In the quest for truth and meaning, mathematics Ph.D. student Luis Suarez found an unexpected path at UMD.

Luis Suarez has a soft spot for the classics. He loves philosophy but won’t read past the 19th century. He enjoys literature but prefers the likes of Goethe, Brontë and Dante (Alighieri of “The Divine Comedy,” that is) over King and Koontz. 

He has studied German, Latin and Greek and even translated an ancient text written by Gorgias, a pre-Socratic philosopher, into Spanish. 

So when Suarez became a mathematics Ph.D. student at the University of Maryland in 2019, he naturally gravitated to logic, a field that blends his two passions, philosophy and math. 

What he didn’t anticipate is that he’d also be creating a model to study the complex interplay between predators and prey in the animal kingdom.

“Before that, I was a pure mathematician,” Suarez said. “To me, a computer was just a thing that you type on.”

At UMD, Suarez found a home for his old interests—plus some new ones. He is studying functional analysis and descriptive set theory with Mathematics Professor Christian Rosendal as well as mathematical biology with Mathematics Professors Doron Levy and Maria Cameron.

Simultaneously studying pure and applied math is no issue for someone like Suarez, who holds bachelor’s and master’s degrees in both philosophy and math. In fact, finding meaning and logic in unexpected places is Suarez’s specialty. 

“I have been working on completely disjointed things for almost 15 years. It's something that's a part of me, and I think it’s a skill that I shouldn’t lose,” Suarez said. “It not only helps in terms of making your CV look better, but it also helps you change perspectives in a very radical way.”

Finding his path

Suarez discovered philosophy by way of literature and math by way of physics. A lover of classic literature, Suarez has read “Wuthering Heights” by Emily Brontë at least once a year since his high school graduation 15 years ago. He has read it in both English and Spanish, squeezing out new meaning each time.
His search for deeper understanding ultimately attracted him to philosophy and, later, mathematics. Reading Plato’s “The Symposium” in high school was Suarez’s entry point, but he later developed an affinity for the German idealists, particularly Kant and Hegel. 

At the same time, Suarez was exploring physics, a subject he planned to pursue in college until reality set in.

“My experimental skills were dreadful,” Suarez joked, adding that he began to explore the mathematical foundations of quantum mechanics instead. That path introduced him to mathematical analysis, and he never looked back.

“I really fell in love with analysis,” Suarez said. “It's just beautiful when you start to understand it.”

Suarez earned his bachelor’s degrees in mathematics and philosophy from the University of the Andes in Bogota, Colombia, where he is from. He then completed a master’s program in mathematics and philosophy at the same university, this time applying Kant's transcendental logic to quantum and Lagrangian mechanics.

For Suarez, math and philosophy are two sides of the same coin, with both fields following a set of rules in search of universal truths.

“Mathematics and philosophy, I believe, proceed in the same way,” he said. “We have a set of hypotheses or a set of axioms, and we start to deduce things from those axioms.”

Worth the wait

What initially attracted Suarez to UMD for his Ph.D. was the Department of Mathematics’ “strong logic program,” but these days he’s most impressed by the flexibility.

“Something that I think is very valuable about UMD is that we have three Ph.D. programs in math, but you can work with any professor in any program,” Suarez said. “Having Doron [Levy] as my advisor helped me to grow in a way that I never thought I could. Every time I come to his office and tell him I want to work on something, he tells me, ‘If you want to do it, do it.’”

For Suarez, that freedom encouraged him to explore new subjects that he never would have considered. In addition to studying abstract analysis on the pure math side, he’s also deeply invested in an applied math project. 

Working alongside Levy and Cameron, Suarez developed a model and computational code to predict how the complex behaviors of predators and prey from different age groups might affect the population dynamics of a given species.

“My favorite example is seen in owls and snakes: the snake can eat the egg of the owl, but the [adult] owl eats the snake, so those dynamics are called role reversal,” Suarez explained. “The prey is the predator at some point, but then the predator becomes prey. It’s like a game.”

In addition to his research, Suarez serves as a teaching assistant and tutor to math majors and non-majors alike. He won two UMD teaching awards in recognition of his impact: a 2020-21 Aziz Osborn Gold Medal in Teaching Excellence and a 2022-23 Outstanding Graduate Assistant Award.

Nicholas Cummins, a senior electrical engineering major who had Suarez as a TA for MATH 241: “Calculus III,” noted that Suarez always offered encouragement and guidance when needed.

“Beyond just being knowledgeable about the material and teaching it well, he made sure that we knew he cared about us as both students and human beings,” Cummins said. “Forming a connection in the classroom led to us being close friends outside of academics, so it is common we talk about the things going on in our lives.” 

