The pi-reciting professor retired from teaching in August 2023 but still has campus ties.

Sidney “Denny” Gulick III is something of a celebrity at the University of Maryland. Alums of all ages and educational backgrounds remember taking one of Gulick’s math classes.
“Everywhere I go in Maryland, I meet people who enthusiastically recall a great teacher they had for calculus, and it almost always turns out to have been Denny, even if it was several

decades ago,” said UMD Mathematics Professor and Associate Chair for Undergraduate Studies Larry Washington. “He's responsible for many people's fond memories of UMD.” 

On August 1, 2023, Professor Gulick retired from teaching after 58 years at UMD, but he hasn’t gone far. He continues to handle class scheduling as the Department of Mathematics’ associate chair for course staffing, a role he’s had for nearly 20 years.

His time in the classroom may have ended, but Gulick said teaching is in his blood—and not even retirement can change that. 

“My father, grandfather, great-grandfather and great-great-grandfather were all teachers. My wife was a teacher, and so was our son and our daughter,” he explained. “Teaching is a part of my system.”

3.14 (and many more)

Gulick is well-known across campus for his ability to recite 100 digits of pi from memory—a feat he demonstrates with the speed of an auctioneer during the annual Pi Day Celebration hosted by the College of Computer, Mathematical, and Natural Sciences. He has been honing this skill ever since a childhood accident claimed his left eye.

“When I was two years old, I tripped and fell on a spike that went through my eye, and at five I became nearsighted. My father didn’t think I should be reading very much because it might hurt my eye, so he gave me multiplication tables, and I learned them really well,” Gulick recalled. “Then he gave me pi to memorize to 15 places. I’ve loved mathematics ever since.”

Gulick’s interest in math flourished in adulthood. He earned a bachelor’s degree in mathematics from Oberlin College and a Ph.D. in the same subject from Yale University. He then did a two-year instructorship at the University of Pennsylvania before joining UMD in 1965, explaining that it was an exciting time to be a scientist.

“Sputnik went up in the late 1950s, and by the early 1960s there was a huge demand for mathematicians and physicists and engineers,” he said. “I was one of 10 math professors to come here in 1965, and the next year there were 18.”

Not long after joining UMD, Gulick met his future wife, Frances, then a postdoctoral fellow who became a longtime lecturer in the math department until her retirement in 2018.

“Every Tuesday evening, we had a seminar in functional analysis at a colleague’s home and Frances would cook for us,” Gulick fondly remembered. “That’s something I relish.”

Over the years, Gulick became a staple in the math department, gaining a reputation for his 8 a.m. calculus courses and charming catchphrases. “Don't fall into the abyss,” he’d often tell his students—a plea to carefully check their work to avoid crucial miscalculations. 

“I have always claimed that there needs to be a little bit of humor in math classes. There needs to be a little bit of smiling,” Gulick said. “My whole goal was for them to learn as much as they could realistically learn without giving them psychological crises.”

‘A lasting impact’

Beyond teaching, Gulick helped mold mathematics curricula at UMD and across the state. He served as the undergraduate chair of UMD’s math department from 2003 to 2006 and was a longtime chair of the Statewide Mathematics Group, an organization of mathematicians from colleges and universities across Maryland. During his career, Gulick co-authored six editions of a calculus textbook and another on chaos theory and fractals—one of his favorite areas of mathematics.

Many of his roles extended beyond his department. Gulick judged high school science fairs and hovercraft competitions, co-chaired an East-Asian Science and Technology Group at UMD, and served on thesis committees (mostly in music, a personal passion of his). 

For many years, he and his wife sent hundreds of “friendship dolls” to schools in Japan, continuing a family tradition started by his missionary grandfather, Sidney Gulick, in the 1920s. The dolls started as a token of kindness to foster cross-cultural understanding between the U.S. and Japan at a time of heightened tensions. Today, they continue to be a treasured gift.

Gulick and his wife now live in a retirement community in Silver Spring, Maryland. He hopes to take more trips to Yosemite National Park—his “favorite place on Earth”—and to their son’s family home in New Hampshire. Gulick, who plays cello, and his wife, a pianist, also plan to fill their free time with music, looking forward to many more duets together. 

At UMD, Gulick’s teaching legacy lives on. Jim Yorke, a Distinguished University Professor Emeritus of Mathematics at UMD, said Gulick’s many contributions won’t soon be forgotten.

“He has always been proactive and vocal when he sees things that need fixing and he never shies away from a challenge, but more than that, Denny is a wonderful person to work with and to know,” Yorke said. “We are so grateful for his service and dedication to our department and to our students. He has made a lasting impact on the department.”

Written by Emily Nunez

A math degree and a passion for hockey helped Brian Carothers (B.S. ’13, mathematics) score his dream job in sports data analytics.

Brian Carothers (B.S. ’13, mathematics) was just 6 years old when he picked up a hockey stick for the first time. Fascinated by the game and inspired by his hometown team, he knew he’d found his passion.

