We remember him today as a great hero partly for his amazing prowess in battle [1] but mostly because he spent time cultivating his own image. He was clearly interested in posterity, and he didn't want to be remembered as just another guy who killed people and took their stuff. He surrounded himself with men of letters and knowledge and of course he had his personal hiostorians, a habit that I'm guessing he helped establish among the world's kings and warlords.
Anyway, all that he did, worked- and he's remembered not as a butcher who drowned entire provinces in their blood, but as a liberator from the blunt tyranny of the barbaric Persian dynasty, as a son of Ammon who saved Egypt and gave the ancient kingdom new life, as the man who cut the Gordian knot with his brains as much as with his sword. Many since have conquered, but noone else brought so much war in his wake and gained such praise for the act -not until Napoleon.
He was mental [2] but he was a smart guy.
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[1] Seriously, Iron Man had nothing on this guy who led from the front and routinely charged ahead of his army scaling enemy walls and having to be rescued when he found himself in the thick of it with just his bodyguard to protect him.
[2] Killed the man who saved his life in battle in a fit of drunken rage during a party.