In many books, articles, or even in folktales, whenever Alexander III of Macedon (referred to as Alexander the Great) is mentioned, it is said that he conquered the world. Even some historian say that he conquered the world, most of the known world at that time.
But if we look at the Macedonian empire at its apex under Alexander we can see that he only controlled a very small part of Europe, most of the central Asia, and part of Africa (Egypt). That map does not include the two biggest & oldest civilizations, India & China.
Alexander did try to enter India, but he was unsuccessful. The reasons for his retreat are ambiguous, ranging from fear of mutiny among soldiers, defeat in India to a very costly victory against a small kingdom in India. Apart from these, until now I've never heard that Alexander had any plans to invade China. (India was much closer & accessible than the Chinese heartland).
Having stated this information, why do people say that Alexander the Great conquered the world? If there are any reasons then what are they?, Why do the conquests of Alexander have so much significance?
Editing my question to clarify intentions. A good answer by the @DevSolar, but only provides numbers as facts. I asked the question from non greek point of view. Yes I've read the concept of Hecataeus map, and as per it yes he indeed conquered the world. But that does not change the fact that a far greater part of civilised world remained unconquered by greeks. So the intention of me asking was why this concept in so prevent in cultures across world that Alexander conquered the world? Why it was not falsified as we grew in knowledge about world?
I know many times, the term 'known world' is used instead of 'world' which best describes this scenario. But I am more interested in the cultural & historical impact of the Macedonian empire which might have strengthened the belief to this extent.