> According to a strengthening of the theorem, every finite point set (not all on one line) has at least a linear number of ordinary lines. An algorithm can find an ordinary line in a set of n points in time O(n log n). [1]

There are many such lines (think convex hull) and they are easy to find. This makes it hard to appreciate the theorem. You keep thinking oh whats the big deal.

[1] https://en.wikipedia.org/wiki/Sylvester%E2%80%93Gallai_theor...