“When I was six, the Pittsburgh Penguins, my favorite team, went on a deep run to the conference championship and it was just a perfect storm of right place, right time,” Carothers recalled. “I just completely fell in love with playing hockey. I was constantly playing in my driveway, my neighbor’s driveway, the street, and it became an obsession, one of my favorite things growing up.”

Many years later, Carothers still loves hockey. And he found a way to make a career out of it—not by taking shots on the ice, but by making an impact behind the scenes. In 2022, Carothers joined Big League Advantage, a D.C.-area investment company that offers financial support to help talented amateur and minor league athletes achieve their dream of a career in professional sports. 

As a data scientist, Carothers leads BLA’s hockey division, developing models, predictive statistics and analytics to measure the value and performance of promising players around the world. It’s difficult, complicated work—and Carothers wouldn’t have it any other way.

“Sports data is incredibly challenging to work with,” Carothers said. “It’s messy, it’s incomplete, there can be small sample sizes, so it requires a unique way of thinking and problem-solving—and I love it.”

A major decision for math

In 2008 when Carothers arrived at the University of Maryland as a freshman, he was still passionate about hockey, but not so certain about his future. His major changed more than once, but when he started taking college-level math and statistics classes he suddenly realized exactly where he belonged. And no one was more surprised than he was.

“If you told me in high school or even my first two years at Maryland that I was going to have a math degree I would have laughed—but I discovered that I really liked it,” Carothers explained. “Math is a way of critical thinking where you’re trying to piece together the information that you know and ways to link that information in ways that are new to you to solve or prove things. It’s like a big puzzle where you’re trying to connect the dots—and that’s what I fell in love with.”

Though Carothers still wasn’t sure what he was going to do with math career-wise, he was confident that with a strong math skill set under his belt, he’d be able to figure that out.

“I finally decided that any door that I wanted to be opened later on down the line, math will be able to open that for me,” Carothers said.

After he graduated, Carothers landed an accounting job with a Maryland construction company. Meanwhile, he was still watching hockey whenever he could and developing a growing interest in the statistical side of the sport. Especially intrigued by programming, Carothers enrolled in a four-month data science boot camp, which inspired him to start experimenting with hockey statistics in his spare time.

“I was starting to build my first models for getting a player rating—one number that encompasses how good I think they are—and this was incredibly basic since I was still really new to data science back then,” Carothers recalled. “It was really fun, but I remember at the time my friends were like, ‘What are you doing? Why are you spending all your free time doing this?’”

In 2017, thanks to his boot camp training, Carothers shifted into a new professional role as a data science manager and consultant, developing systems and products for a variety of business clients. But he was determined to make hockey his career. His first opportunity came a year later with an offer from Analystics Hockey Data Science, a tech startup aimed at providing data analytics to teams in the National Hockey League. 

“We were creating a product to help general managers manage everything about their team—the salary cap, their players, all of that,” Carothers explained. “Our twist was that instead of a player rating, like this guy’s a 5.3, we would try to put his value in terms of salary cap dollars. Is the team getting the most for their money?”

For Carothers, it was a perfect opportunity—while it lasted. After COVID hit in 2020, pro hockey essentially shut down and so did the startup.

Taking another shot

Two years later, Big League Advantage gave Carothers a shot. Launched by a former professional baseball player, the company uses predictive algorithms to identify rising stars in sports and invest in their careers, offering an upfront investment to help pay the players’ expenses in exchange for a future percentage of their professional sports earnings. The company invested in baseball, football and basketball athletes. In 2022, when Big League Advantage decided to add hockey, the company offered Carothers a job.

“They decided they wanted to get into hockey and when they started looking for people, they found me,” Carothers said. “I could be a one-man team and get things running. It’s what I’ve been doing for fun all these years and now I’m doing it for real. I spent about a year just getting all of the data together—that’s how long it took before I could even start to build models and do my real job.”

Now, as BLA’s data scientist for all things hockey, Carothers is assembling mountains of data and developing hockey-specific analytics to identify the most promising players in the game, applying the statistics and problem-solving skills he learned in his classes at UMD.

“The heavy math that I do is typically statistics,” he explained. “I use probably 20 or 25 different sources of data for different amateur leagues around the world, from salary cap information to starting lineups,” he explained, “and we also use advanced statistical data. There are other data sources out there where they tell you every pass, every shot, where the players are on the ice, and these things are really valuable.”

For Carothers, it’s hockey heaven. Years ago, he would never have imagined that a math degree could be the first step to a career in sports, but now, everything just fits.

“It’s the coolest thing,” Carothers reflected. “I never had the skills to make it to the NHL as a player, like far from it. But I’ve kind of made my own way, and it happened to be through math.” 

He can’t imagine doing anything else.

“This is what I want to do for the rest of my life. It’s the best thing ever,” Carothers said. “I get to think about hockey all day every day, and even on the rough, challenging days, I’m like, ‘Ah, it’s hockey, it’s fine, it’s fun, and it’s incredibly rewarding. I’m so lucky to be able to do this.’”

