Alexander the great conquered the Persian Empire, but he did not conquer 'most of the world' - he did not get near East Asia, he did not conquer Europe, he did not conquer most of Africa, he had never even heard of North and South America or the Pacific.
Addition:
The typical expression is that Alexander the Great conquered "most of the known world" meaning that the majority of the areas that he did not conquer were not civilized at that time.
Further:
Alexander wanted to take India, but his army refused, and is recorded to have planned on moving through Europe, with Carthage and North Africa, Italy, Sicily and Spain as targets. Even he did not think that he had conquered 'most of the known world'.
Alexander the Great of Macedon
Alexander the Great.
The most what.
Asia Minor was part of the Persian Empire. Alexander the Great took the Persian Empire by military conquest.
There is no connection between the Aztec Empire and the Persian Empire. They did not know of each other's existence.
The Persian Empire was important to Western Asia, the Mauryan Empire was important to India.
Only the Greek states of the Hellenic League (also called the League of Corinth by historians) which was a federation of most of the Greek states created by Alexander's father, Philip II of Macedon, and were vassals of Macedon, and the Kingdom of Epirus (in western Greece), an ally, had never been part of the Persian Empire. Even Alexander's own kingdom of Macedon, had been part of the Persian Empire. It had been a vassal state of the Persians for nine years (512-493 B.C.) and was conquered by the Persians in 492 B.C. and remained a fully subordinated part of the Persian Empire for thirteen years. The Thracian tribes Alexander's father, Philip II, had conquered had also been part of the Persian Empire
Alexander the Great's Macedonian Empire was the largest in size before the Roman Empire, although it was very short-lived. The largest enduring Empire before Rome was the Persian Empire destroyed by Alexander.
Alexander the Great took over the Persian Empire. After his early death his generals divided the empire into kingdoms of their own. We today call them the Hellenistic kingdoms (= like Greek).
Asia.
the Persian empire
Persia - he took over its empire.