Mathematics
The Gradient Vector as the Direction of Steepest Ascent
Quick fact
The direction of steepest ascent is perpendicular to the level curves (contour lines) of the function. Just as the steepest path up a mountain is straight up the slope, the gradient points at right angles to the lines of equal height.
Why this is interesting
Have you ever wondered which way a ball would roll on a hilly landscape? Or how a search algorithm finds the best solution? The answer lies in a simple vector that points uphill.