Mathematics
The Wave Equation and d'Alembert's Formula for Solutions
Quick fact
In 1746, Jean le Rond d'Alembert discovered that the solution to the one-dimensional wave equation is simply the sum of two arbitrary functions—one moving left and the other moving right—each preserving its initial shape perfectly.
Why this is interesting
If you pluck a guitar string, the bump splits into two waves that run away from each other. Could you predict exactly what the string looks like at any later time?