Mathematics and statistics

Kolmogorov–Sinai entropy

Kolmogorov–Sinai entropy, also called metric entropy or measure-theoretic entropy, measures the average rate at which a dynamical system creates information, introduced by Kolmogorov in 1958 and extended by Sinai in 1959.

Kolmogorov–Smirnov test

The Kolmogorov–Smirnov test, or K–S test, is a nonparametric statistical test comparing probability distributions via the largest gap between cumulative distribution functions, proposed by Kolmogorov and Smirnov in the 1930s.

Kolmogorov's inequality

Kolmogorov's inequality, also called Kolmogorov's maximal inequality, is a probability result bounding the chance that any partial sum of independent, zero-mean, finite-variance random variables exceeds a threshold, key to the strong law of large numbers.

Kolmogorov's three-series theorem

Kolmogorov's three-series theorem, also called the three series theorem, gives necessary and sufficient conditions for almost sure convergence of a series of independent random variables.

Kolmogorov's zero–one law

Kolmogorov's zero–one law, also called Kolmogorov's 0-1 law, is a probability theorem stating every tail event of independent random variables has probability 0 or 1.

Kőnig's theorem (graph theory)

Kőnig's theorem, also called the König–Egerváry theorem, states that in every bipartite graph the maximum matching size equals the minimum vertex cover size, first proved by Dénes Kőnig in 1931.

König's theorem (set theory)

König's theorem is a result in cardinal arithmetic stating that if κᵢ < λᵢ for all i, then the sum of the κᵢ is strictly less than the product of the λᵢ.

Korteweg–de Vries equation

The Korteweg–de Vries equation, or KdV equation, is a nonlinear partial differential equation, derived in 1895, that models long waves such as shallow water waves and supports solitons.

Kosambi–Karhunen–Loève theorem

The Kosambi–Karhunen–Loève theorem, or Karhunen–Loève theorem, represents a square-integrable stochastic process as orthogonal functions weighted by uncorrelated coefficients; developed in the 1940s, its discrete form is equivalent to principal component analysis.

Kosaraju's algorithm

Kosaraju's algorithm, also known as the Kosaraju-Sharir algorithm, is a two-pass method that finds the strongly connected components of a directed graph in O(V+E) time, devised by S. Rao Kosaraju around 1978.

Kostant partition function

The Kostant partition function is a representation theory function counting the ways a weight can be written as a sum of positive roots, introduced by Bertram Kostant in 1958.

Koszul complex

The Koszul complex is a chain complex built from the exterior algebra of a free module over a commutative ring, introduced by Jean-Louis Koszul in 1950 to detect regular sequences.

Kriging

Kriging is a family of geostatistical interpolation techniques that predicts values at unsampled locations as weighted averages of nearby observations, named after mining engineer Danie G. Krige.

Kripke semantics

Kripke semantics, also known as relational semantics, is the standard formal semantics for modal logic, in which formulas are evaluated at possible worlds, introduced by Saul Kripke in 1959.

Kripke–Platek set theory

Kripke–Platek set theory (KP) is a weak axiomatic set theory introduced independently by Saul Kripke and Richard Platek in the 1960s; its transitive models are called admissible sets.

Kronecker delta

The Kronecker delta, written δij, is a mathematical symbol that equals 1 when its two indices are equal and 0 otherwise, serving as the index-notation form of the identity matrix.

Kronecker product

The Kronecker product, also called the tensor product of matrices, replaces each entry of a matrix A with A's entry times matrix B, yielding a block matrix.

Kronecker–Weber theorem

The Kronecker–Weber theorem, sometimes called the Kronecker–Weber–Hilbert theorem, states that every finite abelian extension of the rationals lies inside a cyclotomic field, an early result of class field theory proved by Hilbert in 1896.

Krull dimension

The Krull dimension of a commutative ring is the supremum of the lengths of chains of prime ideals, defined by Wolfgang Krull in 1928 as the standard notion of dimension in commutative algebra.

Kruskal–Wallis test

The Kruskal–Wallis test is a nonparametric statistical test that decides whether three or more independent groups come from the same distribution by comparing pooled rank sums, introduced in 1952.

Kruskal's algorithm

Kruskal's algorithm is a greedy algorithm that finds a minimum spanning tree of any connected, weighted, undirected graph, published by Joseph B. Kruskal in 1956.

Kruskal's tree theorem

Kruskal's tree theorem is a 1960 result in well-quasi-order theory, proved by J. B. Kruskal, stating that finite trees over a well-quasi-ordered label set are well-quasi-ordered under homeomorphic embedding.

Krylov subspace

A Krylov subspace is the vector space spanned by b, Ab, A²b, and so on for a matrix A, named for Aleksey Krylov in 1931.

Krylov subspace methods

Krylov subspace methods are iterative projection methods for large linear systems, eigenvalue problems, and matrix functions, building approximations from repeated matrix-vector products; examples include CG, GMRES, and BiCGSTAB.

Kudryashov method

The Kudryashov method is an analytic technique for finding exact closed-form solutions of nonlinear differential equations, introduced by N.A. Kudryashov in 1990 for the Kuramoto–Sivashinsky equation.

Kullback–Leibler divergence

The Kullback–Leibler divergence, or KL divergence, is an asymmetric measure of how different one probability distribution is from another, introduced by Kullback and Leibler in 1951 and equal to zero only when the distributions coincide.

Kummer theory

Kummer theory, created by Ernst Eduard Kummer, classifies cyclic extensions of a field obtained by adjoining nth roots of elements, assuming the field contains roots of unity.

Oct 22, 2026

Kung's conjecture

Kung's conjecture is a theorem in extremal matroid theory stating that simple matroids over a finite field grow linearly, proved by Geelen and Whittle in 2003.

Kuramoto model

The Kuramoto model, introduced by Yoshiki Kuramoto in 1975, is a mathematical model of synchronization in which coupled phase oscillators entrain into collective oscillation above a critical coupling strength.