When Suarez isn’t teaching, tutoring or working on his dissertation, he enjoys baking, writing short fictional stories and weightlifting, somehow finding time to spend three hours in the gym daily. 

While Suarez has loved his time at UMD, he looks forward to trading his student status for a “real-world” job in mathematics. After graduating, he hopes to land an industry job—potentially in mathematical biology or probability and statistics, two fields he never considered before coming to Maryland.

“I have been in school since 2010, so that's 14 years. I'm a little bit exhausted,” Suarez said with a laugh. “But as I used to tell my students, something I've learned during my Ph.D. is that everything worthwhile in life will take effort and time. So sometimes you just need to be patient.”

Written by Emily Nunez

Maryland and D.C. students compete annually for scholarships to UMD.

For over 45 years, participating in the University of Maryland’s High School Math Competition has been a rite of passage for young aspiring mathematicians from Maryland and the District of Columbia. 

Open to all Maryland and D.C. high school students, the competition rigorously tests participants’ knowledge of pre-calculus topics such as algebra, combinatorics, geometry and number theory. Competitors sit for a proctored, two-part exam consisting of a 75-minute multiple-choice portion and a two-hour proof-based/free-response section. 

The top three scorers are offered full scholarships to attend UMD. In addition, high-scoring students from each county may receive other monetary prizes. Past winners of the contest have gone on to become highly celebrated figures in both academia and industry—among them Google co-founder Sergey Brin (B.S. '93, mathematics and computer science) and mathematics professors at universities across the country.

For the thousands of students who have taken part in the competition over the years, the contest is about more than just awards; it’s also a unique chance to showcase their mathematical problem-solving skills under pressure. 

“In many ways, the contest calls for a different set of skills than what’s required in a standard math curriculum,” said Daniel Yuan, a mathematics and computer science double major who ranked first in the math competitions held in 2018, 2019 and 2021. “Students don’t usually get a chance to flex their ability to solve complex, multi-layered problems by hand. Without tools like calculators, contestants are told to use scrap paper and some creative thinking to get through tough questions on a time limit. It’s a different yet fulfilling experience.”

For Yuan, who also played a major role in UMD’s recent success in the prestigious William Lowell Putnam Mathematics Competition, his experience as a high school math contestant was one of the reasons he chose to attend UMD and why he currently plans to continue pursuing his passion for math as a career after graduation. 

Yuan isn’t alone—many other UMD math competition alums also say that the contest helped shape their academic goals or even their professional ambitions. Sophia Chen, a freshman bioengineering major who competed last fall, noted that the experience gave her a taste of high-level competitive math and triggered her interest in math contests such as the Putnam Competition. Freshman mathematics major Kelin Zhu, who placed second in the 2022 UMD High School Math Competition, believes that experience pushed him to think more creatively and develop skills that later helped him excel in his math classes at UMD. 

“It hones your problem-solving skills in a way that normal math classes just don’t,” Zhu said. “Being a participant helped me smoothly transition into my major classes, especially the upper divisions where we have to be strong in solving proof-based problems. I can see these skills coming in handy after I graduate, especially in the research environments I want to be part of.” 

Building a strong legacy for UMD Math

Mathematics Professor Larry Washington and Principal Lecturer Roohollah Ebrahimian work diligently behind the scenes to organize and expand the competition, which has come a long way since it was launched in 1979 by William "Brit" Kirwan, chancellor emeritus of the University System of Maryland and a former chair of UMD’s Department of Mathematics. 

“[Brit Kirwan] recognized the need to publicize the department to young students around the state, many of whom probably didn’t realize that we have world-class mathematicians here at UMD,” said Washington, who is the longest-standing member of the competition’s organizing committee. “The contest has helped immensely in recruiting top talents to the university, allowing our department to continue its excellence.” 

Ebrahimian, who has served as director of the competition for the past eight years, added that the contest also enables UMD to build strong relationships with the local community. Consistent outreach efforts made a difference when it came to connecting with students who might not have had a chance to be recognized for their math skills before, he said. 

“We’ve built a strong network of participating institutions in Maryland and D.C., some of which send dozens or even hundreds of students to compete each year. There have also been a number of homeschooled students and even middle school students who take the exam with their closest public high school,” Ebrahimian noted. “Thanks to those growing relationships, we’re starting to see a general increase in the amount of diversity in the contest’s top performers, particularly in female top rankers—something that we’re excited to expand upon in upcoming competitions.” 

In 2024, more than 1,200 high school students from 95 schools took the first part of the exam on October 23, with 246 students qualifying for the next round on December 4. As the conclusion of this year’s math competition approaches, Ebrahimian is already planning for 2025, with hopes of reaching—and inspiring—even more aspiring mathematicians and creative problem-solvers than ever.

