Mathematics — Scope and Methods

Mathematics is often regarded as the most certain of all knowledge, the field where proof yields conclusions beyond reasonable doubt. This lesson examines its distinctive scope and methods, which set it apart from every other AOK.

The scope of mathematics

The scope of mathematics is the study of abstract structures: numbers, shapes, patterns, quantities, relations, and the logical relationships among them. Unlike the natural sciences, mathematics does not primarily study the physical world through observation; its objects, such as numbers and perfect circles, are abstract rather than material. Yet mathematics is astonishingly useful in describing reality, a puzzle sometimes called the "unreasonable effectiveness of mathematics." Whether mathematics is a language we invented that happens to