(number theory) The theorem that the number of prime numbers less than n asymptotically approaches n / ln(n) as n approaches infinity.

(aerodynamics) A fundamental theorem used to calculate the lift of an airfoil and any two-dimensional bodies including circular cylinders translating in a uniform fluid at a constant speed large enough so that the flow seen in the body-fixed frame is steady and unseparated.

(graph theory) A theorem stating that the undirected graphs, partially ordered by the graph-minor relationship, form a well-quasi-ordering.

(mathematical logic) A theorem stating that a certain combinatorial principle in Ramsey theory, namely the strengthened finite Ramsey theorem, is true, but not provable in Peano arithmetic.

(game theory) A theorem that describes a necessary and sufficient condition for the non-emptiness of the core of a cooperative game in characteristic function form. The game's core is non-empty if and only if the game is balanced.

(algebra) A theorem which states that for each element of a given set that a given group acts on, there is a natural bijection between the orbit of that element and the cosets of the stabilizer subgroup with respect to that element.

(linear algebra) A theorem about linear transformations (or the matrices that represent them) stating that the rank plus the nullity equals the dimension of the entire vector space (which is the linear transformation’s domain).

(mathematics) An important statement about surfaces in differential geometry, connecting their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic).

(computing theory) A fundamental theorem about the complexity of computable functions, stating that for any complexity measure there are computable functions that are not optimal with respect to that measure.

(mathematics) A theorem showing that all problems about algebraic number fields can be reduced to problems about their absolute Galois groups; one of the foundational results of anabelian geometry.