Plato is most famously associated with the idea that philosopher-kings should run the government. In his work "The Republic," he argues that the most just and effective rulers are those who possess both wisdom and virtue, and thus should be philosophers. This idea is central to his vision of an ideal society.
While Plato did not directly tutor Alexander the Great, his student Aristotle did, and while Plato himself was not condemned to death by poison (that was Socrates), he was profoundly influenced by Socrates' ideas and methods.