Greek mathematics is believed to be derived from the Egyptians and the Babylonians and was much more sophisticated than previous mathematics. Their numbering system was base 10 and they had ideas of addition and multiplication. The Greeks were very concerned about accuracy. They were not satisfied with estimations or rounding and were the first to think about the idea of infinity. There was also a heavy focus on geometry. Including the proof of the Pythagorean Theorem, the squaring of the circle, the doubling of the cube, and the trisection of an angle.
The Pythagorean theorem was discovered during the first period of Greek mathematics in 6th century BC. This period was defined by Thales, Pythagoras, Plato, and Aristotle. The next period was defined by Hippocrates of Chios, Eudoxus of Cnidus, and Zeno of Elea. This is the period when the idea of axioms appeared. They were originally applied in proofs related to Geometry.
The next period is associated with the school of Alexandria and Euclid. Euclid applied the ideas of axioms and used deductive reasoning in order to create rigorous proofs. He wrote The Elements, which includes definitions, postulates, axioms and results that were found from proofs. The Elements is divided into thirteen books. These books cover topics related to number theory, irrational numbers, and geometry. The Elements is still regarded as one of the most important textbooks of all time.
The Greeks lead the way to a new way of thinking. Their ideas laid the foundation to the way we think about mathematics now.