Mathematics
The Heat Equation and Its Fundamental Solution
Quick fact
The fundamental solution of the heat equation is a Gaussian (bell-shaped) curve, and its 'width' grows as the square root of time. This means heat spreads infinitely fast in a mathematical sense—the temperature at any faraway point becomes nonzero instantly, though vanishingly small.
Why this is interesting
Imagine placing a drop of ink in a glass of still water. The ink spreads out slowly, becoming fainter but covering a larger area. The heat equation is the mathematical law that predicts exactly how that spreading happens.