A geometer is a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

whose area of study is the historical aspects that define

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, instead of the analytical geometric studies that becomes conducted from geometricians. Some notable geometers and their main fields of work, chronologically listed, are:

1000 BCE to 1 BCE

* Baudhayana (fl. c. 800 BC) –

Euclidean geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry, ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set ...

* Manava (c. 750 BC–690 BC) –

* Thales of Miletus (c. 624 BC – c. 546 BC) –

* Pythagoras (c. 570 BC – c. 495 BC) –

, Pythagorean theorem * Zeno of Elea (c. 490 BC – c. 430 BC) –

* Hippocrates of Chios (born c. 470 – 410 BC) – first systematically organized '' Stoicheia – Elements'' (geometry textbook) * Mozi (c. 468 BC – c. 391 BC) *

Plato Plato ( ; Greek language, Greek: , ; born BC, died 348/347 BC) was an ancient Greek philosopher of the Classical Greece, Classical period who is considered a foundational thinker in Western philosophy and an innovator of the writte ...

(427–347 BC) * Theaetetus (c. 417 BC – 369 BC) * Autolycus of Pitane (360–c. 290 BC) –

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

, spherical geometry *

Euclid Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...

(fl. 300 BC) – '' Elements'',

(sometimes called the "father of geometry") * Apollonius of Perga (c. 262 BC – c. 190 BC) –

, conic sections *

Archimedes Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...

(c. 287 BC – c. 212 BC) –

* Eratosthenes (c. 276 BC – c. 195/194 BC) –

* Katyayana (c. 3rd century BC) –

1–1300 AD

* Hero of Alexandria (c. AD 10–70) –

* Pappus of Alexandria (c. AD 290–c. 350) –

projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (''p ...

* Hypatia of Alexandria (c. AD 370–c. 415) –

Brahmagupta Brahmagupta ( – ) was an Indian Indian mathematics, mathematician and Indian astronomy, astronomer. He is the author of two early works on mathematics and astronomy: the ''Brāhmasphuṭasiddhānta'' (BSS, "correctly established Siddhanta, do ...

(597–668) –

, cyclic quadrilaterals * Vergilius of Salzburg (c.700–784) – Irish bishop of Aghaboe, Ossory and later

Salzburg Salzburg is the List of cities and towns in Austria, fourth-largest city in Austria. In 2020 its population was 156,852. The city lies on the Salzach, Salzach River, near the border with Germany and at the foot of the Austrian Alps, Alps moun ...

Austria Austria, formally the Republic of Austria, is a landlocked country in Central Europe, lying in the Eastern Alps. It is a federation of nine Federal states of Austria, states, of which the capital Vienna is the List of largest cities in Aust ...

; antipodes, and

* 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 Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīshābūrī (18 May 1048 – 4 December 1131) (Persian language, Persian: غیاث الدین ابوالفتح عمر بن ابراهیم خیام نیشابورﻯ), commonly known as Omar ...

(1048–1131) –

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

, conic sections * Ibn Maḍāʾ (1116–1196)

1301–1800 AD

* Piero della Francesca (1415–1492) *

Leonardo da Vinci Leonardo di ser Piero da Vinci (15 April 1452 - 2 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially rested o ...

(1452–1519) –

* Jyesthadeva (c. 1500 – c. 1610) –

, 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) –

; Desargues' theorem *

René Descartes René Descartes ( , ; ; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and Modern science, science. Mathematics was paramou ...

(1596–1650) – invented the methodology of analytic geometry, also called ''Cartesian geometry'' after him *

Pierre de Fermat Pierre de Fermat (; ; 17 August 1601 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his d ...

(1607–1665) – analytic geometry * Blaise Pascal (1623–1662) –

Christiaan Huygens Christiaan Huygens, Halen, Lord of Zeelhem, ( , ; ; also spelled Huyghens; ; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution ...

(1629–1695) – evolute * Giordano Vitale (1633–1711) * Philippe de La Hire (1640–1718) –

Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...

(1642–1727) – 3rd-degree

algebraic curve In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane cu ...

