A Simple Proof of the Sylvester–Gallai Theorem

The Sylvester–Gallai theorem states that any finite set of points in the Euclidean plane, not all collinear, has a line passing through exactly two of them. This article presents a concise proof by mathematician Leroy Milton Kelly, using the concept of a point-line pair with minimal distance. Assuming a line contains more than two points leads to a contradiction via similar triangles, proving the theorem elegantly.