Mathematics (Greek: μαθηματικά (mathēmatika)) is often defined as the study of quantity, structure (pattern), change, and space. More informally, some might call mathematics the study of "figures and numbers." In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation. In the realist view, it is the investigation of objects or concepts that exist independently of our reasoning about them. Other views are described in the philosophy of mathematics article. Due to its applicability in practically every scientific discipline, mathematics has been called "the language of science" and "the language of the universe."
There are currently approximately 13419 mathematical articles in Wikipedia.
The Catalan numbers are solutions to numerous counting problems which often have a recursive flavour. In fact, one author lists over 60 different possible interpretations of these numbers. For example, the nth Catalan number is the number of full binary trees with n internal nodes, or n+1 leaves. It is also the number of ways of associatingn applications of a binary operator as well as the number of ways that a convex polygon with n + 2 sides can be cut into triangles by connecting vertices with straight lines.
