An important limitative theorem in quantum computing that establishes an upper bound (Holevo's bound) for the amount of information that can be known about a quantum state.

(mathematics) A result concerning certain infinite-dimensional vector spaces, stating that any orthomodular form that has an infinite orthonormal sequence is a Hilbert space over the real numbers, complex numbers or quaternions.

(mathematics) A basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism.

(number theory) A theorem that gives a finite bound on the number of consecutive pairs of smooth numbers that exist, for a given degree of smoothness, and provides a method for finding all such pairs using Pell equations.

(mathematics) A theorem used in complex analysis to establish a bound on the growth rates for an analytic function.

(geometry) A theorem stating that it is not possible to dissect a square into an odd number of triangles of equal area.

(computing theory) A theorem giving a relationship between deterministic and non-deterministic space complexity.

(number theory) A theorem stating that the sum of the reciprocals of the twin primes converges to a finite value (Brun's constant).

(probability theory) A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event.

(mathematics) A theorem stating that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.