It puzzles me that Alexander managed to move so fast from one recently conquered territory to the next target.
How did he have the courage of leaving his back exposed as he advanced, his escape route?
Yes he left garrisons here and there, he appointed viceroys sometimes from among the local population but that doesn't explain it.
Romans had trouble securing their back anytime they had an incursion in new territory, take Gaul and Britannia as examples or even Trajan's conquest in Mesopotamia. Heck, they tried to pacify some regions for decades and barely managed.
So how did he do it?
The legendary /u/iphikrates provided an excellent answer to this exact question.
The answer by /u/Iphikrates along with his previous post is fantastic. I wanted to add at least one point that I don't think was mentioned very much here or in the previous linked post to do with Alexander's choice of carefully choosing the order in which he occupied territory.
If you were to take a course on Alexander's campaign, one of the points that you may hear a lecturer drill into your head (as mine did) was the importance of sea power. Alexander controlled a top notch army thanks largely to his father Philip, but did not have much in the way of a fleet to match his Persian adversaries. To counter this, he sought to deny the coastline to his enemies by rapidly advancing along the Mediterranean. Arrian sums the strategy up in The Campaigns of Alexander with a favorable omen wherein an eagle was spotted as Alexander and one of his top generals Parmenio considered engaging with a numerically superior Persian fleet. Alexander stated that as the eagle had been seen on shore, it clearly indicated his army, not his navy would render the Persian fleet powerless and that he planned to win the sea battle from land.^(1)
The aim of Alexander's conquests remained heavily focused upon the coastline of the Mediterranean which was controlled by the Persians from Asia Minor (modern Turkey) all the way to Egypt. And if you consider the strategy of rendering the superior naval forces of Persia powerless by denying them access to any and all ports within that region it helps to explain both the path of Alexander's conquests and why he felt so confident when he finally began moving eastward into the Persian interior. By controlling access to the ports, he basically secured the western border of his conquests and could advance without worrying about fresh armies appearing behind him.
P.S. - As this is my first post here of any significance I just wanted to thank /u/Iphikrates again for their post as it gave me a great format to follow!