Mathematics and statistics

Lattice-ordered group

A lattice-ordered group, also called an ℓ-group, is a group with a partial order under which every two elements have a meet and join, preserved by all translations.

Laurent series

A Laurent series, also called a Laurent expansion or bilateral power series, is a doubly infinite power series in positive and negative powers of z, valid on an annulus.

Law of averages

The law of averages is an informal, non-mathematical phrase claiming random outcomes even out over time; probability theory rejects its short-run version as the gambler's fallacy.

Law of cosines

The law of cosines, also called the cosine rule, is a Euclidean geometry theorem relating a triangle's sides to one angle, generalizing the Pythagorean theorem.

Law of excluded middle

The law of excluded middle (tertium non datur) is the classical logic principle that every proposition is either true or false, rejected in intuitionistic logic.

Law of large numbers

The law of large numbers is a theorem of probability theory stating that the average of many independent random variables converges to their expected value.

Law of noncontradiction

The law of noncontradiction, also called the principle of non-contradiction, is the logical principle that a proposition and its negation cannot both be true at the same time.

Law of sines

The law of sines, also called the sine rule, states that in any triangle each side divided by the sine of its opposite angle gives the same value.

The law of the iterated logarithm (LIL) is a probability theorem giving the exact envelope, of order sqrt(2n log log n), that random-walk fluctuations touch infinitely often, first proved by Khinchin in 1924.

Law of the unconscious statistician

The law of the unconscious statistician (LOTUS) is a theorem of probability theory stating that the expected value of g(X) can be computed directly from the distribution of X, without first deriving the distribution of g(X).

Law of total expectation

The law of total expectation, also called the law of iterated expectations or tower property, states that a random variable's expected value is the probability-weighted average of conditional expectations.

Law of total probability

The law of total probability, also called the total probability theorem, expresses an event's probability as a weighted sum of its conditional probabilities over a partition of the sample space.

Law of total variance

The law of total variance, also called the variance decomposition formula or Eve's law, states Var(Y) = E[Var(Y|X)] + Var(E[Y|X]), splitting variance into explained and unexplained parts.

Laws of Form

Laws of Form is a 1969 book by the British mathematician G. Spencer-Brown that introduces the calculus of indications, showing it equivalent to Boolean algebra and the propositional calculus.

Oct 22, 2026

Lawson conjecture

The Lawson conjecture, posed by H. Blaine Lawson in 1970, states that the Clifford torus is the only embedded minimal torus in the unit 3-sphere; Simon Brendle proved it in 2012.

Lax entropy condition

The Lax entropy condition is an admissibility criterion, introduced by Peter D. Lax in the 1950s, selecting the physically meaningful weak solution of a hyperbolic conservation law.

Lax pair

A Lax pair is a pair of linear operators or matrices whose compatibility condition reproduces a nonlinear evolution equation, making the eigenvalues of L conserved quantities.

Leader election

Leader election, also called leader finding, is a fundamental problem in distributed computing where the processes of a network single out exactly one of themselves as leader.

Lean Six Sigma

Lean Six Sigma is a process-improvement methodology combining Lean's waste elimination with Six Sigma's statistical reduction of process variation, applied through the structured DMAIC cycle.

Least common multiple

The least common multiple (LCM), also called the smallest common multiple, is the smallest positive integer that two nonzero integers both divide evenly, such as lcm(6, 9) = 18.

Least significant difference test

The least significant difference (LSD) test, also called Fisher's LSD, is a pairwise multiple comparison procedure used after ANOVA to decide which pairs of treatment means differ significantly.

Least squares

Least squares, or the least-squares method, is a statistical estimation method that minimizes the sum of squared deviations between observed data and a model's predictions; Legendre published it in 1805.

Least-upper-bound property

The least-upper-bound property, also called the supremum property, says every nonempty subset of an ordered set that is bounded above has a least upper bound in the set.

Leave-one-out cross-validation

Leave-one-out cross-validation (LOOCV) is a resampling method that estimates a model's out-of-sample prediction error by repeatedly leaving out one observation, equivalent to k-fold cross-validation with k equal to the sample size.

Lebesgue integration

Lebesgue integration is a mathematical technique that partitions a function's range instead of its domain, extending integration to functions with many discontinuities and underpinning modern probability theory.

Lebesgue measure

Lebesgue measure is the standard way of assigning length, area, and volume to subsets of Euclidean space, formulated by Henri Lebesgue in 1901 and underlying the Lebesgue integral.

Lee–Carter model

The Lee–Carter model is a statistical method that forecasts age-specific death rates and life expectancy, proposed by Ronald Lee and Lawrence Carter in 1992 and now the standard starting point for stochastic mortality forecasting.

Leech lattice

The Leech lattice is a lattice in 24-dimensional space, found by John Leech in 1965, whose sphere packing is provably the densest possible in 24 dimensions.

Legendre polynomials

The Legendre polynomials are a sequence of orthogonal polynomials on [-1, 1], introduced by Adrien-Marie Legendre in 1784 and used in numerical analysis and mathematical physics.