The Real Numbers
The mathematical concept of real numbers is the main subject of discussion here.
Mathematical theories, as a rule, are extremely useful since they allow to transform one set of numbers (the initial data) into another set of numbers constituting the intermediate or final purpose of the computations.
Numbers in mathematics are like time in physics: everyone knows what they are, and only experts find them hard to understand. This is one of the basic mathematical abstractions, which seems destined to undergo significant further development.