How models actually learn, from vanilla gradient descent to Adam
First-order methods use gradients. Second-order methods also use curvature, usually through the Hessian. Curvature tells the optimizer how the gradient itself changes as parameters move.
Newton's method uses that curvature to choose a step that can jump directly to the minimum of a quadratic. The price is that Hessians are huge in modern neural networks.
A crane operator uses a load chart because direction is not enough. The load also bends the boom, and that bend changes what move is safe. Second-order optimization reads the bend, not just the pull, before deciding how far to move. In the figure you play the operator: slide the two curvatures and watch the surface become a bowl, a dome, or a saddle. The Hessian's eigenvalues are exactly those two knobs.