In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of...

algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

In mathematics, the mean value theorem (or Lagrange theorem) states, roughly, that for a given planar arc between two endpoints, there is at least one...

In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample...

In theoretical computer science, the CAP theorem, also named Brewer's theorem after computer scientist Eric Brewer, states that any distributed data store...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b...

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through...

Stokes' theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls or simply the curl theorem, is...

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each...

specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship between quotients...

The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate...

In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly...

mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood...

In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map...

In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C....

Several theorems are named after Karl Weierstrass. These include: The Weierstrass approximation theorem, of which one well known generalization is the...

In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers...

Pierre de Fermat engendered many theorems. Fermat's theorem may refer to one of the following theorems: Fermat's Last Theorem, about integer solutions to an + bn = cn...

In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In...

There are several theorems known as the Helmholtz theorem: Helmholtz decomposition, also known as the fundamental theorem of vector calculus Helmholtz...

In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct...

Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law...

Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be...

In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions...

mathematics, Carathéodory's theorem may refer to one of a number of results of Constantin Carathéodory: Carathéodory's theorem (conformal mapping), about...

In mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square...

stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources...