He did it so swiftly it was as if they gave it to him.
But that Old Persian Empire was full of hubris, pride, and ego, and had advanced weapon technology of the day.
Was it because Alexander the Great was a brilliant commander, schooled in Greek Philosophy, understood his enemy as Sun Tzu would have advised, and conquered Persia ruthlessly as Genghis Khan did his hapless opponents? Karl von Clausewitz, as I was recently reminded by an acquaintance, noted that; "Superiority in Numbers at some point becomes overwhelming, thus insuring victory" - loosely translated of course - forgive me if I didn't get it exactly correct, but that is my understanding, that's what he meant.
Okay so, is he right? Is that what made Alexander the Greats victory so easily achievable? Not necessarily, as Alexander was quite strategic, and didn't need a superior force to win, he had the will, along with a long chain of victories, and his men believed they would win, and of course history shows they always did.
So, back to the topic is Clausewitz comment apropos? Yes, in a battle, from Karl von Clausewitz day, one could indeed make that statement.
And yet, tactics, deception, technology, weather, terrain, and force multipliers are real.
Plus, "WILL" - for instance someone defending their homeland over an hired-mercenary army intruder.
Regardless of the human competitive event; politics, sports, war - the WILL to WIN is the most important, size is important, and helpful, but it can also be a hindrance, Rommel running out of fuel and supplies for instance in North Africa.
A superior force, appropriately used, and dedicated to maximum force and the proper interval and point is surely a game changer, and it's a hard advantage to overcome.
Of course, feeding a large army is costly, and keeping up the supply chain even costlier - fuel, munitions, parts, medical, etc.
In Clausewitz's day it was appropriate for armies to gather the spoils, today, it's not and the international community frowns on it, and we do live in a global world, where alliances of the past, present, and future do matter, so, the costs of a large force must come from the army's Nation-State's treasury.
You see, Karl von Clausewitz was perhaps one of the greatest military philosophers of his time, but we do live in the present period where there are many more components to this debate of superior force.
Thus, I hope you will please consider all this.