Much before the world had seen Alexander, in the 6th century BC, King Cyrus established an empire which extended from Egypt to the Indus. Since then, Takshashila was invaded numerous times and it emerged as the cosmopolitan town of the east where great scholarship emerged. It was a historic meelting pot of the east and the west, just like millenias later, Dharward would become the melting pot of the north and the south Indian musical culture.
Takshashila is mentioned as a place of learning in the pre-Buddhist Jataka tales. In fact Takshashila was a well-known place even before Buddha. According to Ramayana, the city was founded by Bharata who named it after his son Taksha. According to Mahabharata, Janamejaya held his court in Takshashila. It was in this city that Panini produced one of the greatest achievement in grammar and Chanakya composed his book on statecraft.
It must be understood that, there never existed one single Takshashila university in the modern sense. Each teacher formed his own institution, teaching as many students as he liked and teaching subjects he liked without conforming to any centralized syllabus. If a teacher had a large number of students, he used to assign one of his advanced students to teach them. The same way some cities like Boston and Kota are better at education than other for no apparent reason but the fact that it attracts both good teachers and students all the same.