My first reaction to your question was The Zero, the next Infinity, but my answer is The Infinitesimal Calculus.
Creating a bridge between the two archetypal fictions 0 and * it makes sense of them. It has become a tool in just about every branch of engineering and science. It provides a language for the formulation of laws and a method for constructing explanations, solutions and predictions. It is alive: its invention in the 17th century — by Leibniz and Newton independently — articulated a concept that had long been vaguely anticipated and applied implicitly, its development is still in progress, leading to the resolution of old puzzles (e.g., Zeno's Paradox) while raising new ones (e.g., the continuum hypothesis). Leibniz had been agonizing over what he called "the labyrinth of the continuum" but the 19th century put the infinitesimal calculus on a firm basis by analyzing the concepts of a limit and of infinity from a variety of view points. Nowadays we are blessed with new developments coming from the quarter of symbolic logic that arose out of a digital (0,1) modeling of rational arguing: non standard analysis vindicates Leibniz' use of "infinitely small" non-zero quantities.