Was Alexander the Great really "Great"?

In my opinion, I believe Alexander the Great really was great. He conquered numerous amounts of civilizations, built his own successful empire from the ground up, and died young at the height of his power with high honor and dignity. When he was at the young age of 20 he inherited and took full responsibility of the huge empire of Macedon, that had complete control of Greece. He then invaded Persia and fully conquered it within 10 years along with having control in Egypt, and expanding to Iran, Afghanistan, and even India. Along with spreading his own empire, he also was responsible for spreading the Greek culture and their extensive education throughout the eastern hemisphere as he expanded. Accompanying his superb leadership was his idealism. He was one of the first to integrate people of other cultures into his army and administration. Persians and Asians made up large quantities of his societies and he made sure they had some important roles. So, in a short span of 12 years he managed to conquer societies from Europe to Southeast Asia and be worshiped highly by not only his own people but by those he conquered too. They thought he was great then and he certainly still is great now.