Often, some claim that Jesus of Nazareth didn't exist because we have no documented evidence of him from his lifetime. But Alexander was viewed (in his time) as conquring the whole world, and we still don't have written evidence from his life.
I met a traveller from an antique land Who said: “Two vast and trunkless legs of stone Stand in the desert . . . Near them, on the sand, Half sunk, a shattered visage lies, whose frown, And wrinkled lip, and sneer of cold command, Tell that its sculptor well those passions read Which yet survive, stamped on these lifeless things, The hand that mocked them, and the heart that fed: And on the pedestal these words appear: ‘My name is Ozymandias, king of kings: Look on my works, ye Mighty, and despair!' Nothing beside remains. Round the decay Of that colossal wreck, boundless and bare The lone and level sands stretch far away.”
Unless it's a matter of speech, he conquered about 3.5% of the world's land mass and about a third of the (estimated) population, neither of which put you in the top 3 and couldn't be considered the 'whole world' either. By land mass it's not even in the top 20 largest empires ever. He was unique not for the greatest empire but rather for being so primely responsible for the massive empire he did create and in doing it all in about 12 years, the British empire for example by comparison has no single persons who were so primely responsible with many leaders emerging over hundreds of years, combined with his personal role in battles, all of which ending in victory, makes him the stuff of legends.
But regardless it strikes me as a pretty ridiculous claim to make, (especially today) when an estimated 70% of the world population lived in places (they obviously know) that weren't conquered by Alexander. After all there is no 'the' known world. You can find many millions of people who have not a clue of the world beyond a few miles away and you'll thereby find many different people who each rule their known world.
It is definitely not the case that "history is (always) written by the victors".