The mathematics of change and the infinite — its two halves, the derivative that measures how fast something changes at a single instant and the integral that accumulates infinitely many tiny pieces into a whole, bound together by the fundamental theorem that makes them inverses: the tool that caught motion in the act and let humanity write the laws of a moving, flowing, continuous world.
Calculus is the mathematics that caught motion in the act. It learned to measure how fast something is moving at a single frozen instant, and to add up an infinite run of tiny pieces into a whole, such as the area under a curve. Two men reached it independently within about a decade of each other: Isaac Newton around 1666, building a tool to do his physics, and Gottfried Wilhelm Leibniz around 1675, with the cleaner notation we still use today. Their followers then spent a generation accusing each other of theft. The feud was bitter, but the mathematics was sound, and almost every law of modern physics is written in it.