Most important invention: CALCULUS
The world today would be very different if the Greeks and not Newton/Leibniz had invented or "discovered" calculus. The world today might have occurred a millennium or two earlier.
Calculus was the real fruit of the renaissance. It began by taking a fresh look at infinity — at the infinitely small rather than the infinitely large. And it led in one stroke to two great advances: It showed how to model change (the differential equation) and it showed how to find the best or worst solution to a well-defined problem (optimization). The first advance freed math from static descriptions of the world to dynamic descriptions that allowed things to change or evolve in time. This is literally where "rocket science" becomes a science. The second advance had more practical payoff because it showed how to minimize cost or maximize profit. Thomas Jefferson claimed to have used the calculus this way to design a more efficient plow. Someday we may use it to at least partially design our offspring to minimize bad health effects or (God forbid) maximize good behavior.
Calculus lies at the heart of our modern world. Its equations led to the prediction of black holes. We built the first computers to run other calculus equations to predict where bombs would land. The recent evolution of calculus itself to the random version called "stochastic calculus" has led to how we price the mysterious financial "derivatives" contracts that underlie the global economy. Calculus has led us from seeing the world as what Democritus called mere "atoms and void" to seeing the world as atoms that move in a void that moves.