Mathematics and statistics

Kähler manifold

A Kähler manifold is a complex manifold carrying compatible complex, symplectic, and Riemannian structures, central to differential geometry and algebraic geometry since Erich Kähler introduced it in 1933.

Kahn–Kalai conjecture

The Kahn–Kalai conjecture, posed by Jeff Kahn and Gil Kalai in 2006, held that thresholds stay within a logarithmic factor of the expectation threshold; Park and Pham proved it in 2022.

Kahn's conjecture

Kahn's conjecture is a name for several combinatorics conjectures associated with Rutgers mathematician Jeff Kahn, including the Kahn–Kalai conjecture on thresholds in random structures, proved in 2022.

Kaiser-Meyer-Olkin measure of sampling adequacy

The Kaiser-Meyer-Olkin measure of sampling adequacy is a statistic, proposed by Henry Kaiser in 1970, that indicates how suitable a set of variables is for factor analysis.

Kakeya conjecture

The Kakeya conjecture is a mathematical conjecture stating that sets containing a line segment in every direction have full dimension, proved in the plane and in 3D in 2025.

Kakeya problem over finite fields

The Kakeya problem over finite fields asks how small a set containing a line in every direction must be; Zeev Dvir proved in 2008 it must have size on the order of q^n.

Kalman filter

The Kalman filter is a recursive algorithm that estimates a system's hidden state by combining a motion model with noisy measurements, introduced by Rudolf E. Kalman in 1960.

Kan extension

A Kan extension is a category theory construction that extends a functor along another functor in a universal way, introduced by Daniel Kan in 1958.

Kano model

The Kano model, also called Kano analysis, is a quality management framework classifying product attributes into five categories by how they affect customer satisfaction, introduced in 1984.

Kaplan–Meier estimator

The Kaplan–Meier estimator, also called the product-limit estimator, is a nonparametric statistic that estimates survival functions from incomplete time-to-event data. Kaplan and Meier published it in 1958.

Kaplan–Yorke conjecture

The Kaplan–Yorke conjecture, proposed by Kaplan and Yorke in 1979, states that for typical chaotic attractors the information dimension equals the Lyapunov dimension, linking dynamics to attractor geometry.

Kaprekar number

A Kaprekar number is a positive integer whose square can be split into two parts that add up to the original number, such as 45.

Karnaugh map

A Karnaugh map (K-map) is a grid-based method for simplifying Boolean algebra expressions, invented by Maurice Karnaugh at Bell Labs in 1953 for telephone switching circuits.

Kazhdan's property (T)

Kazhdan's property (T) is a rigidity property of groups introduced by David Kazhdan in 1967, stating that almost-invariant vectors in unitary representations are close to fixed ones.

Keller–Segel model

The Keller–Segel model is a system of partial differential equations for chemotaxis, introduced by Evelyn Keller and Lee Segel in 1970, predicting whether cells spread diffusively or aggregate.

Kempe's universality theorem

Kempe's universality theorem, announced by Alfred Bray Kempe in the 1870s, states that any plane algebraic curve can be traced exactly by a planar linkage.

Kempner function

The Kempner function, also called the Smarandache function, gives the smallest positive integer m such that n divides m!; it was introduced by Aubrey J. Kempner in 1918.

Kendall rank correlation coefficient

The Kendall rank correlation coefficient, known as Kendall's tau, is a statistic from −1 to +1 measuring the agreement between rankings of two variables, defined by Maurice Kendall in 1938.

Kendall's W

Kendall's W is a nonparametric coefficient of concordance measuring agreement among multiple raters who rank the same items, ranging from 0 (no agreement) to 1 (complete agreement).

Kepler conjecture

The Kepler conjecture, now a theorem, states that no packing of equal spheres in space exceeds the density of about 74.05% achieved by stacking oranges in the usual pyramid way.

Kepler–Poinsot polyhedron

A Kepler–Poinsot polyhedron, also called a Kepler–Poinsot solid, is one of the four regular star polyhedra, non-convex counterparts of the Platonic solids, named for Kepler and Poinsot.

Kernel (algebra)

The kernel (also called the kernel of a homomorphism) in algebra is the set of elements a homomorphism sends to zero, a submodule measuring injectivity.

Kernel (linear algebra)

The kernel of a linear map, also called its null space, is the set of all domain vectors the map sends to zero; it is a linear subspace of the domain.

Kernel (statistics)

In statistics, a kernel is a weighting function used to build nonparametric estimates from data, introduced for density estimation by Rosenblatt in 1956; the word also names Markov transition kernels.

Kernel association test

A kernel association test is a set-based statistical test in genetics that regresses a trait on many variants in a genomic region at once; SKAT is the best known.

Kernel density estimation

Kernel density estimation, or Parzen windowing, is a nonparametric statistical method for estimating the probability density function of a distribution from data by placing a smooth kernel around each observed point.

Kernel principal component analysis

Kernel principal component analysis (kernel PCA) is a nonlinear dimensionality reduction method that performs PCA in a high-dimensional kernel-defined feature space, introduced by Schölkopf, Smola, and Müller in 1998.

Kernel regression

Kernel regression is a nonparametric method for estimating a regression function from data without a fixed parametric form, using weighted averages such as the Nadaraya–Watson estimator.

Khatri-Rao product

The Khatri-Rao product, or column-wise Kronecker product, is a matrix product that applies the Kronecker product column by column, introduced by Khatri and Rao in 1968.