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

(mathematics) A fundamental combinatorial result of Ramsey theory, concerning the degree to which high-dimensional objects must necessarily exhibit some combinatorial structure, and cannot be completely random.

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

(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.

(geometry) A theorem stating that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle.

(number theory) A theorem stating that, if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime.

(mathematics) A theorem in complex analysis concerning the existence of meromorphic functions with prescribed poles.

(geometry) A theorem which states that, in 3-dimensional space, any displacement of a rigid body such that some point on it remains fixed is equivalent to a single rotation about some axis that runs through said point.

(mathematics) A theorem stating that a polynomial ring over a Noetherian ring is Noetherian.