[davidcamel]

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.

[vlasev]

For more such properties, check out this paper [1], section 1.5.

[1]: https://www.cs.elte.hu/blobs/diplomamunkak/mat/2009/hubai_ta...

[JadeNB]

That's neat! If you redundantly add an extra vertex (in its own component) whenever you glue, then you actually get h(x) = f(x)g(x). I wonder if there's some natural way of defining a multiplication of connected graphs so that you get equality on the nose?