Some NFL players spend their offseason working out. Others travel around the world. Baltimore Ravens offensive lineman John Urschel has done both while also getting an article published in a math journal.

Urschel, the Ravens’ 2014 fifth-round pick who graduated from Penn State with 4.0 GPA, also happens to be a brilliant mathematician. This week he and several co-authors published a piece titled “A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians” in the Journal of Computational Mathematics. You can read the full piece here: http://arxiv.org/abs/1412.0565

Here’s the summary of the paper:

“In this paper, we develop a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalue. This vector has been found to have applications in fields such as graph partitioning and graph drawing. The algorithm is a purely algebraic approach based on a heavy edge coarsening scheme and pointwise smoothing for refinement. To gain theoretical insight, we also consider the related cascadic multigrid method in the geometric setting for elliptic eigenvalue problems and show its uniform convergence under certain assumptions. Numerical tests are presented for computing the Fiedler vector of several practical graphs, and numerical results show the efficiency and optimality of our proposed cascadic multigrid algorithm.”

When he’s not protecting Joe Flacco, the 23-year-old Urschel enjoys digging into extremely complicated mathematical models.

“I am a mathematical researcher in my spare time, continuing to do research in the areas of numerical linear algebra, multigrid methods, spectral graph theory and machine learning. I’m also an avid chess player, and I have aspirations of eventually being a titled player one day.”

– See more at: http://yahoo.thepostgame.com/blog/balancing-act/201503/john-urschel-baltimore-ravens-nfl-football-math#sthash.avUHj2Tm.dpuf

Thanks to Kebmodee for bringing this to the attention of the It’s Interesting community.

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4th-and-2. Punt or go-for it?

He should be the one making that decision.

Weirdly, he’s not the first NFL player to also be a published mathematician. Frank Ryan, a professor at Rice while I was there (my wife took some of his classes) also played professionally (long before he was teaching at Rice, of course). ( https://en.wikipedia.org/wiki/Frank_Ryan_%28American_football%29 )

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My math professor in college was briefly a linebacker for the Cleveland Browns

But what is his Erdös number?!?!

4. His coauthor on this paper is Ludmil Zikatanov, who wrote a paper with Frank Deutsch, who wrote a paper with Charles Chui, who wrote a paper with Erdős.

4!

http://www.ams.org/mathscinet/collaborationDistance.html

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I was trying to draw a Venn diagram showing the overlap between NFL players and published mathematicians, but the compass pencil was too fat.

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Urschel is following in the great footsteps of Frank Ryan, QB of the Rice Owls in the 50s and the Cleveland Browns in 50s and 60s. Ryan was a good passer and had the good fortune of having running backs like Jim Brown and Leroy Kelley to hand off to. The Browns won at least one championship under Ryan. After the NFL, Ryan returned to his math studies, earned his PhD in some highly esoteric part of the field, and spent the rest of his life in the ivory tower. Not a bad way to go if you think about it. Don’t know if he ever developed dementia though.

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