I majored in math in undergrad, and I always daydreamed about solving difficult mathematical problems despite a lack of formal training. I even had a teacher that I had to "pretend to understand".

Seeing a real-world example of this fantasy come true is fascinating. The article was also surprisingly well-written; most mention of higher mathematics in the media is oversimplified to death, but this was an honest and yet approachable presentation of the Rota conjecture (now theorem).

By the way, here's another result on chromatic polynomials (proved first by I don't know, but re-discovered by my combinatorics class):

Define a "gluing" operation by taking two graphs and connecting them along a common vertex.

The chromatic polynomial, h(x), of the new graph, is the product of the chromatic polynomials of the subgraphs over x: h(x) = f(x)*g(x) / x.