October 23, 2013 at 5:32 pm

# If Penn State's John Urschel doesn't make NFL, he can always teach integral vector calculus

###### John Urschel will attend the NFL scouting combine in February. (Gene J. Puskar / Associated Press)

State College, Pa. -- The students in Math 232, integral vector calculus at Penn State, can watch their teacher perform on two stages this fall.

One is their yellow-walled classroom in the Willard Building.

The other is Beaver Stadium.

The teacher is John C. Urschel, the 305-pound starting right guard for the Penn State football team, a first-team All-Big Ten selection, and an NFL prospect.

Urschel finished his undergraduate math courses in three years, earning a perfect 4.0 grade-point average. He earned a master's degree last year, and had math research published in a scholarly journal. He has several more papers in the works, including one in a branch of math called spectral graph theory, and plans to pursue a Ph.D.

The broad-chested lineman likes to talk about his football accomplishments, because he did not begin the sport until ninth grade and has had to work hard to reach the upper echelon. Indeed, his coaches say he can make it to the pros. This is his final season of college eligibility, and he plans to attend the NFL scouting combine in February.

But we are here to talk about his math, because, let's face it: How many football players would tweet the following joke?

"There are two types of people in this world: Those who can extrapolate from incomplete data." (Get it? Can you?)

"Some ... can paint."

### The whys and hows

As students trickled into Urschel's classroom before 8 a.m. on a recent Thursday, he teased junior Michael McNamara for handing in an especially thick packet of homework.

"Do you have the right textbook? I'm pretty sure your homework is as thick as their three combined," Urschel said, indicating three classmates who sat nearby.

Then he quickly got down to business. The 22-year-old math teacher was dressed like a student, wearing shorts despite an outdoor temperature of less than 50, but his demeanor was one of professorial confidence.

First, he gave a quiz. Then he strode about the room, covering two walls' worth of chalkboards with equations and functions. He spurred on the class with encouraging words.

"Not quite," Urschel told one student who tried unsuccessfully to answer a question. "But you're thinking."

Most of the students were engineering majors who had to take the class as a prerequisite. Urschel was a budding engineer, too, in his freshman year. But he soon switched to pure math, realizing he enjoyed exploring the elegant "whys" and "hows" of mathematical proof, rather than just using formulas as a tool.

His road to research began during an advanced calculus course in his sophomore year, when professor Vadim Kaloshin noticed that Urschel was getting 100s on every test and quiz.

Kaloshin asked Urschel whether he would like to do some research outside class and suggested he prepare by reading a portion of an advanced text for several months.

Urschel tore through it in two weeks.

He eventually co-wrote a paper titled "Instabilities in the Sun-Jupiter-Asteroid Three Body Problem" -- a 27-page treatise on how the path of an asteroid is perturbed by Jupiter and the sun.

"It could have been a reasonable Ph.D. thesis in mathematics," said Kaloshin, who is now at the University of Maryland.

These days, when Urschel is not teaching or plowing into opposing players, his research includes exploring a field of math called computational finance. His paper on barrier options, a type of financial derivative, has been accepted for publication.

He is the real deal, says Penn State math professor Ludmil T. Zikatanov, who works with Urschel on graph theory.

"This kind of intuition, you don't build it. You kind of are born with it," Zikatanov said of skills like Urschel's. "Some people can paint. Some cannot."

Plenty of big-time football players have starred in the classroom, and a fair number have gone on to careers in academia. But mathematicians?

Let's just say math whizzes tend to be better at describing the properties of a prolate spheroid than they are at throwing and catching it.

One of the very few to excel in both areas is Frank Ryan, who quarterbacked the Cleveland Browns to a championship in 1964, then earned his Ph.D. in math from Rice University the following year.

Ryan continued to play pro ball even after starting to teach. At Case Institute of Technology, a forerunner of Case Western Reserve, he once had to write mathematical proofs on the blackboard with his left hand because his right arm was in a sling from a football injury.

Ah, the injury issue. What about putting such a valuable brain in harm's way?

Urschel gets that question a lot, especially after the lawsuit by former NFL players who alleged the league did not protect them from concussions.

Urschel said he has not had any concussions and does not worry about it.

"I enjoy playing football," Urschel said. "I understand the risks that I take. I thought about it once, and I really haven't seen the need to think about it again."

### Early signs

Urschel's father, also named John, is a retired thoracic surgeon. His mother, Venita Parker, is a nurse-turned-lawyer.

She said signs of her son's math prowess were evident from a young age, growing up in the suburbs of Buffalo. He continually asked for more educational puzzles and games, typically ones designed for kids several years older.

When Urschel was 8, Parker started her own game. Whenever she bought something at a store, she let her son keep the change if he could calculate the right amount faster than the store clerk. That game lasted about a month, because it was too easy.

She switched to a similar game that involved calculating percentages. That one didn't last long, either.

"Anything I could make a math game of, he'd be like, 'C'mon mom, let's do this! Let's do that!' " she recalled. "There was that spark in his eye."

Urschel, who is working on a second master's degree, in math education, said he wants to transmit his enthusiasm to students.

"I feel bad for kids who go through the math system and really miss out on the beauty of math," Urschel said. "I feel like sometimes when they're teaching kids math, they really focus too much on just computation, doing problems. They treat it more like a methodical exercise."

Students say he is getting it right. McNamara, the student with the thick homework packet, gave his prof high marks, praising his ability to explain tough concepts in a laid-back manner.

McNamara, a junior from Allentown, Pa., who majors in electrical engineering, has seen Urschel play on the football field and said it was pretty cool to see him in front of the blackboard.

"Having him as your teacher is crazy."