In mathematics, the word "data" is often used for the most general mathematical noun. One may consider a set, a function, a category, a group, or seven groups "data."

But for data to be interesting, it must have some sort of structure. Thus the data must satisfy certain properties.

A set-with-binary-operation consists only of data: a set S and a function f: S x S ---> S. It becomes a semi-group when we add a requirement to this data: the function must be associative.

In general, people speak of "data" and "structure." These are the raw materials and craftsmanship that create the mathematical universe.