Mathematics
The Method of Separation of Variables for Partial Differential Equations
Quick fact
Separation of variables was pioneered by d'Alembert, Euler, and Fourier in the 18th century, and it is the reason Fourier series were invented.
Why this is interesting
You have a complicated equation that describes how heat spreads through a rod, or how a drumhead vibrates. Wouldn't it be great if you could split it into simpler pieces and solve each one separately?