For This Professor, Combinatorics Class Is Where It Counts

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Dartmouth President Philip J. Hanlon ’77 explains why he continues to teach.

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Philip Hanlon teaching math class
President Philip J. Hanlon ’77 leads his Introduction to Combinatorics class in Kemeny Hall last month. “I love to do it,” he says. “I also feel that teaching is the most important work we do at Dartmouth.” (Photos by Katie Lenhart)
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The Hanlon Years

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As a Dartmouth undergraduate, President Philip J. Hanlon ’77 thought he was done with math.

“I had taken a couple of mathematics classes and was not particularly turned on by them, so I wanted to major in something else,” he says. But before he gave up the field for good, an adviser persuaded him to try Math 28: Introduction to Combinatorics, at the time taught by Joan Hutchinson, a John Wesley Young Research Instructor in mathematics.

Combinatorics is an area of discrete mathematics concerned with counting and the structures of finite sets of objects.

“I fell in love with the subject from the very first day,” says President Hanlon, who was drawn to the field’s emphasis on rigorous reasoning, as well as to its long intellectual tradition.

“It was great to know that there was a whole body of work that had been developed over hundreds of years. This is the course that set me on the path to becoming a mathematician. I’ve taught it for 40 years, and I still find the material incredible.”

During winter term—and for the last time in his dual role as president and professor before he steps down from the former in June—Hanlon has once again stood in front of a Kemeny Hall classroom to lead Math 28 students through proofs of combinatoric theorems, which he writes out on the blackboard in swift, legible chalk (“a dying art,” he says).

If you were ever asked in elementary school to figure out how many ways you could make change for a dollar, you’ve done simple combinatorics. “It’s probably the most common kind of math you move into from an early age,” Hanlon says. At its more advanced levels, combinatorics has crucial applications in computer science, probability, statistics, and other fields.

On a recent visit to the class, Hanlon’s Math 28 students—about 20 in all—were deeply engaged in graph theory, considering the minimum number of colors a planar graph can use without the same color abutting itself. Hanlon drew a simple graph of three vertices on the board, and the students easily developed a formula to determine the colors. But they soon found that adding a fourth vertex complicates the problem.

“It’s simple to see, but hard to compute,” Hanlon told them. “We need a method—a fundamental theorem of graph coloring.”

Hanlon conducts the class as a lecture, but continuously asks questions, taking a Socratic approach to honing students’ logic.

“I put a lot of thought into how I can divide the material into focused pieces so that we can reason together in class about each step,” he says. “I’m moving fast in this class, and they seem to be keeping up. So they’re up to the challenge, and it’s my job to help develop their intellectual capacity.”

Joana Lame ’23, a chemistry and Italian major from Albania, has found the class—and regular office hours in Hanlon’s Parkhurst office—accessible and welcoming.

“Professor Hanlon is very open to discussion and always encourages us to talk things through,” says Lame, who plans a career in medicine. “He truly encourages active learning, which I appreciate. As someone who hasn’t taken as many math classes and doesn’t have the strongest background in the class, it’s very helpful.”

Julia Redstone ’24, a math major and art history and religion minor from Bellingham, Wash., describes Hanlon as “the quintessential Dartmouth professor: chatting with students before class, eager to learn more about what each of us studies, how our weekends were, what winter sports we’ve partaken in recently. He is patient at explaining confusing concepts, fostering a comfortable environment for us to ask questions.”

On the other hand, Redstone observes, most Dartmouth professors don’t occasionally leave class early to meet with trustees or the leadership of the NCAA.

No matter how demanding his administrative duties, Hanlon has made it a priority to teach at least one term a year throughout his presidency—not unlike one of his own former professors, President John Kemeny.

Asked why, Hanlon says, “Number one, I love to do it. It’s especially important to me to have a set of students that I see on a regular basis and get to know as people. But I also feel that teaching is the most important work we do at Dartmouth. Ultimately, Dartmouth will be measured by its positive impact on the world, and we achieve that impact by preparing students to lead lives of leadership and impact. So it’s important for me to be part of that work of creating a quality of mind in our students that can allow them to be highly successful.”

Time spent in the classroom is also energizing, he says. “There’s really nothing more exhilarating than that moment when you can see that students are getting it. I think we all teach for those moments. It’s a daily reminder of why we do this.”

“It was a privilege to be in a course taught by President Hanlon and to see what a genuine and great person he is,” says Carmen Braceras ’20, who majored in economics at Dartmouth and is now an associate at Northlane Capital Partners in Maryland.

As a junior, Braceras took a Sports Analytics class co-taught by Hanlon and Michael Herron, the Remsen 1943 Professor of Quantitative Social Science. “One of the reasons I chose to attend Dartmouth was the small class sizes and the attention that professors provide their students. President Hanlon’s leadership showed that those values are at the core of the administration, as well,” Braceras says.

Redstone agrees. Having Dartmouth’s president as her professor “speaks volumes about the Dartmouth community and the incredible opportunities afforded to Dartmouth students to meet anyone and do anything,” she says. “To me, the fact that President Hanlon has made a commitment to teaching while in office embodies the culture of the Dartmouth faculty and its commitment to teaching undergraduates.”

Though his 10-year tenure as president is coming to an end, Hanlon plans to return to the classroom after taking a sabbatical and enjoying some travel with his wife, Gail Gentes.

“I hope to keep at it for at least a few years,” he says.

Hannah Silverstein