Mathematics and statistics

Dual polyhedron

A dual polyhedron is a polyhedron paired with another so that the faces of one occupy the positions of the vertices of the other, exchanged by reciprocation.

Dual quaternion

A dual quaternion is an eight-component number, formed from two quaternions and the nilpotent dual unit ε, that represents a rigid-body pose, combining rotation and translation compactly.

Dual representation

The dual representation, or contragredient representation, is the representation a group or Lie algebra induces on the dual space of its representation space, preserving the natural pairing.

Dual space

The dual space of a vector space V is the vector space V of all linear functionals on V, that is, linear maps from V to its scalar field.

The dualizing sheaf is a coherent sheaf on a Noetherian scheme representing duality on coherent sheaves, generalizing the canonical bundle to singular spaces and underlying Serre and Grothendieck duality.

Dudley's theorem

Dudley's theorem, also called the Dudley entropy integral bound, bounds the expected supremum of a sub-Gaussian process by an integral of the metric entropy of its index set.

Oct 22, 2026

Duffin–Schaeffer conjecture

The Duffin–Schaeffer conjecture, posed by R. J. Duffin and A. C. Schaeffer in 1941, gave a criterion for when almost every real number is approximated infinitely often by reduced fractions.

Dummy variable (statistics)

A dummy variable, also called an indicator variable, is a binary variable that takes the value 1 or 0 to include categorical data in regression models.

Duodecimal

Duodecimal, also called dozenal or base twelve, is a positional numeral system using twelve digits. Its base twelve divides evenly by 2, 3, 4, and 6, so fractions like 1/3 terminate.

Dustin Clausen

Dustin Clausen is an American mathematician known for algebraic K-theory and for developing condensed mathematics with Peter Scholze; he has been a permanent professor at IHES since 2023.

Dutch book arguments

Dutch book arguments, also called Dutch book theorems, hold that degrees of belief should satisfy the probability axioms because incoherent beliefs allow bets guaranteeing a loss.

Dyadic analysis

Dyadic analysis is a set of statistical methods for data from pairs of people, such as couples or friends, whose outcomes are interdependent, most commonly modeled with the actor–partner interdependence model.

Dyadics

Dyadics, also called dyadic tensors or dyadic products, are second-order tensors built as sums of dyads, introduced by Josiah Willard Gibbs in the early 1880s.

Dyck path

A Dyck path is a lattice path of up and down steps that starts and ends at level 0 and never goes below, counted by Catalan numbers.

Dynamic Bayesian network

A dynamic Bayesian network (DBN) is a Bayesian network extended to model probability distributions over time-indexed variables, introduced by Thomas Dean and Keiji Kanazawa in 1989.

Dynamic connectivity

Dynamic connectivity is the algorithmic problem of updating a graph edge by edge and quickly answering whether two vertices are connected, aiming for polylogarithmic time per operation.

Dynamic epistemic logic

Dynamic epistemic logic (DEL) is a family of modal logics in which operators describe actions, like public announcements, that transform what a group of agents knows.

Dynamic factor model

A dynamic factor model (DFM) is a statistical model representing many time series as driven by a few unobserved common factors, used in econometrics for forecasting and nowcasting.

Dynamic logic (computer science)

Dynamic logic is a family of modal logics whose modalities are indexed by programs, generalizing box and diamond; its propositional variant PDL was introduced by Fischer and Ladner in 1979.

Dynamic mode decomposition

Dynamic mode decomposition (DMD) is a data-driven technique, proposed by Peter Schmid in 2008, that decomposes snapshot sequences into modes, each with one frequency and growth rate.

Dynamic panel model

The dynamic panel data model, or dynamic panel data model, is a panel regression with a lagged dependent variable, estimated consistently by Arellano–Bond difference GMM or system GMM.

Dynamic treatment regime

A dynamic treatment regime, also called an adaptive treatment strategy, is a sequence of decision rules for tailoring treatment to a patient's changing status over time.

Dynamical system

A dynamical system is a mathematical model of a process whose future is determined by its present state, through a state space and an evolution rule.

Dynkin diagram

A Dynkin diagram is a graph encoding a root system, with one vertex per simple root, introduced by Evgeny Dynkin in 1947 to classify semisimple Lie algebras.

Dyson equation

The Dyson equation is the integral equation of quantum field theory relating the full interacting Green's function to a reference one and the self-energy, introduced by Freeman Dyson in 1949.

E (mathematical constant)

e, also known as Euler's number or Napier's constant, is the base of the natural logarithm, an irrational and transcendental number approximately equal to 2.71828, named for Leonhard Euler.

E-Government Act of 2002

The E-Government Act of 2002 is a United States federal law signed by President George W. Bush on December 17, 2002, to improve electronic government services.

E-value

The E-value is a sensitivity-analysis measure in epidemiology that quantifies the minimum confounding strength needed to explain away an observed association, introduced by VanderWeele and Ding in 2017.

E-values

An e-value is a nonnegative measure of statistical evidence against a null hypothesis, central to anytime-valid inference where researchers may stop or continue studies at will.