45 lives in this collection worked in number theory, from 325 BC to today. Each has a full course on their life and the mathematics and physics they made.
Often together with: algebra, analysis, astronomy, algebraic geometry, differential geometry, geometry, mathematical physics, representation theory, calculus of variations, group theory. All fields
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
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
Alexandrian author of the Arithmetica, whose rational solutions of indeterminate equations founded algebraic notation and Diophantine analysis.
arithmetic, algebra, number theory
Author of the Aryabhatiya (499), the earliest surviving Indian mathematical-astronomical treatise by a named author, with a sine table, the kuttaka method, pi as 3.1416 and a rotating Earth.
astronomy, mathematics, trigonometry
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
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
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
Minim friar who established the laws of the vibrating string, gave his name to the primes 2^p − 1, and ran the correspondence network at the centre of European science in the 1630s and 1640s.
acoustics, music theory, number theory
Toulouse magistrate whose letters founded modern number theory, co-founded analytic geometry and probability, anticipated differential calculus and introduced the principle of least time.
number theory, analytic geometry, calculus
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
The most prolific mathematician in history, who shaped modern analysis and notation, founded graph theory, and wrote the equations of rigid bodies and ideal fluids.
analysis, number theory, graph theory
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
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
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
Self-taught French mathematician who proved the main nineteenth-century result on Fermat's Last Theorem before Kummer and won the Paris Academy prize for a theory of vibrating elastic plates.
number theory, elasticity, differential geometry
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
Leipzig astronomer and geometer who introduced barycentric and homogeneous coordinates, the Möbius function and Möbius transformations, and described the one-sided Möbius band.
projective geometry, astronomy, topology
Prussian mathematician who founded the theory of elliptic and theta functions with Abel, created Hamilton–Jacobi mechanics, and introduced the Jacobian, the Jacobi identity and the Jacobi symbol.
elliptic functions, analytical mechanics, number theory
Founder of analytic number theory, who proved the theorem on primes in arithmetic progressions and gave the first rigorous convergence theorem for Fourier series.
number theory, analysis, fourier series
French analyst who founded the Journal de Mathématiques Pures et Appliquées, published Galois's work, constructed the first transcendental numbers and gave his name to theorems on eigenvalue problems, phase-space volume, elementary integrals and conformal maps.
analysis, differential equations, mathematical physics
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
Founder of the St Petersburg school who proved Bertrand's postulate, created minimax approximation and Chebyshev polynomials, and gave the general law of large numbers.
number theory, approximation theory, probability 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
Berlin algebraist who created the character theory of finite groups and left his name on results across linear algebra, differential equations and number theory.
group theory, representation theory, linear algebra
St Petersburg mathematician who created the theory of Markov chains and contributed to number theory, the moment problem, polynomial inequalities and the limit theorems of probability.
probability theory, number theory, approximation theory
Founder of the analytic theory of continued fractions who posed and solved the moment problem and introduced the Stieltjes integral.
analysis, continued fractions, moment problem
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
Creator of the geometry of numbers and of the four-dimensional spacetime formulation of special relativity.
number theory, geometry of numbers, convex geometry
Berlin algebraist who founded much of the representation theory of finite groups and of GL(n), and whose name is attached to results across algebra, combinatorics and analysis.
representation theory, group theory, linear algebra
Leader of the Warsaw school of mathematics, pioneer of set theory and the continuum hypothesis, and creator of the Sierpiński triangle, carpet and numbers.
set theory, number theory, topology
Universal mathematician who founded gauge theory and the representation theory of compact Lie groups, and proved the Weyl law and the equidistribution theorem.
analysis, lie groups and representation theory, differential geometry
Number theorist who proved the functional equation of Dedekind zeta functions, introduced Grössencharaktere and their L-functions, and created the theory of Hecke operators linking modular forms to Euler products.
number theory, modular forms, l-functions
Number theorist whose theorems on Diophantine equations, class numbers, quadratic forms, modular forms of several variables and small divisors each founded a field.
number theory, diophantine approximation, transcendence theory
Founder of Bourbaki who proved the Riemann hypothesis for curves over finite fields and formulated the Weil conjectures.
number theory, algebraic geometry, arithmetic geometry
Itinerant Hungarian mathematician, author of some 1,500 papers with over 500 co-authors, who founded the probabilistic method and the theory of random graphs.
number theory, combinatorics, graph 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
French mathematician who transformed algebraic topology, algebraic geometry and number theory, youngest Fields medallist and first Abel laureate.
algebraic topology, algebraic geometry, number theory
Rebuilt algebraic geometry on the theory of schemes, sheaves and topoi, creating the tools behind the proof of the Weil conjectures and much of modern number theory.
algebraic geometry, homological algebra, functional analysis
Founder of the Langlands programme, which conjectures deep correspondences between Galois representations and automorphic forms through the principle of functoriality.
number theory, automorphic forms, representation theory
Belgian mathematician who proved the Riemann hypothesis over finite fields and created the theory of weights, mixed Hodge structures and Deligne–Mumford stacks.
algebraic geometry, number theory, hodge theory
Proved superrigidity and arithmeticity of higher-rank lattices, built the first explicit expanders, and solved the Oppenheim conjecture by founding homogeneous dynamics.
lie groups, ergodic theory, homogeneous dynamics
Number theorist who proved Fermat's Last Theorem by establishing the modularity of semistable elliptic curves.
number theory, arithmetic geometry, iwasawa theory
Proved the Langlands correspondence for GL(2) over function fields with Drinfeld modules and shtukas, and created quantum groups, associators and, with Beilinson, the geometric Langlands framework of opers and chiral algebras.
number theory, algebraic geometry, representation theory
Mathematician who used rigidity in dynamics to solve counting problems in number theory, geometric group theory and the moduli space of flat surfaces, including the magic wand theorem with Maryam Mirzakhani.
dynamical systems, homogeneous dynamics, teichmüller dynamics