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A copositive matrix is a real n×n square matrix A=(a_(ij)) that makes the corresponding quadratic form f(x)=x^(T)Ax nonnegative for all nonnegative n-vectors x. Copositive ...

A doubly nonnegative matrix is a real positive semidefinite n×n square matrix with nonnegative entries. Any doubly nonnegative matrix A of order n can be expressed as a Gram ...

A googol is a large number equal to 10^(10^2)=10^(100) (i.e., a 1 with 100 zeros following it). Written out explicitly, ...

A random graph is a graph in which properties such as the number of graph vertices, graph edges, and connections between them are determined in some random way. The graphs ...

If the Taniyama-Shimura conjecture holds for all semistable elliptic curves, then Fermat's last theorem is true. Before its proof by Ribet in 1986, the theorem had been ...

If M^n is a differentiable homotopy sphere of dimension n>=5, then M^n is homeomorphic to S^n. In fact, M^n is diffeomorphic to a manifold obtained by gluing together the ...

The first Hardy-Littlewood conjecture is called the k-tuple conjecture. It states that the asymptotic number of prime constellations can be computed explicitly. A particular ...

If M^n is a finite simplicial complex of dimension n>=5 that has the homotopy type of the sphere S^n and is locally piecewise linearly homeomorphic to the Euclidean space ...

A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...