1,733 articles
Catalan numbers
The Catalan numbers are the integer sequence beginning 1, 1, 2, 5, 14, 42, counted by Euler in 1751, that enumerates balanced parentheses, binary trees, and polygon triangulations.
Catastrophic cancellation
Catastrophic cancellation is the loss of significant digits that occurs when two nearly equal numbers are subtracted, inherent to approximations rather than floating point itself, and fixed by algebraic rewriting.
Category (mathematics)
In mathematics, a category is a structure consisting of objects together with morphisms between them, with identity morphisms and associative composition, introduced by Eilenberg and Mac Lane in 1945.
Category theory
Category theory is a branch of abstract algebra that studies mathematical structures through morphisms between objects. Eilenberg and Mac Lane introduced it in the 1940s.
Cauchy matrix
A Cauchy matrix is a matrix with entries 1/(a_i − b_j) for two distinct node sets, named for Augustin-Louis Cauchy, who computed its determinant in 1841.
Cavalieri's principle
Cavalieri's principle, also called the method of indivisibles, is a geometric rule stating that two solids of the same height with equal cross-sectional areas at every level have equal volumes.
Cayley graph
A Cayley graph, also called a Cayley diagram, is a graph built from a group and a generating set. Arthur Cayley introduced it in 1878 to represent abstract groups graphically.
Cayley–Dickson construction
The Cayley–Dickson construction is a method in algebra that doubles an algebra's dimension; applied to the real numbers, it yields the complex numbers, quaternions, octonions, and sedenions in turn.
Cayley–Hamilton theorem
The Cayley–Hamilton theorem, or Cayley-Hamilton, is a linear algebra result stating every square matrix satisfies its own characteristic equation; Cayley proved the 2 × 2 case in 1858.
Center (group theory)
The center of a group, also called the group center, is the subgroup Z(G) of elements commuting with every element, and it is normal and characteristic.
Central carrier
The central carrier, also called central support or central cover, is the smallest projection in the center of a von Neumann algebra that dominates a given projection or operator.
Champernowne constant
The Champernowne constant, formed by writing the positive integers in order as 0.123456789101112..., is normal in base 10, proved by David Champernowne in 1933.
Change of basis
Change of basis, also called a coordinate change, converts vector coordinates and matrices of linear maps between bases of a vector space using an invertible matrix.
Change of rings
Change of rings is a body of results in homological algebra comparing module invariants such as projective dimension, Tor, and Ext before and after a base ring is changed.
Character theory
Character theory studies finite groups through characters, trace functions attached to representations. Created by Georg Frobenius in 1896, it remains a standard tool in group theory, physics, and chemistry.
Characteristic (algebra)
In algebra, the characteristic of a ring, also called the field characteristic for fields, is the smallest n > 1 with n·1 = 0, or 0 otherwise.
Characteristic polynomial
The characteristic polynomial of a square matrix is the determinant of the matrix minus a scalar variable λ, and its roots are the matrix's eigenvalues.
Characteristic set
A characteristic set is a minimal triangular system of polynomials for a polynomial or differential ideal, introduced by Ritt in 1932 and reshaped by Wu Wen-tsün in the late 1970s.
Chebyshev function
The Chebyshev functions are two number-theory functions, θ(x) and ψ(x), that weigh primes and prime powers by the logarithm of the prime; ψ(x) ~ x is equivalent to the prime number theorem.
Chebyshev polynomials
Chebyshev polynomials, also called Tchebycheff polynomials, are orthogonal polynomials on −1 to 1 introduced by Pafnuty Chebyshev in 1854, used in approximation, spectral methods, and quantum algorithms.
Chern class
Chern classes are characteristic classes assigned to complex vector bundles, cohomology classes introduced by Shiing-Shen Chern in 1946 that measure how a bundle is globally twisted.
Chevalley group
A Chevalley group is a finite or algebraic group built from a complex semisimple Lie algebra and a field, introduced by Claude Chevalley in 1955.
Chinese remainder theorem
The Chinese remainder theorem, or Sunzi's theorem, is a number theory result stating that congruences with pairwise coprime moduli always have a solution, unique modulo their product.
Chiral algebra
A chiral algebra is an algebraic structure introduced by Alexander Beilinson and Vladimir Drinfeld to formulate the chiral part of two-dimensional conformal field theory, published as Chiral Algebras in 2004.
Cholesky decomposition
The Cholesky decomposition, also called Cholesky factorization, uniquely expresses a symmetric positive definite matrix as A = R^T R and is used to solve linear systems stably.
Chow group
The Chow group of an algebraic variety, written CH k(X), is the group of algebraic cycles modulo rational equivalence, the algebraic geometer's analog of a homology group.
Chow group of a stack
The Chow group of an algebraic stack assigns to the stack its algebraic cycles modulo rational equivalence, generalizing Chow groups of schemes; the standard definitions are due to Vistoli, Edidin and Graham, Totaro, and Kresch.
Christian Goldbach
Christian Goldbach (1690–1764) was a Prussian jurist and amateur mathematician, secretary of the St Petersburg Academy of Sciences, best known for the Goldbach conjecture posed to Euler in 1742.
Chronology of computation of π
The chronology of computation of π traces record-setting calculations of the circle's ratio, from Babylonian approximations through Archimedes and Madhava to 314 trillion digits computed in 2025.
Cichoń's diagram
Cichoń's diagram, named after the Polish mathematician Jacek Cichoń, is a diagram in set theory displaying the ZFC-provable inequalities among ten cardinal characteristics of the continuum.