The Sylvester–Gallai Theorem

> Every finite set of points in the Euclidean plane that is not collinear has a line that passes through exactly two of the points.

I can't make out the point here (no pun). Of course a line can pass through any two points. It could pass through three if those points were collinear but the statement says they're not. So what is the new fact?

I might be too stupid to understand why this is interesting and useful. If it helps I am a working physicist, and a lot of pure math is lost on me. I think I followed this, but I don't know why one would care or this would be interesting.

Futility closet is fantastic!