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The first group isomorphism theorem, also known as the fundamental homomorphism theorem, states that if phi:G->H is a group homomorphism, then Ker(phi)⊴G and ...

In the field of functional analysis, the Krein-Milman theorem is a result which characterizes all (nonempty) compact convex subsets K of "sufficiently nice" topological ...

The square of the area of the base (i.e., the face opposite the right trihedron) of a trirectangular tetrahedron is equal to the sum of the squares of the areas of its other ...

There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...

A theorem which plays a fundamental role in computer science because it is one of the main tools for showing that certain orderings on trees are well-founded. These orderings ...

The second theorem of Mertens states that the asymptotic form of the harmonic series for the sum of reciprocal primes is given by sum_(p<=x)1/p=lnlnx+B_1+o(1), where p is a ...

The fundamental theorem of game theory which states that every finite, zero-sum, two-person game has optimal mixed strategies. It was proved by John von Neumann in 1928. ...

If the three straight lines joining the corresponding vertices of two triangles ABC and A^'B^'C^' all meet in a point (the perspector), then the three intersections of pairs ...

Jackson's theorem is a statement about the error E_n(f) of the best uniform approximation to a real function f(x) on [-1,1] by real polynomials of degree at most n. Let f(x) ...

The Paris-Harrington theorem is a strengthening of the finite Ramsey's theorem by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...