1) Euclid had a significant influence on Greek culture during a golden age of intellectual advancement. He created the Elements, considered the most influential mathematics textbook ever written, which established the idea of formal proof in geometry. 
2) The Elements contained many foundational propositions and theorems, including the first written proof of the Pythagorean theorem. This was important because prior to Euclid, there was no formal proof of the theorem despite its wide acceptance.
3) Euclid helped establish geometry as a formal deductive system through his use of definitions, postulates, and proofs in the Elements, which influenced mathematics and science for centuries.