Imagine a person so computational in nature that without being taught anything about calculus, with no means to deduce it except for his experience of the universe, suddenly, this man taught us most of what we know about calculus. But those works were not nearly the whole of Leibniz's career. As a devout religious man, as well as a rationalist and a scientist, Leibniz was defined by his bizarre affinity for mystic beliefs and scientific beliefs coinciding.
That's basically the thrust of his Discourse on Metaphysics. There must be a rational explanation, he says, between the world of material and the world past material. It is not a surprise that the same mind who invented systematic integration in calculus also viewed this realm as the differential of some other realm, perhaps a platonic formal realm. But it seems that he did not turn to Plato with these questions, instead preferring the mystic systems of the far-East. He was especially fond of Confucianism.
For that, take a closer look at his Monadologie. What is a monad anyway? A monad is a fundamental particle much like subatomic particles which correspond to various forces. Hundreds of years before such discoveries would be made in science, Leibniz published this essay, arguing that these subatomic particles called monads were responsible for the intelligibility of the universe, because they are perceiving it. In other words, he saw that the universe, if it is intelligible, must rely on an intuition much more basic in nature than animal life. Therefore, he concluded that the universe is made up of an infinite amount of infinitely small beings that have perspectives and points of view which are combined when those being start to represent larger bodies.
So basically, Leibniz sees the universe as a living organism where each 'cell' of the organism is a living being in its own right. But he didn't just apply this view to organic life. He also applied it to non-organic matter, meaning that basically, at every conceivable level, the universe is perceiving itself.
