometry
* Eratosthenes (c. 276 BC – c. 195/194 BC) – Euclidean geometry
* Katyayana (c. 3rd century BC) – Euclidean geometry

## 1–1300 AD

* Hero of Alexandria (c. AD 10–70) – Euclidean geometry
* Pappus of Alexandria (c. AD 290–c. 350) – Euclidean geometry, projective geometry
* Hypatia of Alexandria (c. AD 370–c. 415) – Euclidean geometry
* Brahmagupta (597–668) – Euclidean geometry, cyclic quadrilaterals
* Vergilius of Salzburg (c.700–784) – Irish bishop of Aghaboe, Ossory and later Salzburg, Austria; antipodes, and astronomy
* Al-Abbās ibn Said al-Jawharī (c. 800–c. 860)
* Thabit ibn Qurra (826–901) – analytic geometry, non-Euclidean geometry, conic sections
* Abu'l-Wáfa (940–998) – spherical geometry, spherical triangles
* Ibn al-Haytham (965–c. 1040)
* Omar Khayyam (1048–1131) – algebraic geometry, conic sections
* Ibn Maḍāʾ (1116–1196)

## 1301–1800 AD

80px
Leonardo da Vinci | 80px
Johannes Kepler | 80px
Girard Desargues

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80px
René Descartes | 80px
Blaise Pascal | 80px
Isaac Newton
80px
Leonhard Euler | 80px
Carl Gauss  | 80px
August Möbius
80px
Nikolai Lobachevsky | 80px
John Playfair  | 80px
Jakob Steiner

* Piero della Francesca (1415–1492)
* Leonardo da Vinci (1452–1519) – Euclidean geometry
* Jyesthadeva (c. 1500 – c. 1610) – Euclidean geometry, cyclic quadrilaterals
* Marin Getaldić (1568–1626)
* Jacques-François Le Poivre (1652–1710) – projective geometry
* Johannes Kepler (1571–1630) – (used geometric ideas in astronomical work)
* Edmund Gunter (1581–1686)
* Girard Desargues (1591–1661) – projective geometry; Desargues' theorem
* René Descartes (1596–1650) – invented the methodology of analytic geometry, also called Cartesian geometry after him
* Pierre de Fermat (1607–1665) – analytic geometry
* Blaise Pascal (1623–1662) – projective geometry
* Christiaan Huygens (1629–1695) – evolute
* Giordano Vitale (1633–1711)
* Philippe de La Hire (1640–1718) – projective geometry
* Isaac Newton (1642–1727) – 3rd-degree algebraic curve
* Giovanni Ceva (1647–1734) – Euclidean geometry
* Johann Jacob Heber (1666–1727) – surveyor and geometer
* Giovanni Gerolamo Saccheri (1667–1733) – non-Euclidean geometry
* Leonhard Euler (1707–1783)
* Tobias Mayer (1723–1762)
* Johann Heinrich Lambert (1728–1777) – non-Euclidean geometry
* Gaspard Monge (1746–1818) – descriptive geometry
* John Playfair (1748–1819) – Euclidean geometry
* Lazare Nicolas Marguerite Carnot (1753–1823) – projective geometry
* Joseph Diaz Gergonne (1771–1859) – projective geometry; Gergonne point
* Carl Friedrich Gauss (1777–1855) – Theorema Egregium
* Louis Poinsot (1777–1859)
* Siméon Denis Poisson (1781–1840)
* Jean-Victor Poncelet (1788–1867) – projective geometry
* Augustin-Louis Cauchy (1789–1857)
* August Ferdinand Möbius (1790–1868) – Euclidean geometry
* Nikolai Ivanovich Lobachevsky (1792–1856) – hyperbolic geometry, a non-Euclidean geometry
* Michel Chasles (1793–1880) – projective geometry
* Germinal Dandelin (1794–1847) – Dandelin spheres in conic sections
* Jakob Steiner (1796–1863) – champion of synthetic geometry methodology, projective geometry, Euclidean geometry

## 1801–1900 AD

80px
Julius Plücker | 80px
Arthur Cayley | 80px
Bernhard Riemann

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80px
Richard Dedekind | 80px
Max Noether | 80px
Felix Klein
80px
Hermann Minkowski | 80px
Henri Poincaré | 80px
Evgraf Fedorov

* Karl Wilhelm Feuerbach (1800–1834) – Euclidean geometry
* Julius Plücker (1801–1868)
* János Bolyai (1802–1860) – hyperbolic geometry, a non-Euclidean geometry
* Christian Heinrich von Nagel (1803–1882) – Euclidean geometry
* Johann Benedict Listing (1808–1882) – topology
* Hermann Günther Grassmann (1809–1877) – exterior algebra
* Ludwig Otto Hesse (1811–1874) – algebraic invariants and geometry
* Ludwig Schlafli (1814–1895) – Regular 4-polytope
* Pierre Ossian Bonnet (1819–1892) – differential geometry
* Arthur Cayley (1821–1895)
* Joseph Bertrand (1822–1900)
* Delfino Codazzi (1824–1873) – differential geometry
* Bernhard Riemann (1826–1866) – elliptic geometry (a non-Euclidean geometry) and Riemannian geometry
* Julius Wilhelm Richard Dedekind (1831–1916)
* Ludwig Burmester (1840–1927) – theory of linkages
* Edmund Hess (1843–1903)
* Albert Victor Bäcklund (1845–1922)
* Max Noether (1844–1921) – algebraic geometry
* Henri Brocard (1845–1922) – Brocard points
* William Kingdon Clifford (1845–1879) – geometric algebra
* Pieter Hendrik Schoute (1846–1923)
* Felix Klein (1849–1925)
* Sofia Vasilyevna Kovalevskaya (1850–1891)
* Evgraf Fedorov (1853–1919)
* Henri Poincaré (1854–1912)
* Luigi Bianchi (1856–1928) – differential geometry
* Alicia Boole Stott (1860–1940)
* Hermann Minkowski (1864–1909) – non-Euclidean geometry
* Henry Frederick Baker (1866–1956) – algebraic geometry
* Élie Cartan (1869–1951)
* Dmitri Egorov (1869–1931) – differential geometry
* Veniamin Kagan (1869–1953)
* Raoul Bricard (1870–1944) – descriptive geometry
* Ernst Steinitz (1871–1928) – Steinitz's theorem
* Marcel Grossmann (1878–1936)
* Oswald Veblen (1880–1960) – projective geometry, differential geometry
* Nathan Altshiller Court (1881–1968) – author of College Geometry
* Emmy Noether (1882–1935) – algebraic topology
* Harry Clinton Gossard (1884–1954)
* Arthur Rosenthal (1887–1959)
* Helmut Hasse (1898–1979) – algebraic geometry

