If so, what circumstances allowed him to conquer the known world with so few casualties? The history podcast that cited this number states that there is some debate among military historians as to whether Alexander really suffered so few casualties over the course of his campaigns, so I thought I'd turn to actual historians to see if there is any veracity to this claim. Is this something that is widely debated among scholars in this area, or does this number merely represent a controversial claim by a single historian?
Regarding Alexander's last and most injurious victory, the Battle of the Hydaspes, Diodorus Siculus says:
Many were slain in their flight, but then Alexander, satisfied with his brilliant victory, ordered the trumpets to sound the recall. Of the Indians, there fell in the battle more than twelve thousand, among whom were the two sons of Porus and his best generals and officers. Above nine thousand men were taken alive, together with eighty elephants. Porus himself was still breathing, and was turned over to the Indians for medical attention. On the Macedonian side, the losses were two hundred and eighty cavalry and more than seven hundred infantry.
Arrian claims that Porus suffered 23,000 casualties; the Macedonians, 230 cavalry and a mere 80 infantry - but I think Diodorus' numbers are more plausible. If that's the case, then the Macedonians lost nearly a thousand men in that one battle.
With the imprecision of our sources' figures, it's impossible to say how many he would've lost in across his entire campaigns, but a medial estimate might be between 1,000 and 2,000 with high estimates exceeding that range by another thousand or two and the lowest (and unlikeliest, imo) summations coming to less than a thousand.
Edit: I decided to try a bit harder. Looking at the battle of Gaugamela, another of Alexander's biggest, the range of greek deaths reported in that fight is between >300 and 1,100; in the battle of the Grancius before that he'd lost 300-400, so I think it's safe to say Alexander definitely lost at least 3,000 soldiers totally and possibly a good deal more than that (I'm redacting my estimate ranges, those numbers were very crude guesses).