" The overall structure of the calculus is simple. The subject is defined by a fantastic leading idea, one basic axiom, a calm and profound intellectual invention, a deep property, two crucial definitions, one ancillary definition, one major theorem, and the fundamental theorem of the calculus.
The fantastic leading idea: the real world may be understood in terms of the real numbers.
The basic axiom: brings the real numbers into existence.
The calm and profound invention: the mathematical function.
The deep property: continuity.
The crucial definitions: instantaneous speed and the area underneath a curve.
The ancillary definition: a limit
The major theorem: the mean value theorem.
The fundamental theorem of the calculus is the fundamental theorem of the calculus.
These are the massive load-bearing walls and buttresses of the subject. "

― David Berlinski