Algebra

Alexandrian author of the Arithmetica, whose rational solutions of indeterminate equations founded algebraic notation and Diophantine analysis.

arithmetic, algebra, number theory

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

Baghdad scholar whose book on al-jabr founded algebra as the systematic solution of equations, whose arithmetic carried Indian decimal numerals and his name (algorithm) to Europe, and who compiled the Zij al-Sindhind and a coordinate geography of the world.

algebra, arithmetic, astronomy

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

Pisan merchant mathematician whose Liber abaci taught Europe the Hindu-Arabic numerals and Arabic algebra, and whose Book of Squares is the outstanding medieval European work of number theory.

arithmetic, algebra, number theory

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

Renaissance physician and polymath whose Ars Magna published the solutions of the cubic and quartic and the first computations with square roots of negative numbers, and who wrote the first book on the mathematics of chance.

algebra, probability theory, medicine

Bolognese engineer whose L'Algebra (1572) gave the first rules for calculating with complex numbers, resolved the irreducible case of the cubic, and introduced Diophantus's problems to Western readers.

algebra, complex numbers, number theory

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

algebra, theory of equations, trigonometry

Flemish engineer who popularized decimal fractions and founded modern statics and hydrostatics.

arithmetic, algebra, statics

Philosopher and mathematician who joined algebra to geometry, published the sine law of refraction and the theory of the rainbow, and built a mechanical physics of inertia and vortices.

analytic geometry, algebra, optics

Savilian Professor of Geometry at Oxford whose Arithmetica infinitorum extended quadrature to fractional powers, gave the infinite product for π and led Newton to the binomial series.

analysis, infinitesimal methods, number theory

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

Founder of analytical mechanics and the calculus of variations, discoverer of the Lagrange points, and author of the four-square theorem and the resolvent method that led to group theory.

calculus of variations, analytical mechanics, celestial mechanics

Founder of modern number theory and the intrinsic geometry of surfaces, and author of least squares, the normal law and Gauss's law.

number theory, algebra, differential geometry

Founder of rigorous analysis and complex function theory, and creator of the stress tensor and the theory of linear elasticity.

analysis, complex analysis, differential equations

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

Proved the general quintic unsolvable by radicals, founded the theory of elliptic and abelian functions, and gave his name to commutative groups.

algebra, analysis, elliptic functions

Irish mathematician who unified optics and mechanics through a single characteristic function, created Hamiltonian mechanics, and discovered the quaternions.

optics, classical mechanics, algebra

Mathematician and logician who formulated De Morgan's laws, named mathematical induction, founded the logic of relations and was first president of the London Mathematical Society.

logic, algebra, analysis

Founder of Galois theory, who linked the solvability of equations by radicals to the structure of their symmetry groups and introduced finite fields.

algebra, group theory, theory of equations

Prolific Victorian algebraist who founded matrix algebra, gave the first abstract definition of a group, and built classical invariant theory.

algebra, invariant theory, group theory

French analyst and number theorist who proved the transcendence of e, solved the quintic with modular functions, and introduced Hermitian forms.

number theory, elliptic functions, invariant theory

Berlin number theorist who stated the Kronecker–Weber theorem, dreamed of class field theory through complex multiplication, and argued that all mathematics should be built from the integers.

number theory, algebra, elliptic functions

The king of invariant theory, who proved constructively that the covariants of binary forms are finitely generated.

invariant theory, algebra, algebraic geometry

Teacher of Hilbert and Minkowski, whose name is attached to the Hurwitz zeta function, the Riemann–Hurwitz formula, the Routh–Hurwitz stability criterion and the 1, 2, 4, 8 theorem on composition algebras.

number theory, complex analysis, riemann surfaces

Algebraist who introduced the Brauer group, founded modular representation theory and set the strategy that led to the classification of finite simple groups.

representation theory, finite group theory, algebra

Polish-American logician who gave the semantic definition of truth, proved the decidability of real closed fields and elementary geometry, co-discovered the Banach–Tarski paradox, and founded the Berkeley school of model theory.

mathematical logic, model theory, set theory

Founder of Teichmüller theory through quasiconformal mappings and quadratic differentials, author of key ideas in valuation theory and Galois cohomology, and an active Nazi who led the 1933 boycott of Edmund Landau.

complex analysis, riemann surfaces, quasiconformal mappings