[civilized]

It's more like, high-order polynomials are fundamentally wild animals. You can use a math trick to make them to go through specified points, and to early statisticians & data analysts, this seemed like a good way to model a nonlinear trend based on a set of sample points. But that trick doesn't make polynomials tame. And it gets worse the more points you need to interpolate - you have to add a degree to the polynomial every time you want to go through another point. Each new degree makes the polynomial wilder and wilder outside of the points you're interpolating.

We later discovered that the tame functions that usually work well for extrapolating from a sample are things called splines.