## 1901–present

H. S. M. Coxeter  | 80px
Ernst Witt | 80px
Benoit Mandelbrot

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80px
Branko Grünbaum | 80px
Michael Atiyah | 80px
J. H. Conway
80px
William Thurston | 80px
Mikhail Gromov | 80px
George W. Hart
80px
Shing-Tung Yau | 60px
Károly Bezdek | 80px
Grigori Perelman

Denis Auroux

* William Vallance Douglas Hodge (1903–1975)
* Patrick du Val (1903–1987)
* Beniamino Segre (1903–1977) – combinatorial geometry
* J. C. P. Miller (1906–1981)
* André Weil (1906–1998) – Algebraic geometry
* H. S. M. Coxeter (1907–2003) – theory of polytopes, non-Euclidean geometry, projective geometry
* J. A. Todd (1908–1994)
* Daniel Pedoe (1910–1998)
* Shiing-Shen Chern (1911–2004) – differential geometry
* Ernst Witt (1911–1991)
* Rafael Artzy (1912–2006)
* Aleksandr Danilovich Aleksandrov (1912–1999)
* László Fejes Tóth (1915–2005)
* Edwin Evariste Moise (1918–1998)
* Aleksei Pogorelov (1919–2002) – differential geometry
* Magnus Wenninger (1919–2017) – polyhedron models
* Jean-Louis Koszul (1921–2018)
* Isaak Yaglom (1921–1988)
* Eugenio Calabi (1923–2023)
* Benoit Mandelbrot (1924–2010) – fractal geometry
* Katsumi Nomizu (1924–2008) – affine differential geometry
* Michael S. Longuet-Higgins (1925–2016)
* John Leech (1926–1992)
* Alexander Grothendieck (1928–2014) – algebraic geometry
* Branko Grünbaum (1929–2018) – discrete geometry
* Michael Atiyah (1929–2019)
* Lev Semenovich Pontryagin (1908–1988)
* Geoffrey Colin Shephard (1927–2016)
* Norman W. Johnson (1930–2017)
* John Milnor (1931–)
* Roger Penrose (1931–)
* Yuri Manin (1937–2023) – algebraic geometry and diophantine geometry
* Vladimir Arnold (1937–2010) – algebraic geometry
* Ernest Vinberg (1937–2020)
* J. H. Conway (1937–2020) – sphere packing, recreational geometry
* Robin Hartshorne (1938–) – geometry, algebraic geometry
* Phillip Griffiths (1938–) – algebraic geometry, differential geometry
* Enrico Bombieri (1940–) – algebraic geometry
* Robert Williams (1942–)
* Peter McMullen (1942–)
* Richard S. Hamilton (1943–2024) – differential geometry, Ricci flow, Poincaré conjecture
* Mikhail Gromov (1943–)
* Rudy Rucker (1946–)
* William Thurston (1946–2012)
* Shing-Tung Yau (1949–)
* Michael Freedman (1951–)
* Egon Schulte (1955–) – polytopes
* George W. Hart (1955–) – sculptor
* Károly Bezdek (1955–) – discrete geometry, sphere packing, Euclidean geometry, non-Euclidean geometry
* Simon Donaldson (1957–)
* Kenji Fukaya (1959–) – symplectic geometry
* Yong-Geun Oh (1961–)
* Toshiyuki Kobayashi (1962–)
* Hiraku Nakajima (1962–) – representation theory and geometry
* Hwang Jun-Muk (1963–) – algebraic geometry, differential geometry
* Grigori Perelman (1966–) – Poincaré conjecture
* Maryam Mirzakhani (1977–2017)
* Denis Auroux (1977–)

## Geometers in art

150px
God as architect of the world, 1220–1230, from Bible moralisée  | 150px
Kepler's Platonic solid model of planetary spacing in the Solar System from Mysterium Cosmographicum (1596)  | 150px
The Ancient of Days, 1794, by William Blake, with the compass as a symbol for divine order  | 240px
Newton (1795), by William Blake; here, Newton is depicted critically as a "divine geometer".[4]

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## See also

* Mathematics and architecture

## References

1. ↑ Bill Casselman. "One of the Oldest Extant Diagrams from Euclid". University of British Columbia. https://www.math.ubc.ca/~cass/Euclid/papyrus/papyrus.html.
2. ↑ "Definition of GEOMETER" (in en). https://www.merriam-webster.com/dictionary/geometer.
3. ↑ "Definition of GEOMETRICIAN" (in en). https://www.merriam-webster.com/dictionary/geometrician.
4. ↑ "Newton, object 1 (Butlin 306) "Newton"". William Blake Archive. September 25, 2013. http://www.blakearchive.org/exist/blake/archive/copyinfo.xq?copyid=but306.1.

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