A geometer is a mathematician whose area of study is geometry. Some important geometers and their main fields of work are:
Mathematicians
- Apastamba - Euclidean geometry, geometric algebra
- Apollonius of Perga - Euclidean geometry, conic sections
- Archimedes - Euclidean geometry
- Albert Victor Bäcklund
- Henry Frederick Baker - algebraic geometry
- Baudhayana - Euclidean geometry, geometric algebra
- Luigi Bianchi - differential geometry
- Janos Bolyai - non-Euclidean geometry
- Pierre Ossian Bonnet - differential geometry
- Brahmagupta - Euclidean geometry, cyclic quadrilaterals
- Raoul Bricard - descriptive geometry
- Lazare Nicolas Marguerite Carnot - projective geometry
- Élie Cartan
- Arthur Cayley
- Giovanni Ceva - Euclidean geometry
- Shiing-Shen Chern - differential geometry
- Delfino Codazzi - differential geometry
- J. H. Conway - sphere packing, recreational geometry
- H. S. M. Coxeter - theory of polytopes, non-Euclidean geometry, projective geometry
- Germinal Dandelin - Dandelin spheres in conic sections
- Julius Wilhelm Richard Dedekind
- René Descartes - invented the methodology analytic geometry
- Joseph Diaz Gergonne - projective geometry; Gergonne point
- Girard Desargues - projective geometry; Desargues' theorem
- Eratosthenes - Euclidean geometry
- Euclid - Elements, Euclidean geometry
- Leonhard Euler
- Karl Wilhelm Feuerbach - Euclidean geometry
- Carl Friedrich Gauss - Theorema Egregium.
- Phillip Griffiths - algebraic geometry, differential geometry
- Mikhail Gromov
- Branko Grünbaum - discrete geometry.
- Richard Hamilton - differential geometry, Ricci flow, Poincaré conjecture
- Hero of Alexandria - Euclidean geometry
- Robin Hartshorne - All kinds of geometry, algebraic geometry
- William Vallance Douglas Hodge
- Hypatia of Alexandria - Euclidean geometry
- Jyesthadeva - Euclidean geometry, cyclic quadrilaterals
- Katyayana - Euclidean geometry
- Felix Klein
- Sofia Vasilyevna Kovalevskaya
- Philippe de La Hire - projective geometry
- Nikolai Ivanovich Lobachevsky - non-Euclidean geometry
- Manava - Euclidean geometry
- Tobias Mayer
- John Milnor
- Hermann Minkowski - non-Euclidean geometry
- August Ferdinand Möbius - Euclidean geometry
- Gaspard Monge - descriptive geometry
- Christian Heinrich von Nagel - Euclidean geometry
- Max Noether - algebraic geometry
- Omar Khayyam - algebraic geometry, conic sections
- Blaise Pascal - projective geometry
- Daniel Pedoe
- Grigori Perelman
- John Playfair - Euclidean geometry
- Julius Plücker
- Henri Poincaré
- Jean-Victor Poncelet - projective geometry
- Pappus of Alexandria - Euclidean geometry, projective geometry
- Siméon-Denis Poisson
- Pythagoras - Euclidean geometry
- Bernhard Riemann - non-Euclidean geometry
- Giovanni Gerolamo Saccheri - non-Euclidean geometry
- Jakob Steiner - a champion of synthetic geometry methodology, projective geometry, Euclidean geometry
- Thabit ibn Qurra - analytic geometry, non-Euclidean geometry, conic sections
- Thales of Miletus - Euclidean geometry
- William Thurston
- Oswald Veblen - projective geometry, differential geometry
- Abu'l-Wáfa - spherical geometry, non-Euclidean geometry
- Shing-Tung Yau
- Zeno of Elea - Euclidean geometry
Others
- Albert Einstein - non-Euclidean geometry
- Maurits Cornelis Escher (trained as architect; worked as artist; was not a mathematician but used geometrical ideas extensively)
- George W. Hart - sculptor
- Buckminster Fuller
- Leonardo da Vinci - Euclidean geometry
- Isaac Newton - 3rd degree algebraic curves
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