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Class formation
A class formation is a cohomological datum, introduced by Emil Artin and John Tate, from which the main theorems of class field theory can be derived abstractly.
Class number
The class number h_K of a number field K is the order of its ideal class group, and h_K = 1 exactly when K has unique factorization.
Class number formula
The class number formula expresses the residue at s = 1 of a number field's Dedekind zeta function through its class number, regulator, discriminant, and roots of unity.
Class number problem
The class number problem, or class number conjecture, asks which imaginary quadratic fields have each class number; posed by Gauss in 1801 and settled for N = 100.
Classical cipher
A classical cipher is an encryption method used before the mid-twentieth century, mostly based on substitution (replacing symbols) or transposition (rearranging them), like the Caesar and Vigenère ciphers.
Classical Wiener space
The classical Wiener space is the probability space of continuous paths on [0,1] starting at 0, equipped with Wiener measure, under which the coordinate process is Brownian motion.
Classification and regression tree
Classification and regression trees (CART) is a decision-tree method that predicts outcomes by recursively splitting data, using the Gini index for classification and squared residuals for regression.
Classification of finite simple groups
The classification of finite simple groups (CFSG) is a theorem listing every finite simple group as cyclic, alternating, of Lie type, or one of 26 sporadic groups.
Classification of Kac–Moody algebras
The classification of Kac–Moody algebras divides their generalized Cartan matrices into finite, affine, and indefinite types; finite recovers the nine classical semisimple families, and hyperbolic matrices are too numerous to classify.
Classification of states in Markov chains
Classification of states in Markov chains sorts states into communicating classes, recurrence types, and periods, determining whether returns are certain and how long they take.
Classifying space
A classifying space BG for a topological group G carries a universal principal G-bundle, so bundles over X correspond to homotopy classes of maps X → BG.
Clay Mathematics Institute
The Clay Mathematics Institute, founded in 1998 by Landon T. Clay, is a private foundation in Cambridge, Massachusetts, best known for its seven $1 million Millennium Prize Problems.
Cleo (mathematician)
Cleo was a pseudonymous Mathematics Stack Exchange user who posted 39 unproven answers to hard integrals from 2013 to 2015, identified in 2025 as Vladimir Reshetnikov.
Clifford algebra
A Clifford algebra is an associative algebra in which vectors square to scalars given by a quadratic form, generalizing complex numbers and quaternions and underlying spinors.
Clifford analysis
Clifford analysis is the branch of mathematics that studies functions taking values in a Clifford algebra, centered on monogenic functions, the null solutions of a generalized Cauchy–Riemann operator.
Clinical endpoint
A clinical endpoint, also called a study endpoint or clinical outcome, is a measured outcome in a clinical trial that directly reflects how a patient feels, functions, or survives.
Clique (graph theory)
A clique in graph theory is a set of vertices in a graph where every pair is adjacent, forming a complete subgraph; the largest size is the clique number.
Clique problem
The clique problem asks for a clique, a subset of graph vertices in which every pair is connected; its decision version is among Karp's original 21 NP-complete problems.
Clique-width
Clique-width is a graph parameter, introduced by Bruno Courcelle and Stephan Olariu in 2000, measuring the minimum number of labels needed to construct a graph from single vertices.
Clock (model checking)
In model checking, a clock is a real-valued variable that advances with time and can be reset to zero, turning a finite automaton into a timed automaton.
Close-packing of equal spheres
Close-packing of equal spheres is the arrangement of identical spheres in which each touches the most neighbors, filling about 74% of space; Thomas C. Hales proved this in 1998.
Closed geodesic
A closed geodesic is a locally shortest path on a Riemannian manifold that returns to its starting point with its starting direction, repeating periodically; its smallest period is its length.
Closed monoidal category
A closed monoidal category, also called a monoidal closed category, is a monoidal category in which tensoring with any fixed object has a right adjoint, yielding an internal hom object.
Closed set
A closed set, or closed subset, contains all its limit points; equivalently, its complement is open. It is one of two primitive dual notions, with openness, underlying topology.
Closed-form expression
A closed-form expression, also called an analytical solution, evaluates a quantity using a finite number of standard operations such as roots, exponentials, and logarithms, without limits or infinite sums.
Closest vector problem
The closest vector problem (CVP) asks, given a basis for a lattice and a target vector, for the closest lattice vector; it is NP-hard and underpins lattice-based cryptography.
Closure (mathematics)
Closure in mathematics is the property that applying an operation to elements of a set produces results that stay within that set; examples include topological and transitive closure.
Closure operator
A closure operator is a function c on subsets of a set that is extensive, monotone, and idempotent, so c(X) is the smallest closed set containing X.
Cluster algebra
Cluster algebra is a commutative algebra whose generators, called cluster variables, are produced from an initial seed by iterative mutation, created by Fomin and Zelevinsky in 2000.
Cluster graph
A cluster graph is an undirected graph in which every connected component is a complete graph, equivalently a vertex-disjoint union of cliques used in data clustering.