Leibniz was a noted polymath who was deeply interested in philosophy as well as mathematics, among other things. From my mathematical readings I have the impression that Leibniz's stature as a mathematician has grown in the last fifty years as some of his philosophically oriented mathematical ideas have connected with modern mathematicians and mathematics. That because of Leibniz's philosophical reflections, he foresaw aspects or parts of modern mathematics. Can anyone elaborate on these connections and recommend any references?

EDIT, Will Jagy. Editing mostly to bump this to the front of active. It is evident that Jacques and Sergey have good, substantial answers in mind. Please do not answer unless you have read Leibniz at length. I kind of liked philosophy in high school and college, or thought I did. Recently, I read one page of Spinoza and gave up.