A geometer is a mathematician whose area of study is geometry. Some important geometers and their main fields of work are:

Mathematicians

• Apollonius of Perga - euclidean geometry, conic sections
• Archimedes - euclidean geometry
• Albert Victor Bäcklund
• Luigi Bianchi -- differential geometry
• Janos Bolyai - non-euclidean geometry
• Pierre Ossian Bonnet -- differential geometry
• Lazare Nicolas Marguerite Carnot - projective geometry
• Arthur Cayley
• Shiing-Shen Chern - differential geometry
• Delfino Codazzi - differential geometry
• J. H. Conway - sphere packing, recreational geometry
• H. S. M. Coxeter -- polytopes, projective geometry, ...
• Germinal Dandelin -- Dandelin spheres in conic sections
• Julius Wilhelm Richard Dedekind
• René Descartes -- invented the methodology analytic geometry
• Joseph Diaz Gergonne - Gergonne point, projective geometry
• Girard Desargues (projective geometry, Desargues' theorem)
• Eratosthenes - euclidean geometry
• La Hire - projective geometry
• Euclid - Thirteen Books of Euclid
• Leonhard Euler - everything
• Karl Wilhelm Feuerbach - euclidean geometry
• Carl Friedrich Gauss - Theorema Egregia.
• Hero of Alexandria - euclidean geometry
• Hypatia of Alexandria - euclidean geometry
• Felix Klein
• Sofia Vasilyevna Kovalevskaya
• Nikolai Ivanovich Lobachevsky - non-euclidean geometry
• Hermann Minkowski - non-euclidean geometry
• August Ferdinand Möbius - euclidean geometry
• Gaspard Monge - differential geometry
• Max Noether - ?? algebraic geometry
• Blaise Pascal - projective geometry
• Julius Plucker
• Henri Poincaré
• Jean Victor Poncelet - projective geometry
• Pappus of Alexandria - euclidean 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
• Thales of Miletus - euclidean geometry
• 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)
• Buckminster Fuller
• Leonardo da Vinci - euclidean geometry
• Isaac Newton - 3rd degree algebraic curves