Often the imperative is usefulness. We need numbers, for example, so that we can count (heads of cattle, say) and geometric objects such as rectangles to measure, for example, the areas of fields.

So, for example, the natural numbers are the objects of a category, and one particular arrow in that category would connect each number to its double.

Category theory is a branch of mathematics that explains how distinct mathematical objects can be considered “the same.” ...

Films of soap with complex shapes can be used to model and understand mathematical singularities across a range of fields.

Notions of size for different kinds of mathematical objects are ubiquitous. The volume or of a set in Euclidean space (the study of which is fundamental to the field of Convex Geometry) and the ...

In a new article, mathematicians describe how modern computer technology has vastly expanded our ability to discover new mathematical results. By computing mathematical expressions to very high ...

Various combinations of those two basic symmetries form symmetry groups, which are mathematical constructs that show all the different symmetries of a particular object.

By extending the scope of a key insight behind Fermat’s Last Theorem, four mathematicians have made great strides toward building a unifying theory of mathematics.