Greeks had a sophisticated theory of geometry, and they built theory of number (less well developed from geometry).
The Greek mathematician Euclid wrote a treatise called the Elements that codified what was known a few hundred years BC. This was considered the last word on geometry for 2000 years. It was the most widely printed book in history, after the Bible.
After the discovery of non-Euclidean geometry in the 19th century, mathematicians realized that were a lot of holes in Euclid's axioms. Alternative axiom systems, such as those of David Hilbert, were developed, but there are more axioms and more work to get to theorems about geometry that are not "obvious facts."
Modern math curriculum is heavy on real numbers and light on geometry. So rather than start at the very beginning, the American mathematician G. D. Birkhoff developed a shorter set of axioms that depend on knowledge of the real numbers. These are called the Ruler and Protractor Axiom System, for reasons that will become clear.
This is the system that we will use in 444. Later, we will have a look at history and Euclid's point of view.