In this paper, we presented the beginnings and the development of mathematics in ancient Greece. Old Greeks inuenced science, especially mathematics, and their inuence is of great importance today. At the beginning of the paper we introduced the Greek numerical system, the way the Greeks wrote the numbers and the lack of such inscription. Furthermore, we presented the earliest Greek mathematician, Thales of Miletus. He wrote many theories and the results of his studies, so in Greek tradition he is called 'the founder of mathematics' with reason. After Thales, we came to the next great mathematician, Pythagoras. Pythagoras and his followers achieved numerous results in the eld of music, numerical theory and geometry. We also wrote about Pythagorean theorem, Pythagorean triple and an irrational number. Then we mentioned something about Plato and his forms, Aristotle and Zeno's paradoxes. Near the end of the paper we introduced the most famous Greek mathematician, Euclid. Euclid, often named the father of geometry, inscribed 13 books which he included in one great work called 'Elements'. Elements are still one of the most translated and the most studied works of human history. We gave some denitions, postulates, axioms and propositions written in Elements, and briey described each of the 13 books. In the end we mentioned the most important facts about Archimedes, with whom the ancient era of mathematics ended.