List of geometers

​) by providing proofs and applications to mensuration problems, enhancing practical geometry for surveying and architecture.^[55][56] Leonardo Fibonacci (c. 1170–1250 CE), an Italian mathematician, bridged Islamic and European geometry in Liber Abaci (1202), introducing Hindu-Arabic numerals to the West and applying them to geometric series and proportions in problems involving areas, volumes, and commercial measurements. His text included geometric constructions for irrational numbers like $\sqrt{10}$10

​ using circles and lines, and explored series sums geometrically, such as the infinite series for polygonal numbers, fostering arithmetic-geometry links in medieval Europe.^[57] Jordanus de Nemore (c. 1220 CE), a European scholar, pioneered arithmetical geometry in mechanics through treatises like De ratione ponderis, where he analyzed levers and statics using proportional reasoning and geometric models of weights on inclined planes, deriving formulas for equilibrium (e.g., $w_1 d_1 = w_2 d_2$w1​d1​=w2​d2​) via virtual displacements and pyramid volumes. His work represented an early fusion of Euclidean geometry with physical applications, influencing later statics.^[58] Nasir al-Din al-Tusi (1201–1274 CE), a Persian polymath, advanced spherical geometry in his planetary models at the Maragha Observatory, refining Ptolemy's system with the "Tusi couple"—a geometric device using two circles to produce linear motion from circular ones, eliminating equants for more accurate epicycles. He also applied polyhedral geometry to architectural designs, such as hospital layouts incorporating regular polyhedra for structural symmetry, and commented extensively on Euclid's Elements to preserve and clarify Greek geometric foundations.^[50][59]

Early Modern Geometers (1501 – 1800 CE)

19th Century Geometers (1801 – 1900 CE)

20th Century Geometers (1901 – 2000 CE)

• David Hilbert (1862–1943): Hilbert formalized the foundations of geometry through a set of 21 axioms that provided a complete and consistent basis for Euclidean geometry, addressing gaps in Euclid's original postulates by incorporating incidence, order, congruence, parallelism, and continuity.^[67] These axioms enabled the rigorous analysis of geometric constructions and influenced the development of modern axiomatic mathematics. In 1900, Hilbert presented 23 unsolved problems at the International Congress of Mathematicians, several of which—such as the foundations of geometry—spurred advancements in algebraic geometry and topology by challenging mathematicians to unify disparate geometric traditions.^[68]
• Hermann Weyl (1885–1955): Weyl pioneered gauge theory in 1918 as an extension of general relativity, introducing local symmetries in spacetime that unified gravity and electromagnetism through infinitesimal scale transformations, laying the groundwork for modern particle physics.^[69] His work on symmetric geometries, including the classification of compact Lie groups and their representations, bridged differential geometry with group theory, providing tools for analyzing symmetric spaces in both pure mathematics and quantum field theory.^[70]
• H.S.M. Coxeter (1907–2003): Coxeter systematized the study of regular polytopes in higher dimensions through his 1948 book Regular Polytopes, classifying all finite regular polytopes in Euclidean spaces up to dimension four and extending Schläfli's work to non-Euclidean geometries.^[71] He introduced Coxeter groups as reflection groups generated by mirrors, which describe the symmetry groups of these polytopes and tessellations, integrating combinatorial algebra with geometric visualization and influencing crystallography and computer graphics.^[72]
• Emmy Noether (1882–1935): Noether's 1918 theorem established a profound link between continuous symmetries of geometric systems—such as invariances under translations, rotations, or scaling in Lagrangian mechanics—and corresponding conservation laws, like momentum, angular momentum, and energy, providing a geometric foundation for classical and relativistic physics.^[73] In geometric contexts, the theorem applies to variational problems on manifolds, where symmetries of the action integral yield conserved quantities that underpin the structure of differential equations in curved spaces, influencing fields from general relativity to algebraic topology.^[74] Her work emphasized the role of invariance groups in unifying geometric and physical laws, with applications to Noether currents that quantify charge conservation in gauge theories.
• Benoit Mandelbrot (1924–2010): Mandelbrot introduced the Mandelbrot set in 1980 as the iconic boundary of the Julia set for the quadratic map $z_{n+1} = z_n^2 + c$zn+1​=zn2​+c in the complex plane, revealing intricate self-similar structures that challenged traditional notions of dimension and smoothness in geometry.^[75] He defined fractal dimension as $D = \log N / \log (1/s)$D=logN/log(1/s), where $N$N is the number of self-similar copies at scale factor $s$s, quantifying the roughness of irregular shapes like coastlines or natural forms and integrating geometric measure theory with chaos and dynamical systems.^[76]
• John von Neumann (1903–1957): Von Neumann developed geometric operator theory in the 1930s through his work on rings of operators in Hilbert space, introducing von Neumann algebras as self-adjoint operator algebras that capture the spectral properties of quantum observables in infinite-dimensional geometric settings.^[77] His spectral theorem for normal operators extended geometric intuitions from finite matrices to unbounded spaces, providing a framework for measuring geometric invariants like distances and angles in abstract Hilbert geometries, with profound impacts on functional analysis and quantum mechanics.^[78]
• Shiing-Shen Chern (1911–2004): Chern defined Chern classes in 1940s as topological invariants in the cohomology ring of complex manifolds, constructed via the curvature form of connections on vector bundles, which measure obstructions to flatness in differential geometry.^[79] These classes unified de Rham cohomology with characteristic classes, enabling the computation of Euler characteristics and signatures for manifolds, and became essential in algebraic geometry for studying bundles over projective spaces.^[80]
• William Thurston (1946–2012): Thurston formulated the geometrization conjecture in the 1970s, positing that every compact 3-manifold decomposes uniquely into pieces admitting one of eight geometric structures—such as Euclidean, hyperbolic, or spherical—via a canonical hierarchy of tori and spheres, integrating low-dimensional topology with Riemannian geometry.^[81] This conjecture classifies 3-manifolds by their geometric invariants, resolving the Poincaré conjecture as a special case and providing a blueprint for understanding the topology of 3-dimensional spaces through uniformization and orbifold theorems.^[82]

21st Century Geometers (2001 – present)

Diverse Perspectives

Women Geometers

Non-Western Geometers