In addition to his youth and enthusiasm, which inspired his troops, Alexander actually knew how to keep them from dying, while plundering the hell out of every territory he came to. This was important to his soldiers, as there was little point in attacking a place if you were too dead to enjoy the traditional victory rape/plunder.
It began to be whispered – then screamed in utter terror – that Alexander was a tactical genius. Early scoffing that he simply had a supernaturally good PR team was quickly proven wrong as the scoffers were either A) killed, or B) forced to swear allegiance. This latter was the key point: a tiny band of Greeks could not bestride the known world like a colossus, no matter how many poets might say so – but if you got everyone you conquered to turn their troops over to you, you could get along just fine.
He invaded the Achaemenid Empire, which you’ve never heard of, but which stretched from Macedonia to Pakistan, and included Egypt, nearly all of Asia-minor, and the entire Tigris-Euphrates valley, making it easily the largest empire the world had ever seen and claiming boundaries nearly identical to those Alexander later boasted about.
The Achaemenids had two critical weaknesses: first they didn’t bother with all that carving monuments nonsense (to be more accurate, they were a confederation of many peoples, most of whom did carve monuments - but about themselves, not the Achaemenids, which everyone had trouble spelling, thus explaining why you’ve never heard of them). Secondly, they were astonishingly civilized: they had a postal system, well established communications and trade routes, fostered by a huge network of well-made roads, and had established Aramaic as the official language of that entire region. All of these accomplishments are awesome during peacetime – but can become inconvenient during an invasion.
Alexander attacked the communications and trade routes, marched his army up the well-made roads, and featured prominently in the increasingly frantic letters clogging up the postal system. Fortunately, nearly all the screaming was in Aramaic, so pretty much everyone was able to understand who was causing it. The borders of the Empire he eventually conquered were suspiciously similar to the borders of the Achaemenid Empire, except, of course, for the addition of Greece.
Each territory he conquered had already sworn fealty to the Achaemenids, and they quickly decided they’d be better-off switching sides and swearing fealty to Alexander than getting themselves killed for an empire that no one was going to remember later, because no one could spell its name (later historians would get around this by calling it 'Achaemenid Persia', then just 'Persia', on the grounds that the guy running it lived in Persia, and that history would remember what historians damned-well told it to, whereupon everyone heaved a great sigh of relief, and got back to the important business of dying under Alexander's sword.)
As Alexander conquered territories, each was left with a ruler he chose, or endorsed, and a small army of occupation from another territory. This last bit was the genius move: a ruler is pretty much unable to revolt without his own army. It allowed Alexander to keep his own band of Greeks intact, but left a force behind that had no local loyalties – everyone knows it’s easier to oppress someone else’s people, than your own!
At some point, some of Alexander’s enemies got together and decided that, since Alexander was kicking their asses with Greeks, maybe they could even things out by hiring some other Greeks – specifically, a guy named Memnon, and his Greek mercenaries. Memnon, was a competent, if ruthless, general and advised what would today be called a "scorched earth" campaign: burn all the crops in the Villages that Alexander would have to pass, thereby starving Alexander's army. Either they'd get sick of being hungry all the time and go home, where the crops were doing quite nicely, thank you, or they'd continue, but be too weak for battle.
The Achaemenids, who in this case actually were Persians, decided that Memnon couldn't be trusted because he was a Greek – despite the fact that they'd hired him for that specific reason. The Earth remained unscorched, and Alexander's army breezed through. While historians are silent on the matter, we can assume that the army pretty much ate whatever they damned-well pleased, and thus were not falling down with weakness when they finally came to battle with the Persians.
It really ought not to come as a surprise to anyone that the Greeks kicked the hell out of them – so badly, in fact, that when the vast majority of the Greek foot soldiers arrived on the battlefield, they found everyone had already been defeated by, and fled from, Alexander’s cavalry – all but Memnon and about 18,000 of his men, who figured Alexander would be merciful, either because A) "we're all Greeks here" or B) "we're mercenaries - it was nothing personal!"
When it came to them all being Greeks, Alexander must have belonged to a different Fraternity; he wasn't impressed, and he couldn't help but notice that those Greeks had been completely ok with killing his Greeks. As for them being mercenaries, hey, Alexander was a king, he knew it wasn't personal, knew it was just business ...
So he ordered his men to impersonally kill all of them in a businesslike fashion.
He's said to have relented and sent 2,000 of them back to Greece as slaves, but one has to wonder if this 'mercy' might have been motivated by his men: slaughter is loads of fun, after all, but after the first 16,000 or so, it may have been getting a little boring.
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