6,052 articles
Gibbs sampling
Gibbs sampling, also known as the heat bath algorithm, is a Markov chain Monte Carlo method that samples each variable from its conditional distribution given all the others.
Gilbert–Varshamov bound
The Gilbert–Varshamov bound is a lower bound in coding theory: proved by Gilbert in 1952 and Varshamov in 1957, it guarantees codes of a certain size exist.
Gillespie algorithm
The Gillespie algorithm, also called the stochastic simulation algorithm, is a Monte Carlo method proposed by Daniel T. Gillespie in 1976 for simulating chemical reactions exactly.
Gimel function
The gimel function, named after the Hebrew letter gimel, maps each infinite cardinal κ to κ^cf(κ), where cf(κ) is κ's cofinality, and determines cardinal exponentiation.
Giorgi Japaridze (გიორგი ჯაფარიძე)
Giorgi Japaridze (გიორგი ჯაფარიძე), also published as Giorgie Dzhaparidze, is a Georgian-born logician and full professor at Villanova University in Pennsylvania, known for creating computability logic and cirquent calculus.
Girsanov theorem
The Girsanov theorem, also called the Cameron–Martin–Girsanov theorem, is a stochastic analysis result stating Brownian motion with drift becomes driftless under an equivalent probability measure.
Girth (graph theory)
In graph theory, the girth of a graph is the length of its shortest cycle in edges; graphs with no cycles are assigned girth 0 or infinity by convention.
Giuseppe Peano
Giuseppe Peano (1858–1932) was an Italian mathematician and logician at the University of Turin who formulated the Peano axioms and found the first space-filling curve.
Givens rotation
A Givens rotation is a plane rotation in numerical linear algebra, acting on two coordinates of a vector to turn one chosen entry into zero.
Gladys West
Gladys Mae West, born Gladys Mae Brown, was an American mathematician who spent 42 years at the U.S. Navy's Dahlgren facility modeling the Earth's shape for GPS.
Glaisher's theorem
Glaisher's theorem is an 1883 result stating that partitions into parts not divisible by d equal partitions with no part repeated d or more times.
Glide reflection
A glide reflection is an isometry of the plane that combines a reflection across a line with a translation along that line, one of the four plane isometries.
Global dimension
Global dimension, also called global homological dimension, is the supremum of the projective dimensions of modules over a ring, measuring how far the ring is from semisimple.
Global field
A global field is a field that is either a number field, a finite extension of the rationals, or a function field over a finite field.
GNU MPFR
GNU MPFR (Multiple Precision Floating-Point Reliable) is a portable C library for arbitrary-precision floating-point arithmetic, built on GNU MP and providing correctly rounded, reproducible results.
GNU Octave
GNU Octave is a free, high-level programming language and interactive environment for numerical computations, with syntax mostly compatible with Matlab. It runs on Linux, macOS, and Windows.
Goal programming
Goal programming is a branch of multi-objective optimization that finds a single compromise solution minimizing deviations from conflicting targets, introduced by Charnes, Cooper, and Ferguson in 1955.
Gödel numbering
Gödel numbering is a method assigning a unique natural number to each symbol, formula, and proof of a formal language, introduced by Kurt Gödel in his 1931 incompleteness paper.
Gödel, Escher, Bach
Gödel, Escher, Bach is a 1979 book by Douglas Hofstadter exploring self-reference and consciousness through mathematics, art, and music, and it won the Pulitzer Prize.
Gödel's completeness theorem
Gödel's completeness theorem, proved in Kurt Gödel's 1929 doctoral thesis, states that every valid formula of first-order predicate logic is provable, answering a 1928 question of Hilbert and Ackermann.
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two results of mathematical logic published by Kurt Gödel in 1931, showing that any consistent formal system with elementary arithmetic contains undecidable statements.
Gödel's ontological proof
Gödel's ontological proof, also known as Gödel's ontological argument, is a formal modal argument for the existence of God written by Kurt Gödel around 1970.
Golay code
The Golay codes are two perfect error-correcting block codes, one binary and one ternary, introduced by Marcel Golay in 1949 and used for error control in the Voyager mission.
Gold standard (test)
Gold standard (test), also called reference standard, is the best available diagnostic benchmark for a target condition in medicine. Rarely error-free; verification, incorporation, and misclassification bias; alternatives include composite and latent class standards.
Goldbach's conjecture
Goldbach's conjecture, the strong Goldbach conjecture, says every even number greater than 2 is the sum of two primes; proposed in 1742, it remains unproved.
Goldbach's weak conjecture
Goldbach's weak conjecture, also called the ternary Goldbach conjecture, states every odd integer greater than 5 is a sum of three primes; Helfgott proved it in 2013.
Golden ratio
The golden ratio, or golden section, is the irrational number φ ≈ 1.618, defined by a line divided so the parts keep the same proportion.
Golden rectangle
A golden rectangle, also called a golden mean rectangle, has sides in the golden ratio of about 1.618 to 1; removing its largest square leaves a smaller golden rectangle.
Golden spiral
The golden spiral is a logarithmic spiral that widens by the golden ratio, about 1.618, at every quarter turn, often approximated by nested golden rectangles.
Gömböc
The Gömböc is a convex, homogeneous body with exactly one stable and one unstable equilibrium point, first built by Gábor Domokos and Péter Várkonyi in 2006.