* Giovanni Ceva (1647–1734) –

* Johann Jacob Heber (1666–1727) – surveyor and geometer * Giovanni Gerolamo Saccheri (1667–1733) – non-Euclidean geometry *

Leonhard Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...

(1707–1783) * Tobias Mayer (1723–1762) * Johann Heinrich Lambert (1728–1777) – non-Euclidean geometry * Gaspard Monge (1746–1818) –

descriptive geometry Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design an ...

* John Playfair (1748–1819) –

* Lazare Nicolas Marguerite Carnot (1753–1823) –

* Joseph Diaz Gergonne (1771–1859) –

; Gergonne point * Carl Friedrich Gauss (1777–1855) – Theorema Egregium * Louis Poinsot (1777–1859) * Siméon Denis Poisson (1781–1840) * Jean-Victor Poncelet (1788–1867) –

* Augustin-Louis Cauchy (1789–1857) * August Ferdinand Möbius (1790–1868) –

* Nikolai Ivanovich Lobachevsky (1792–1856) – hyperbolic geometry, a non-Euclidean geometry * Michel Chasles (1793–1880) –

* Germinal Dandelin (1794–1847) – Dandelin spheres in conic sections * Jakob Steiner (1796–1863) – champion of synthetic geometry methodology,

1801–1900 AD

* Karl Wilhelm Feuerbach (1800–1834) –

* Julius Plücker (1801–1868) * János Bolyai (1802–1860) – hyperbolic geometry, a non-Euclidean geometry * Christian Heinrich von Nagel (1803–1882) –

* Johann Benedict Listing (1808–1882) –

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

* Hermann Günther Grassmann (1809–1877) – exterior algebra * Ludwig Otto Hesse (1811–1874) – algebraic invariants and

* Ludwig Schlafli (1814–1895) – Regular 4-polytope * Pierre Ossian Bonnet (1819–1892) –

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

* Arthur Cayley (1821–1895) * Joseph Bertrand (1822–1900) * Delfino Codazzi (1824–1873) –

Bernhard Riemann Georg Friedrich Bernhard Riemann (; ; 17September 182620July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the f ...

(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) –

* 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) –

* Alicia Boole Stott (1860–1940) * Hermann Minkowski (1864–1909) – non-Euclidean geometry * Henry Frederick Baker (1866–1956) –

* Élie Cartan (1869–1951) * Dmitri Egorov (1869–1931) –

* Veniamin Kagan (1869–1953) * Raoul Bricard (1870–1944) –

* Ernst Steinitz (1871–1928) – Steinitz's theorem * Marcel Grossmann (1878–1936) * Oswald Veblen (1880–1960) –

* Nathan Altshiller Court (1881–1968) – author of ''College Geometry'' *

Emmy Noether Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's theorem, Noether's first and Noether's second theorem, second theorems, which ...

(1882–1935) –

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

* Harry Clinton Gossard (1884–1954) * Arthur Rosenthal (1887–1959) * Helmut Hasse (1898–1979) –

1901–present

* 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 Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

* H. S. M. Coxeter (1907–2003) – theory of polytopes, non-Euclidean geometry,

* J. A. Todd (1908–1994) * Daniel Pedoe (1910–1998) * Shiing-Shen Chern (1911–2004) –

* 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) –

* 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 Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, Philosophy of science, philosopher of science and Nobel Prize in Physics, Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics i ...

(1931–) * Yuri Manin (1937–2023) –

and diophantine geometry * Vladimir Arnold (1937–2010) –

* Ernest Vinberg (1937–2020) * J. H. Conway (1937–2020) – sphere packing, recreational geometry * Robin Hartshorne (1938–) – geometry, algebraic geometry * Phillip Griffiths (1938–) –

* Enrico Bombieri (1940–) –

* Robert Williams (1942–) * Peter McMullen (1942–) * Richard S. Hamilton (1943–2024) –

, Ricci flow, Poincaré conjecture * Mikhail Gromov (1943–) * Rudy Rucker (1946–) *

William Thurston William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thurst ...

(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,

, 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

References

{{Reflist Geometers *