“This competition started as a way to give the university and our math department some publicity among local high schools,” Ebrahimian said. “But today, it’s a point of pride for many Maryland and D.C. students who participate, as well as an opportunity for us to highlight and recognize their exceptional mathematical talent. We welcome anyone who’s looking for a challenge beyond what they see in a regular math class.” 

Written by Georgia Jiang

Mathematics, computer science, and electrical and computer engineering majors can take a cryptography class to learn how modern communications and transactions are kept secure. 

UMD mathematics, computer science, and electrical and computer engineering majors can take a cryptography class to learn how modern communications and transactions are kept secure.

What keeps our emails and messages private? How do passwords protect our online accounts from hackers? Why is it safe to make purchases from retailers using our credit cards?

The answer to all those questions is cryptography—the process of hiding or coding information so that only the intended users can access it.

In 1997, just as the internet and digital communications like email became more commonplace, University of Maryland Mathematics Professor Larry Washington designed a new cryptography course. An expert in number theory and cryptography, Washington wanted to make sure students had some exposure to the rapidly advancing field and its potential applications before they graduated and encountered cryptography in real-life situations.

“There’s a lot of interest in cryptography here at UMD because the National Security Agency and other government agencies use cryptographic methods,” Washington said. “Cryptography is a subject that has developed very greatly in the past 50 years and a lot of that development happened in the past 20 years. As a result, we continually update the course to keep up.”

An evolving interdisciplinary approach

Nearly 30 years later, UMD’s cryptography course still lives on as MATH 456, CMSC 456 and ENEE 456. Due to its interdisciplinary nature, faculty members from the mathematics and computer science departments have taught the class and influenced the curriculum.

“It’s a blend of math and computer science ideas,” Washington explained. “The students see real-world applications of theoretical math ideas while students who are accustomed to only theoretical math have the chance to see the issues that arise in applied areas.”

Senior computer science major Harshit “Archie” Garg says the course was among the toughest classes he had ever taken at UMD but also one of the most eye-opening. He took the class in fall 2023, when it was taught by Computer Science Professor Daniel Gottesman, who also holds a Brin Family Endowed Professorship in Theoretical Computer Science. Initially unfamiliar with topics like encryption, Garg believes that the class gave him the tools he needed to understand cryptography’s place in everyday life and how it could be applied to seemingly unrelated fields.  

“The class showed that you could use these fundamental math concepts like logarithms and exponents to create these very robust encryption protocols. I learned how we could generate key hashes dynamically on the fly, where something can be understood in one context but be complete nonsense in another,” explained Garg, who plans to pursue a career in machine learning. “I ultimately feel confident that wherever life takes me after graduation, I can use the concepts I learned from this class.”

That sentiment was echoed by many other students, including computer engineering Ph.D. student Russell Chiu (B.S. ’23, computer engineering), who took the class as an undergraduate. The class made such an impression on Chiu that he decided to become a graduate teaching assistant for the course in spring 2024. He hopes to apply what he learned in the course to his graduate research and eventually pursue a career where he can put his knowledge of cryptography and algorithms to work.

“With the rise in new types of computing, there are many interesting questions within both academia and industry. In fact, there were several new topics introduced to the course curriculum within the two years since I took it,” he added. “I definitely recommend this class to undergrads interested in cybersecurity and beyond—it covers a wide scope of topics that quickly evolve over time.”

Cryptography today and tomorrow

Todd Rowland, who worked at computational technology company Wolfram Research before he joined UMD as a mathematics lecturer, is excited to teach the newest iteration of the class in fall 2024. He hopes his experience with more abstract forms of cryptography at Wolfram will add an extra dimension to the course and underscore the ever-changing impact of cryptography.

“It’s no longer just about secret messages and passwords,” Rowland said. “Cryptography has become increasingly relevant to us ever since the internet came into existence. There are obvious things that cryptography plays a role in, like keeping credit card information safe while making secure payments over the internet. But it’s also helping you make sure the webpage you’re on is the right one and that no one altered it—authentication of integrity is more important than ever.”

In Rowland’s class this fall, students will explore concepts from basic ciphers to secret sharing schemes (a technique where a “secret” is split into multiple shares to different parties and can’t be fully accessed unless all shares are recombined). The curriculum will also cover the Data Encryption Standard and the Advanced Encryption Standard, globally used ciphers established by the U.S. government to protect sensitive electronic data. Rowland hopes the class will help students become more aware of the technology around them and how newer trends in cryptography—like blockchains and quantum cryptography—can impact society.

“The class is a peek into how the world works today, from knowing how to manage passwords and authentications to dealing with things like cryptocurrencies,” Rowland said. “As technology advances, it’s better to be prepared as best we can to work with those advancements. If you want to understand all these processes, this would be the class to take.”