Contrary to the other answers given, I argue that higher category theory is currently the most viable framework for formalizing mathematics as a whole. read more
In this sense, geometry may not be the most fundamental area of mathematics. I would think that logic and set theory are more fundamental. In one form or another, they seem to permeate nearly all domains of mathematics including geometry as taught at the university level. read more
Around 300 BC, geometry was revolutionized by Euclid, whose Elements, widely considered the most successful and influential textbook of all time, introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom, theorem, and proof. read more