Mathematics
Itô Calculus and Stochastic Differential Equations
Quick fact
In classical calculus, the chain rule works because smooth functions have zero quadratic variation; but Brownian motion accumulates quadratic variation at rate one per unit time, forcing stochastic calculus to add an extra drift term—the Itô correction.
Why this is interesting
A particle jiggles in a glass of water, a stock price graphs a jagged path—these unpredictable motions inspired a calculus that turns randomness into a readable language.