A few weeks ago, my social media world got pretty excited that Ravens offensive lineman John Urschel and his collaborators recently published a paper in the Journal of Computational Mathematics: “A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians.” (That link is to the arxiv version.) I’m pretty sure this is the most the world has ever cared about the eigenvector corresponding to the second smallest eigenvalue of a matrix. There were quite a few articles and blog posts about his paper, although not always from the usual math suspects.
Deadspin reported Ravens lineman John Urschel loves math more than you love anything. Rolling Stone published an interview with this lover of graph Laplacians. Bloomberg informed us that one of the Baltimore Ravens just published an insanely complex study in a math journal, and I’m going to pick on them a little bit. How silly! “Oh no, I can’t immediately understand a technical paper in a field I’m not an expert in. It must be insanely complex!” It’s not that the paper isn’t impressive. The Journal of Computational Mathematics is a fine, upstanding journal, and it’s a legitimate result. But calling it “insanely complex” just makes me roll my eyes. And this isn’t just a case of a hyperbolic headline. The article, instead of presenting a gentle explanation of linear algebra or graph theory, shows us an equation-filled page to prove to us how “insanely complex” this paper is.
Luckily, Urschel himself wrote an explanatory post about his paper on Forbes. It’s clear, easy to read, and even has a few football analogies for good measure. He defines all the terms in the title and gives us the idea of what the main idea of the paper is: use simpler graphs to approximate a problem on a more complicated graph. I couldn’t use it to compute the Fiedler vector of a graph Laplacian, but I have an idea of why someone might want to.
I was unaware that the Ravens had a mathematician on the team until I heard about this paper, so I went poking around his online presence. Urschel has a bachelor’s degree in math and a master’s in math education from Penn State, and he’s taught a few classes there. He seems like a really fun guy, at least as measured in topology jokes on Twitter, and I’d like to meet him. (Sadly, my request to be his bestie has so far gone unanswered.)
Urschel also writes the Advanced Stats column for the Players’ Tribune, a relatively new website that features articles by pro athletes. There, he’s written about the transitive property as it relates to head-to-head matchups and the distribution of college majors among football players. I really admire his public math outreach, especially his constantly positive, upbeat attitude, and his defiance of the stereotype that jocks aren’t good students. (Of course, there are many college and professional athletes who show us that, but another one doesn’t hurt.) I hope that when his NFL days are over, he’ll be able to share math with students who will see him as a role model for both sports and academics.