Mathematics and statistics

Gompertz function

The Gompertz function is an asymmetric sigmoid growth model used for tumor, microbial, and animal growth curves, proposed in 1825 as a law of human mortality.

Goodness of fit is a statistical measure and test of how well a hypothesized probability distribution or fitted model is consistent with observed data, using tests such as Pearson's chi-square, Kolmogorov-Smirnov, and Anderson-Darling.

Goodstein's theorem

Goodstein's theorem is a statement in number theory, proved by Reuben Goodstein in 1944, that every Goodstein sequence eventually reaches 0 but cannot be proved in Peano Arithmetic.

Googol

A googol, ten duotrigintillion, is the number 10 to the 100th power, named in 1938 by nine-year-old Milton Sirotta, whose uncle Edward Kasner popularized it.

Gorenstein ring

A Gorenstein ring, named after Daniel Gorenstein, is a commutative Noetherian local ring of finite injective dimension over itself; every Gorenstein ring is Cohen–Macaulay and is its own canonical module.

Gosset polytope

A Gosset polytope is one of a family of semiregular polytopes in six, seven, and eight dimensions discovered by Thorold Gosset in 1900, the most famous being the eight-dimensional 421 polytope.

Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz (1646–1716) was a German philosopher and mathematician who invented calculus independently of Newton and built one of the first calculators able to multiply and divide.

Gowers norm

The Gowers norm, or Gowers uniformity norm, is a measure of how far a function on a finite group deviates from a low-degree polynomial phase, introduced by Timothy Gowers in 1998.

Graceful labeling

A graceful labeling assigns graph vertices distinct integers from 0 to q so that the edge differences are also distinct; whether every tree has one is open.

Graded ring

A graded ring is a ring decomposed as a direct sum of pieces indexed by nonnegative integers, where multiplying elements of degrees i and j gives degree i + j.

Graded vector space

A graded vector space, also called a graded linear space, is a vector space decomposed as a direct sum of subspaces indexed by degree, often integers.

Gradient

The gradient, also called the gradient vector, is a vector calculus operator that collects a scalar function's partial derivatives and points in the direction of fastest increase.

Gradual typing

Gradual typing is a programming language design approach where parts of a program are statically type checked and others dynamically, introduced by Jeremy Siek and Walid Taha in 2006.

Graeco-Latin square

A Graeco-Latin square, also called an Euler square, is an n × n array formed by superimposing two orthogonal Latin squares, named by Euler in 1782.

Graham's number

Graham's number is an enormous integer, built from Knuth's up-arrow notation, that arose as a Ramsey theory upper bound and was popularized by Martin Gardner in 1977.

Gram matrix

The Gram matrix is a square matrix whose entries are the pairwise inner products of a set of vectors, encoding lengths, angles, and linear dependence; it is always positive semidefinite.

Granger causality

Granger causality is a statistical test, proposed by Clive Granger in 1969, where one time series causes another if its past values improve prediction of it.

Graph (discrete mathematics)

A graph in discrete mathematics is a structure of vertices joined by edges that models relationships; its study, graph theory, dates to Euler's 1736 Königsberg analysis.

Graph Cartesian product

The graph Cartesian product, denoted G square H and also called the box product, is a binary operation on graphs whose vertices are ordered pairs, adjacent when they differ in exactly one coordinate.

Graph drawing

Graph drawing, also called graph layout, is the branch of computer science that positions graph vertices and routes edges to render networks as readable diagrams.

Graph embedding

A graph embedding is a placement of a graph on a surface with vertices as points and edges as noncrossing curves, the central object of topological graph theory.

Graph Fourier transform

The graph Fourier transform decomposes a signal defined on a graph's vertices into components carried by the eigenvectors of the graph Laplacian, like the classical Fourier transform.

Graph invariant

A graph invariant, also called a graph property, is a quantity of a graph that depends only on its structure, not on vertex labels or how it is drawn.

Graph isomorphism

Graph isomorphism, also called testing isomorphic graphs, asks whether two graphs have the same structure up to renaming vertices; László Babai's 2015 quasipolynomial algorithm was a major breakthrough.

Graph isomorphism problem

The graph isomorphism problem asks whether two graphs can be relabeled to be identical. It lies in NP, and László Babai gave a quasipolynomial-time algorithm in 2015.

Graph minor

A graph minor is a graph derived from another by deleting or contracting edges and removing isolated vertices; Robertson and Seymour developed the theory of it.

Graph of a function

The graph of a function, also called a function graph, is the set of all ordered pairs relating each input to its output, plotted as points in the plane.

Graph partitioning

Graph partitioning divides a graph's vertices into roughly equal blocks while minimizing the edges crossing between blocks, an NP-hard problem used in parallel computing and VLSI design.

Graph reduction

Graph reduction is an implementation technique for functional programming languages in which a program is a graph rewritten in place during evaluation, introduced by Christopher Wadsworth in 1971.