I think that Genghis Khan's got a good case. He may have conquered less territory than Alex, but he had to use innovative tactics, military discipline and mobility to defeat some pretty well-armed and well-trained European armies, as well as the Chinese and the Arab cities of Baghdad (the greatest city in the Muslim world at the time) and Damascus. Although to be fair, I think Genghie had carked it by then - it was Ogodei (his son), Guyug, Mongke and then Kublai Khan who went on with things.
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