6,052 articles
Jacob Bernoulli
Jacob Bernoulli, also known as Jacques Bernoulli, was a Swiss mathematician from Basel who founded mathematical probability, proving the law of large numbers in Ars Conjectandi.
Jacobi elliptic functions
The Jacobi elliptic functions sn(z, k), cn(z, k), and dn(z, k) are doubly periodic meromorphic functions that invert the elliptic integral of the first kind, generalizing trigonometric functions.
Jacobi method
The Jacobi method, also known as Jacobi iteration, is an iterative algorithm of numerical linear algebra that solves systems of linear equations; Jacobi described it in 1845.
Jacobi polynomials
Jacobi polynomials, written P(α, β), are a family of classical orthogonal polynomials on (-1, 1), initiated by Carl Jacobi in 1826 and used in Gauss–Jacobi quadrature and spectral methods.
Jacobi's formula
Jacobi's formula is a theorem of matrix calculus stating that the differential of a square matrix's determinant equals the trace of its adjugate times the matrix differential.
Jacobian conjecture
The Jacobian conjecture, posed by Ott-Heinrich Keller in 1939, asks whether polynomial maps with constant nonzero Jacobian determinant must have polynomial inverses; it was refuted in dimension 3 in 2026.
Jacobian matrix and determinant
The Jacobian matrix of a vector-valued function is the matrix of its first-order partial derivatives; when square, its Jacobian determinant measures local volume scaling and appears in change of variables.
Jacobson radical
The Jacobson radical of a ring R, written J(R), is the intersection of all maximal left ideals, equivalently of all maximal right ideals; it was introduced by Nathan Jacobson in 1945.
Jacobson ring
A Jacobson ring, also called a Hilbert ring, is a commutative ring in which every radical ideal is the intersection of the maximal ideals containing it.
Jacobsthal numbers
The Jacobsthal numbers are the sequence 0, 1, 1, 3, 5, 11, ... defined by the recurrence J(n) = J(n−1) + 2J(n−2), named for the German mathematician Ernst Erich Jacobsthal.
jamovi
jamovi is a free and open statistical spreadsheet built on the R statistical language, providing point-and-click data editing and analysis as an intuitive alternative to commercial packages such as SPSS.
Janko groups
The Janko groups J₁, J₂, J₃, and J₄ are four of the 26 sporadic finite simple groups, named after mathematician Zvonimir Janko, who found them between 1964 and 1975.
János Bolyai
János Bolyai (1802–1860) was a Hungarian mathematician and army officer who independently discovered non-Euclidean geometry, published in 1832 as a 24-page appendix to a textbook by his father, Farkas Bolyai.
Jeffrey Todd Borggaard
Jeffrey Todd Borggaard is an American applied and computational mathematician, Professor of Mathematics at Virginia Tech, known for the sensitivity equation method and POD reduced-order modeling of fluid flows.
Jensen–Shannon divergence
The Jensen–Shannon divergence is a symmetric, bounded measure of dissimilarity between two probability distributions, formalized by J. Lin in 1991 and widely used in statistics and machine learning.
Jensen's inequality
Jensen's inequality is a theorem of probability theory stating that a convex function of an expectation is at most the expectation of the convex function.
Jeu de taquin
Jeu de taquin is an algorithm in algebraic combinatorics, introduced by Marcel-Paul Schützenberger in 1977, that transforms a skew Young tableau into a straight-shape tableau by sliding entries.
JMP (statistical software)
JMP, pronounced "jump," is a family of statistical analysis software created by SAS co-founder John Sall in 1989, linking interactive data visualization with statistics through a point-and-click interface.
Job shop scheduling
Job shop scheduling is the combinatorial problem of scheduling job operations on machines, each job following a fixed route, to minimize the makespan; it is strongly NP-hard.
Joel David Hamkins
Joel David Hamkins is an American mathematician and philosopher working in logic and set theory, known for the set-theoretic multiverse view and infinite time Turing machines.
Johann Bernoulli
Johann Bernoulli, also known as Jean Bernoulli, was a Swiss mathematician who helped master Leibniz's calculus, posed the brachistochrone problem in 1696, and taught Euler.
John Charles Fields
John Charles Fields (1863–1932) was a Canadian mathematician at the University of Toronto who organized the 1924 International Congress of Mathematicians and established the Fields Medal.
John Edensor Littlewood
John Edensor Littlewood (1885–1977) was an English mathematician and Cambridge professor who worked on series, inequalities, and the zeta function, forming a famed partnership with G. H. Hardy.
John Horton Conway
John Horton Conway, also known as John Conway, was an English mathematician at Cambridge and Princeton known for the Game of Life and work in group theory.
John Napier
John Napier of Merchiston (1550–1617) was a Scottish mathematician and theologian who invented logarithms, published the first table of them in 1614, and devised the calculating rods known as Napier's bones.
Johnson graph
The Johnson graph J(n, k) is a graph whose vertices are the k-element subsets of an n-element set, with edges joining subsets that differ by exchanging one element.
Johnson solid
A Johnson solid, also called a Johnson polyhedron, is one of the 92 strictly convex polyhedra with regular polygon faces that are not Platonic or Archimedean solids, prisms, or antiprisms.
Joinpoint analysis
Joinpoint analysis is a statistical method that fits segmented linear regression to time-trend data such as disease rates, identifying where the trend changes; it is widely used in cancer surveillance.
Joint characteristic function
The joint characteristic function of a random vector is φ(t) = E[exp(i·tᵀX)], the ordinary characteristic function extended to several arguments; it always exists and uniquely determines the joint distribution.
Joint probability distribution
The joint probability distribution, or joint distribution function, gives the probability law of two or more random variables together, and is the basis for marginal and conditional distributions.