Geometry

Pythagorean mathematician and general of Tarentum who defined the three musical means, proved that superparticular ratios have no mean proportional, and gave the first solution of the doubling of the cube.

geometry, theory of proportion, music theory

Greek mathematician and astronomer who created the theory of proportion and the method of exhaustion preserved in Euclid's Elements, and the first geometrical model of planetary motion.

geometry, theory of proportion, astronomy

Greek mathematician of Alexandria whose Elements organized the geometry and arithmetic of his predecessors into the model of an axiomatic deductive science.

geometry, number theory, optics

Greek astronomer of the third century BC who proposed that the Earth rotates and orbits a motionless Sun, and whose surviving treatise measured the sizes and distances of the Sun and Moon by geometry.

astronomy, geometry

Greek geometer of Syracuse who measured areas and volumes of curved figures by exhaustion and founded statics and hydrostatics.

geometry, mechanics, hydrostatics

Hellenistic scholar and head of the Library of Alexandria who measured the circumference of the Earth, drew a gridded world map, founded scientific chronology and gave his name to the prime-number sieve.

geography, geodesy, number theory

Hellenistic geometer, called the Great Geometer in antiquity, whose eight-book Conics named and systematized the ellipse, parabola and hyperbola and who proved the theorem on planetary stationary points.

geometry, conic sections, astronomy

Alexandrian geometer whose Mathematical Collection preserved much of Greek geometry and contains the hexagon theorem, the cross-ratio lemma and the centroid rule for solids of revolution.

geometry, projective geometry, mechanics

Neoplatonist head of the Athenian school whose Commentary on the First Book of Euclid's Elements is the main source for early Greek geometry and contains an influential attempted proof of the parallel postulate.

philosophy, history and philosophy of mathematics, geometry

Author of the Brāhmasphuṭasiddhānta (628), which gave the first systematic rules for zero and negative numbers, a general quadratic rule, the composition law for x² − Ny² = k, and formulas for cyclic quadrilaterals.

astronomy, mathematics, algebra

Persian mathematician and astronomer who classified and solved cubic equations by intersecting conics, helped design the Jalali calendar, and analysed Euclid's parallel postulate.

algebra, geometry, astronomy

Persian scholar who devised the Tusi couple and equant-free planetary models, made trigonometry an independent discipline, and directed the Maragha observatory.

astronomy, trigonometry, geometry

Self-taught Venetian abacus master who independently found the solution of the cubic in 1535, founded mathematical ballistics, and made the first translation of Euclid's Elements into a modern European language.

algebra, ballistics, mechanics

French lawyer and royal councillor who introduced letters for known quantities, founding symbolic algebra and the theory of equations.

algebra, theory of equations, trigonometry

Jesuate friar and Bologna professor whose method of indivisibles, with Cavalieri's principle and the quadrature of the higher parabolas, prepared the integral calculus.

geometry, method of indivisibles, logarithms and trigonometry

Holder of the Ramus chair at the Collège Royal who squared the cycloid, drew tangents by composing motions, integrated powers and the sine, and invented the Roberval balance.

geometry, method of indivisibles, kinematic geometry

Galileo's successor at the Medici court who invented the mercury barometer, found the law of efflux, and showed that an infinitely long solid can have finite volume.

geometry, mechanics, hydrodynamics

Dutch mathematician and physicist who invented the pendulum clock, discovered Titan and the ring of Saturn, founded probability theory in print and proposed the wave theory of light.

mechanics, optics, astronomy

First Lucasian Professor of Mathematics at Cambridge, whose geometric lectures proved that tangent and area problems are inverse to each other.

geometry, calculus, optics

English mathematician and astronomer who rectified the cycloid, stated the law of elastic collision and proved the hyperboloid ruled, then became the architect of St Paul's Cathedral and of London rebuilt after the Great Fire.

geometry, astronomy, mechanics

Jesuit mathematician and logician whose Euclides ab omni naevo vindicatus (1733), meant to prove the parallel postulate, derived the first systematic theorems of hyperbolic geometry.

geometry, foundations of geometry, logic

Scottish Newtonian whose Treatise of Fluxions gave a rigorous calculus, the integral test and the Euler–Maclaurin formula, and who found the equilibrium figures of rotating fluid bodies.

calculus, analysis, geometry

Self-taught polymath of the Berlin Academy who proved π irrational, founded photometry, introduced the Lambert map projections and developed the acute-angle hypothesis of the parallel problem.

number theory, geometry, cartography

French analyst who introduced Legendre polynomials, the Legendre transformation and symbol, stated quadratic reciprocity, first published least squares, and founded the theory of elliptic integrals.

number theory, elliptic integrals, calculus of variations

Engineer, geometer and revolutionary statesman who founded the theory of machines, proved the law of energy loss in inelastic shocks, and organized the armies of the French Republic.

mechanics, geometry, foundations of calculus

Kazan mathematician who published the first non-Euclidean (hyperbolic) geometry in 1829 and was rector of Kazan University for nineteen years.

geometry, non-euclidean geometry, analysis

Hungarian army engineer who independently discovered hyperbolic geometry and published it in 1832 as the Appendix to his father's Tentamen, together with an absolute geometry valid with or without the parallel postulate.

geometry, non-euclidean geometry, foundations of mathematics

Stettin schoolteacher whose Ausdehnungslehre founded linear algebra and the exterior product, and whose work on Sanskrit gave linguistics Grassmann's law.

linear algebra, exterior algebra, geometry

Founder of the theory of continuous transformation groups, now Lie groups and Lie algebras, developed to integrate differential equations by their symmetries.

transformation groups, differential equations, geometry

Geometer who defined geometry through transformation groups in the Erlangen Program, pioneered automorphic functions, and made Göttingen the world centre of mathematics.

geometry, group theory, complex analysis

Radiochemist who with Rutherford explained radioactivity as atomic transmutation, formulated the displacement law and the concept of isotopes, and later wrote on monetary economics and the geometry of tangent circles.

radiochemistry, physical chemistry, economics

Geometer who founded topological K-theory, proved the index theorem with Isadore Singer, and joined geometry to gauge theory and quantum field theory.

geometry, topology, k-theory