6,052 articles
Grundlagen der Geometrie
Grundlagen der Geometrie (Foundations of Geometry) is a monograph by the German mathematician David Hilbert, first published in Leipzig in 1899, which supplied the first complete axiom system for Euclidean geometry and shaped twentieth-century mathematics.
Guillaume de l'Hôpital
Guillaume de l'Hôpital, Guillaume François Antoine, Marquis de l'Hôpital (1661–1704), was a French mathematician who wrote the first differential calculus textbook in 1696; l'Hôpital's rule is named for him.
Gumbel distribution
The Gumbel distribution, also called the Log-Weibull or Type I extreme value distribution, models the maximum of a large sample and is traditionally used for annual flood and rainfall maxima.
Gurobi Optimization
Gurobi Optimization is an optimization software company co-founded in 2008 by Robert Bixby, Zonghao Gu, and Edward Rothberg, named from the first two letters of their surnames.
h-cobordism theorem
The h-cobordism theorem, proved by Stephen Smale around 1961, states that a simply connected h-cobordism of dimension at least 5 is diffeomorphic to a product.
H-space
An H-space is a pointed topological space with a continuous multiplication whose base point acts as a unit up to homotopy, named after Heinz Hopf and studied since his 1941 work.
H-vector
An h-vector is a sequence of integers encoding the number of faces of a simplicial complex, polytope, or poset in each dimension; it determines, and is determined by, the f-vector.
Haar measure
Haar measure is a measure on a locally compact group that is invariant under translation, finite on compact sets, and unique up to a positive constant; on R it coincides with Lebesgue measure.
Haar wavelet
The Haar wavelet is the simplest orthonormal wavelet, a step function equal to +1 and −1 on halves of its support, introduced by Alfréd Haar in 1909.
Haar wavelet transform
The Haar wavelet transform decomposes a signal or image into averages and differences at successive dyadic scales, and its coefficients are used for compression, denoising, and edge extraction.
Hadamard matrix
A Hadamard matrix is a square matrix whose entries are all +1 or −1 and whose rows are mutually orthogonal, achieving the largest determinant possible of n^(n/2).
Hadamard product (matrices)
The Hadamard product, also called the Schur product or entrywise product, multiplies two matrices of the same size entry by entry, unlike ordinary matrix multiplication.
Hadamard's inequality for integrals
Hadamard's inequality for integrals, more often called the Hermite–Hadamard inequality, bounds the integral of a convex function between its midpoint value and its endpoint average.
Hadwiger conjecture (graph theory)
Hadwiger's conjecture, proposed by Hugo Hadwiger in 1943, states that every graph with no complete graph Kt as a minor can be colored with t − 1 colors.
Hadwiger–Nelson problem
The Hadwiger–Nelson problem, or chromatic number of the plane, asks the fewest colors needed so points a unit distance apart differ, known to be 5, 6, or 7.
Hahn–Banach theorem
The Hahn–Banach theorem, a result of functional analysis, states that a bounded linear functional on a subspace of a Banach space extends to the whole space with the same norm.
Hairy ball theorem
The hairy ball theorem, also called the hedgehog theorem, is an algebraic topology result: a hairy ball cannot be combed flat without creating a cowlick.
Half-precision floating-point format
Half-precision floating-point format, also called FP16 or binary16, is a 16-bit IEEE 754 encoding that stores numbers in half the memory of single precision, widely used in graphics and machine learning.
Hall's marriage theorem
Hall's marriage theorem, proved by Philip Hall in 1935, states that a bipartite graph has a matching covering one side if and only if every subset has enough neighbors.
Halting problem
The halting problem, also known as Turing's halting theorem, asks whether a program halts on a given input; Alan Turing proved in 1936 that no algorithm solves it.
Ham sandwich theorem
The ham sandwich theorem, also called the Stone–Tukey theorem, states that n measurable sets in n-dimensional space can all be bisected at once by one hyperplane.
Hamilton–Jacobi–Bellman equation
The Hamilton–Jacobi–Bellman (HJB) equation is a nonlinear partial differential equation whose solution gives the minimum achievable cost in continuous-time optimal control, forming the basis of Bellman's 1957 dynamic programming method.
Hamiltonian cycle
A Hamiltonian cycle is a closed path in a graph that visits every vertex exactly once and returns to its start; it was posed as Hamilton's Icosian Game in 1857.
Hamiltonian neural networks
Hamiltonian neural networks, introduced at NeurIPS 2019 by Sam Greydanus, Misko Dzamba, and Jason Yosinski, learn a system's energy function from data so the learned dynamics conserve energy.
Hamming bound
The Hamming bound, also called the sphere-packing bound, is an upper limit on the size of an error-correcting code with given length and minimum distance.
Hamming distance
The Hamming distance between two equal-length strings is the number of positions where their symbols differ, named for Richard Hamming, who introduced it in 1950.
Hankel matrix
A Hankel matrix is a square or rectangular matrix whose entries are constant along each anti-diagonal, named after the German mathematician Hermann Hankel.
Hankel transform
The Hankel transform, also called the Bessel transform, is an integral transform with a Bessel-function kernel, used on radially symmetric problems in cylindrical coordinates.
Hannah Cairo
Hannah Cairo, also known as Hannah Mira Cairo, is a Bahamian-born mathematician who disproved the 40-year-old Mizohata–Takeuchi conjecture in 2025 at age 17 and began a mathematics Ph.D. at the University of Maryland in fall 2025.
Hannah Fry
Hannah Fry is a British mathematician, author, and broadcaster known for mathematical models of human behavior and her viral TED talk on the mathematics of love.