The theorem that the prime counting function is of the same order of magnitude as x / ln x, i.e., for the prime counting function π, there are positive constants c and C such that:

Alternative form of Pythagorean theorem

(geometry) A mathematical theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of those of the two other sides.

(fluid dynamics) A theorem which states that to achieve propulsion at low Reynolds number in simple (i.e. Newtonian) fluids, a swimmer must deform in a way that is not invariant under time-reversal.

(computing theory) A theorem stating that all nontrivial semantic properties of programs are undecidable.

The theorem that any graph labelling (with colours) of a sufficiently large complete graph contains monochromatic cliques.

(graph theory) A characterization of the connectivity in finite undirected graphs in terms of the minimum number of disjoint paths that can be found between any pair of vertices.

(physics) A theorem stating that the energy eigenstates for an electron in a crystal can be written as Bloch waves.

(mathematics) A theorem that gives a lower bound on the size of a disc in which an inverse to a holomorphic function exists.

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