(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.

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

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.

(politics) A theorem stating that no voting system can be perfectly fair in all circumstances

plural of spectral theorem

(mathematics) A theorem stating that any non-singular algebraic curve defined by algebraic number coefficients represents a compact Riemann surface which is a ramified covering of the Riemann sphere, ramified at three points only.

(economics) A theorem stating that, if trade in an externality is possible and there are sufficiently low transaction costs, bargaining will lead to a Pareto efficient outcome regardless of the initial allocation of property.

plural of deduction theorem

(group theory) A theorem which proves that, given a mind swap machine that can't be used on the same pair of people more than once, it is possible to reverse any number of mind swaps by introducing two more people that did not have their minds swapped with anyone before.