(number theory) A theorem stating that the sequence of prime numbers contains arbitrarily long arithmetic progressions.

(complex analysis) A theorem that gives a geometric relation between the roots of a polynomial P and the roots of its derivative P′. It states that the roots of P′ all lie within the convex hull of the roots of P.

(algebra) A theorem which states a constraint on rational solutions of a polynomial equation with integer coefficients.

(mathematics) A theorem stating that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding.

(mathematics) A theorem that establishes the transcendence of a large class of numbers, stating that, if a and b are algebraic numbers with a ≠ 0, 1, and b irrational, then any value of aᵇ is a transcendental number.

(mathematics) A result on the class group of certain number fields, strengthening Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity iff p divides the numerator of the n-th Bernoulli number Bₙ for some n, 0 < n < p − 1. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an Bₙ.

(physics) A theorem that states the moment of inertia of a rigid body about any axis is equal to its moment of inertia about a parallel axis through its center of mass plus the product of the mass of the body and the square of the distance between the two parallel axes.

(physics) A theorem that states the moment of inertia of a planar lamina (i.e. 2-D body) about an axis perpendicular to the plane of the lamina is equal to the sum of the moments of inertia of the lamina about the two axes at right angles to each other, in its own plane intersecting each other at the point where the perpendicular axis passes through it.

(mathematics) A theorem stating that every finite group of odd order is solvable.

(artificial intelligence, computing) A theorem that implies that no single machine learning algorithm is universally the best-performing algorithm for all problems.