Should Alexander be referred to as "The Great"

In my humble opinion, I believe that Alexander of Macedon truly deserves the title of "the Great". He grew up in a small kingdom, one that you wouldn't think could spawn the person who would conquer much of the known world. Between 336 and 331 BCE he had conquered Ionia, Antolia, Syria, Palestine, Egypt, Mesopotamia, and was preparing to do battle with the biggest empire of the world at that time, Persia. By 330 BCE, Darius III, the ruler of Persia, was dead, and Alexander was free to conquer all of southwest Asia and into India, creating one of the largest land empires of the ancient world, second only to that of the Mongols.

Ok, first off, the guy was ballsy. At the start of his campaign, he only had 37,000 troops, compared to the numbers in the hundreds of thousands he'd have to face against Persia. Secondly, he was an insane strategist. He found his army in what seemed to be unwinnable scenarios a lot, sometimes where they were entirely surrounded, and yet he found the opposing army's one week point, broke through, and destroyed army #2. Third, he marched his army all the way across the most barren, desert terrain on the earth, kept their spirits high and mighty, and encouraged them to conquer one society after another after another. The guy was a natural born leader. Not to mention he did this all before he turned 30. NBD. So ya, if you come to me and say "Should Alexander be referred to as 'the great'?", I'll probably give you a sarcastic look, and then reply "No. He should be referred to as 'the Greatest'."