A geometer is a mathematician whose area of study is geometry.
Some important geometers and their main fields of work, chronologically listed are:
Baudhayana (fl. c. 800 BC) - Euclidean geometry, geometric algebra
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–died 410 BC) - first systematically organized Stoicheia Elements (geometry textbook)
Mozi (c. 470 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
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, non-Euclidean geometry
Alhazen (965–c. 1040)
Omar Khayyam (1048–1131) - algebraic geometry, conic sections
Ibn Maḍāʾ (1116–1196)
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)
Johannes Kepler (1571–1630) - (used geometric ideas in astronomical work)
Girard Desargues (1591–1661) - projective geometry; Desargues' theorem
René Descartes (1596–1650)) - invented the methodology of analytic geometry, also called Cartesian geometry after him
Blaise Pascal (1623–1662) - projective geometry
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
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
August Ferdinand Möbius (1790–1868) - Euclidean geometry
Nikolai Ivanovich Lobachevsky (1792–1856) - hyperbolic geometry, a non-Euclidean geometry
Germinal Dandelin (1794–1847) - Dandelin spheres in conic sections
Jakob Steiner (1796–1863) - champion of synthetic geometry methodology, projective geometry, Euclidean geometry
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
Ludwig Otto Hesse (1811-1874) - algebraic invariants and geometry
Pierre Ossian Bonnet (1819–1892) - differential geometry
Arthur Cayley (1821–1895)
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)
Albert Einstein (1879–1955) - non-Euclidean geometry
Oswald Veblen (1880–1960) - projective geometry, differential geometry
Emmy Noether (1882–1935) - algebraic topology
Harry Clinton Gossard (1884–1954)
Arthur Rosenthal (1887–1959)
Buckminster Fuller (1895–1983)
Helmut Hasse (1898–1979) - algebraic geometry
Maurits Cornelis Escher (1898–1972) - artist who used geometrical ideas extensively
William Vallance Douglas Hodge (1903–1975)
Patrick du Val (1903–1987)
Beniamino Segre (1903–1977) - combinatorial geometry
Samuel L. Greitzer (1905–1988) - founding chairman of USA Mathematical Olympiad
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–)
Isaak Yaglom (1921–1988)
Benoît Mandelbrot (1924–2010) - fractal geometry
Katsumi Nomizu (1924–2008) - affine differential geometry
Michael S. Longuet-Higgins (1925–2016)
John Leech (mathematician) (1926–1992)
Alexander Grothendieck (1928–2014) - algebraic geometry
Branko Grünbaum (1929–) - discrete geometry
Michael Atiyah (1929–)
Geoffrey Colin Shephard (c. 1930–)
Norman W. Johnson (1930–)
John Milnor (1931–)
Roger Penrose (1931–)
Yuri Manin (1937–) - algebraic geometry and diophantine geometry
Vladimir Arnold (1937–2010) - algebraic geometry
Ernest Vinberg (1937–)
J. H. Conway ( 1937–) - sphere packing, recreational geometry
Robin Hartshorne (1938–) - geometry, algebraic geometry
Phillip Griffiths (1938–) - algebraic geometry, differential geometry
Enrico Bombieri (1940–) - algebraic geometry
Robert Williams (geometer) (1942–)
Peter McMullen (1942–)
Richard S. Hamilton (1943–) - differential geometry, Ricci flow, Poincaré conjecture
Mikhail Gromov (1943–)
Roger Burrows (1945–) - applied close packing theory in education
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–)
Grigori Perelman (1966–) - Poincaré conjecture
Maryam Mirzakhani (1977–)
List of geometers Wikipedia (Text) CC BY-SA