Written by Leslie Miller

Brin Postdoctoral Fellow Hannah Hoganson’s love of mathematics inspired her to study geometric group theory and to rethink the way math can be taught. 

Hannah Hoganson’s passion for math took her across the U.S.—from her hometown in Pennsylvania to Ohio to Utah—before she finally arrived at the University of Maryland as a postdoc in fall 2022.

“Even though I always liked math and was pretty good at it, I wasn’t always in the highest-level classes as a kid. In fact, I even struggled with a couple math classes in college,” Hoganson recalled. “But after I attended more classes and experienced more opportunities, I realized that sometimes, you just need more time and more exposure to content to really understand it. Having different perspectives or different teachers can make difficult things finally click.”

Hoganson brought this philosophy with her as she conducts research and teaches courses at UMD as a National Science Foundation Postdoctoral Fellow and one of five Brin Postdoctoral Fellows who are supported by a generous gift from Mathematics Professor Emeritus Michael Brin. The Brin Postdoctoral program supports young mathematicians whose research shows remarkable promise for up to three years. 

Hoganson works with Assistant Professor of Mathematics Lei Chen in the field of geometric group theory, a branch of math that involves using geometric tools and objects to study algebraic groups (such as a set of functions). By examining geometric symmetries or other behaviors like a geometric object’s possible transformations, Hoganson and Chen can learn more about the structure and properties of algebraic groups. 

“Think back to the algebra classes you used to take—you have symbols and equations that you’re manipulating to find answers. It’s all fairly abstract,” Hoganson explained. “Now add in what you learned in geometry class, like measuring shapes and angles. Those are more physical interpretations or visualizations of the abstract. I’m interested in finding connections between the two, kind of like creating a ‘dictionary’ that translates one concept by using the other.”

Similar to how she finds connections between two different concepts in her research, Hoganson has a knack for finding ways to connect her work to people as well. Her experience partnering with peers, leading discussions and organizing conferences with mathematicians from across the country helped her become an effective communicator. She thrives when she’s bouncing ideas off collaborators, often moving her research forward after considering different perspectives and possibilities as she takes on intricate problems. 

“Even if we’re all in the same field of study, we don’t always have the same ideas, understanding of concepts or conclusions,” she explained. “We have to know how to explain our findings and theories with each other in a way that we can all understand. And that requires the ability to tweak what you’re saying to different people and communicate well.”

And Hoganson practices what she preaches. She works to improve her teaching every semester, adjusting her lessons to each new batch of students by relying on feedback and her own positive experiences with allowing students to revise and resubmit assignments. Chen, who is Hoganson’s mentor, believes that these efforts are the reason why Hoganson is an effective teacher—and that sentiment is shared by the many undergraduate students who have taken her introductory calculus classes at UMD. 

“Hannah is a super enthusiastic and talented mathematician,” Chen said. “She likes to work with other people, often communicating with various mathematicians and organizing new research activities with them. This love for collaboration and communication is also why she is a fantastic teacher. I cannot wait to see her as a professor.” 

The path to math

Hoganson’s journey to UMD began when she attended a summer research experience for undergraduates program held at Miami University. 

“I didn’t have much experience that first summer there, but I thought it was cool how math research worked. It was complex and dynamic. As an undergrad, you don’t usually get the chance to see that,” said Hoganson, who was a math major at Lehigh University at the time. "The program left such a big impression on me that I went again—this time, as the graduate student mentor for the undergraduate participants. It ignited my interest in continuing this sort of work."

Inspired by her undergraduate research experiences, Hoganson completed a master’s degree in mathematics at Miami University and later earned a Ph.D. in mathematics at the University of Utah. She found her research calling in low dimensional topology (a branch of math that studies shapes and spaces that can be visualized in two or three dimensions) and geometric group theory. She also resolved to bring that same exhilarating experience she had as an undergrad to other young mathematicians. 

As she neared the end of her doctoral studies, Hoganson wanted to explore new research opportunities, and that eventually led her to UMD.

“I was drawn to UMD because I wanted a chance to work with Lei Chen, whose work shares many overlaps with my own research interests,” Hoganson said. “Another big attraction was the Brin Mathematics Research Center, which was brand new when I first learned about it. Having a big research center dedicated to pure math research was something that really set UMD apart from other schools and I knew I wanted to be a part of that.”

Since landing the postdoctoral position at UMD, Hoganson has gone on to teach several introductory math classes at UMD and publish several papers on mapping class groups with longtime collaborators and friends. She’s taking a break from teaching this semester to focus more on her research but hopes to return with new teaching tactics and an updated approach to conveying new ideas. 

“It’s definitely a good time to be here at UMD,” said Hoganson. “There’s a lot going on right now in terms of research, workshops and collaborations that I look forward to exploring.”  

Written by Georgia Jiang