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The classification theorem of finite simple groups, also known as the "enormous theorem," which states that the finite simple groups can be classified completely into 1. ...

The Banach-Steinhaus theorem is a result in the field of functional analysis which relates the "size" of a certain subset of points defined relative to a family of linear ...

Schur's partition theorem lets A(n) denote the number of partitions of n into parts congruent to +/-1 (mod 6), B(n) denote the number of partitions of n into distinct parts ...

In the above figure, let E be the intersection of AD and BC and specify that AB∥EF∥CD. Then 1/(AB)+1/(CD)=1/(EF). A beautiful related theorem due to H. Stengel can be stated ...

Two distinct theorems are referred to as "the de Bruijn-Erdős theorem." One of them (de Bruijn and Erdős 1951) concerns the chromatic number of infinite graphs; the other (de ...

Let M be a Riemannian manifold, and let the topological metric on M be defined by letting the distance between two points be the infimum of the lengths of curves joining the ...

Suppose that in some neighborhood of x=0, F(x)=sum_(k=0)^infty(phi(k)(-x)^k)/(k!) (1) for some function (say analytic or integrable) phi(k). Then ...

A theorem outlined by Kolmogorov (1954) which was subsequently proved in the 1960s by Arnol'd (1963) and Moser (1962; Tabor 1989, p. 105). It gives conditions under which ...

A special case of Apollonius' problem requiring the determination of a circle touching three mutually tangent circles (also called the kissing circles problem). There are two ...

In the most commonly used convention (e.g., Apostol 1967, pp. 205-207), the second fundamental theorem of calculus, also termed "the fundamental theorem, part II" (e.g., ...