6,052 articles
Legendre transformation
The Legendre transformation, or Legendre transform, re-expresses a convex function in terms of its slope instead of its value, a key tool of convex analysis.
Legendre's conjecture
Legendre's conjecture is an unsolved problem in number theory stating that there is at least one prime between every pair of consecutive squares, proposed by Adrien-Marie Legendre in 1808 and still unproven.
Leibniz formula for determinants
The Leibniz formula for determinants expresses the determinant of an n × n matrix as a signed sum over all n! permutations, a definition introduced by Leibniz in 1693.
Leibniz formula for π
The Leibniz formula for π, also called the Gregory–Leibniz series, is the alternating series 1 − 1/3 + 1/5 − 1/7 + ⋯ that sums to π/4.
Leibniz integral rule
The Leibniz integral rule, or differentiation under the integral sign, is a calculus formula for differentiating a definite integral whose limits or integrand depend on a parameter.
Leibniz–Newton calculus controversy
The Leibniz–Newton calculus controversy was a priority dispute between Isaac Newton and Gottfried Wilhelm Leibniz over who invented calculus, fought mainly from 1708 to 1716.
Leibniz's notation
Leibniz's notation is the standard calculus notation introduced by Gottfried Wilhelm Leibniz in 1675, using dx, dy, the derivative dy/dx, and the integral sign ∫, first published in 1684.
Leiden algorithm
The Leiden algorithm is a community detection method for large networks, created by Traag, Waltman, and van Eck at Leiden University in 2018 as a faster improvement on Louvain.
Leiden Declaration on Artificial Intelligence and Mathematics
The Leiden Declaration on Artificial Intelligence and Mathematics, published in June 2026, calls for action on AI's challenges to mathematics research and was endorsed by the International Mathematical Union.
Leimkuhler–Matthews method
The Leimkuhler–Matthews method is a numerical integrator for overdamped Langevin dynamics that modifies Euler–Maruyama by averaging consecutive Gaussian noise increments, giving second-order accuracy for invariant averages.
Lemniscate
The lemniscate of Bernoulli is a figure-eight plane curve, defined by a constant product of distances from two fixed points, published by Jacob Bernoulli in 1694.
Lens space
A lens space, written L(p,q), is a closed 3-dimensional manifold formed by gluing two solid tori, or as a quotient of the 3-sphere by a cyclic group.
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
The Lenstra–Lenstra–Lovász (LLL) algorithm, introduced by Arjen Lenstra, Hendrik Lenstra, and László Lovász in 1982, transforms any lattice basis into a reduced basis with short, nearly orthogonal vectors in polynomial time.
Leon van der Torre
Leon van der Torre, also known as Leendert van der Torre, is a Dutch-born computer scientist and professor of artificial intelligence at the University of Luxembourg.
Leonhard Euler
Leonhard Euler was a Swiss mathematician and physicist of the 18th century who introduced much of modern mathematical notation, including f(x), e, i, and π.
Leray spectral sequence
The Leray spectral sequence is a spectral sequence, introduced by Jean Leray in 1945 alongside sheaf theory, that computes the cohomology of a space from a continuous map's fibers.
Less-than sign
The less-than sign, or less-than symbol, is the mathematical symbol <, indicating that the value on its left is smaller than the value on its right.
Level of measurement
Level of measurement, also called scale of measurement, classifies variables into nominal, ordinal, interval, and ratio levels, a framework introduced by S. S. Stevens in 1946.
Level set
A level set of a function f is the set of all points where f equals a single constant value, such as a level curve or level surface.
Level set method
The level set method is a numerical technique that tracks moving curves and surfaces as the zero level set of a higher-dimensional function, introduced by Osher and Sethian in 1988.
Levenberg–Marquardt algorithm
The Levenberg–Marquardt algorithm, also known as the Levenberg–Marquardt method or damped least squares, is an iterative numerical method for nonlinear least squares that interpolates between Gauss–Newton and gradient descent.
Levene's test
Levene's test is a statistical test of whether several independent samples come from populations with equal variances, proposed by Howard Levene in 1960 and used to check an assumption of ANOVA.
Levent Alpöge
Levent Alpöge is an American–Turkish number theorist known for results on elliptic curves and a negative solution of Hilbert's tenth problem over rings of integers.
Leverage (statistics)
Leverage, in statistics, measures how far an observation's independent-variable values lie from the center of the others in a regression, indicating its potential to move the fitted line.
Levi graph
The Levi graph, also called the incidence graph, is the bipartite graph of an incidence structure, with vertices for points and lines and edges for incidences.
Levi-Civita field
The Levi-Civita field is a non-Archimedean ordered field extension of the real numbers containing infinitesimals, the smallest such extension that is real closed and Cauchy complete.
Levi-Civita symbol
The Levi-Civita symbol, also called the permutation symbol, is a collection of numbers based on the sign of a permutation, equal to +1, −1, or 0.
Lévy distribution
The Lévy distribution is a heavy-tailed continuous probability distribution with no finite mean or variance, arising as the first time Brownian motion reaches a fixed level.
Lévy flight
A Lévy flight is a random walk whose step lengths follow a heavy-tailed power-law distribution, named for Paul Lévy; the rare long jumps make the motion superdiffusive.
Lévy measure
A Lévy measure assigns to each set of jump sizes the expected number of jumps per unit time in a Lévy process, allowing infinitely many small jumps.