Students Speak: Five Lessons Learned at my first REU
By Barry Henaku
Barry Henaku
In the winter of 2019, when I was still a senior in highschool, I saw an article in the New York Times, “For a Black Mathematician, What It’s Like to Be the ‘Only One.’” It detailed the story of Dr. Edray Goins, a current professor at Pomona College, and the struggles he faced being one of the few African-American mathematicians. When I read the article, although I was impressed by Professor Goins, the natural question that arose was, “Was I bound to encounter the same problems?” I filed away this concern, but it remained ever-present in the back of my mind.
The winter of my junior year in college, I started searching for Research Experience for Undergraduates (REUs) to participate in. The concept of research was scary to me. Anytime I would glance at a math research journal, I felt like I was reading another language. Until now, most of the work I’ve done was guaranteed to have a solution, but that stops at research. One of the REUs that I came across was the Pomona Research Experience in Mathematics Experience (PRiME). It consisted of algebraic geometry and number theory research and aimed to support minority students. It was also led by the professor whom I had read about, Edray Goins. Algebra happened to be my worst subject; my first exposure to it was two semesters my sophomore year in a graduate class, where on the final I earned a result very close to the low of the class. My professor wrote an ominous “pass...” on the top of my paper. That is to say, I had been disillusioned with algebra and thought it wasn’t for me. However, I was intrigued by the structure of this program and wanted to meet this person whom I had read about.
I applied to the program and was accepted. I was ecstatic, excited about the prospect of working in California outside of my home institution. I was determined to hit the ground running so I started reviewing my abstract algebra.
When I entered the REU, since it was the summer before graduate school applications, I was determined to patch up what I thought was a relatively weak part of my application: research. I came in with the mindset that I would work 60+ hours and that I wouldn’t have time to socialize. The REU emphasized collaboration; there were five groups and five different projects. Each group consisted of three undergraduates, one graduate student, and one senior faculty member. The first two weeks were spent on exposing students to higher level topics. All of us were coming from different places, some of us had taken multiple semesters of abstract algebra and some people had never taken abstract algebra at all. Most people were rising juniors, but there was a slew of rising sophomores and rising seniors as well. I really liked the collaboration aspect of the program: the directors did not have a mindset of mathematics as a solitary activity. At PRiME, I learned many valuable lessons. Here are five highlights and lessons.
Collaboration is the Norm
I read once about the successful, productive collaboration of Hardy and Littlewood, nearly a century ago, when such collaborations in mathematics were uncommon. Nowadays, collaboration has become more the norm in mathematical research. In a classroom environment, professors rarely emphasize the collaborative nature of mathematics and examinations rarely reflect this reality. PRiME and other REUs do a great job of providing a more complete picture in this sense by pairing multiple students on a single project. In addition, collaboration helps students learn to communicate the mathematics and confront questions that may not otherwise be asked while working in isolation.
PRiME vertically-integrated its groups to contain undergraduate students, a graduate student, and a senior faculty member. Collaboration, however, is not without its difficulties. My research partner Elise and I had different working styles. For example, I preferred a more independent work time and then reconvening later to discuss, and Elise preferred to bounce ideas off one another and talk through problems from the beginning. I also had a penchant for working at odd hours late in the night, but Elise preferred that we work at the same time to keep each other in the loop. Needless to say, this led to a number of heated discussions over the course of the eight weeks. However, Elise proved to be a wonderful partner. Along with being an extremely hard-worker, Elise possessed the extraordinary quality of posing good questions. Her questions often forced me to reassess my understanding of the questions that we were tackling. In addition to this, Elise worked more concretely. She had much more experience in Python than me, and, as a result, she was able to automate tasks and collect empirical evidence for conjectures whereas I would try to tackle many problems abstractly (codeword for “without evidence but based on intuition”).
Although we had different ideas of collaboration, our research was ultimately successful and we won an Outstanding Poster Award at MathFest. I learned that in a research collaboration, communication is critical because ideas brew through discussion, and diversity of thought leads to varied solutions that may not have been possible otherwise. Finally, everyone has different strengths and weaknesses; if a problem can be subdivided along these lines, it is of great benefit to utilize everyone’s strengths or even weaknesses.
2. Communication and Community Trump All
At the beginning of PRiME, I convinced myself that I would be all work and no play. However, I failed to realize that at an REU, the connections that you develop along the way are far more important than anything you produce. If you have the opportunity to decide between different REUs, contact the alumni and ask about the faculty, research projects, and community as a whole. Advisors, fellow students, and other members of the community can make the difference between an amazing and a miserable summer. When I interacted with the PRiME alumni, they expressed the strength of the connections they had formed while at PRiME and how that defined their experiences.
The faculty at PRiME single-handedly redefined my notion of a mentor. They supported us at every turn. As an undergraduate who hopes to be a professor one day, the path to professorship often feels like trying to summit a mountain without trail markers. The faculty at PRiME provided the markers by giving advice, offering to read essays, and demystifying complex topics. At the end of the program, they were like family in the fact that their support was unconditional. In every action they took, it was obvious that they only wanted us to succeed.
The diversity of PRiME gave me hope for the future of the field I was entering. In PRiME alone, I met more students of color than I’ve had in all of my math classes combined to date. The community that we built was worth its weight in gold. In fact, two of our senior faculty members, Cory Colbert and Alex Barrios, met at an REU at Cornell nearly a decade ago and still maintain a strong friendship to date. I recall that I had once asked near the end, “Do you think any of us have found the Cory to our Alex?” And one student replied, “I think of all of you as my Corys”. Ambitious, but in the words of my mentor, John McCarthy, “Mathematics is a human activity and a social activity. We may prove theorems on our own, but we need to communicate with others.” At an REU, the people you meet may be your future collaborators and these connections will have more meaning than any undergraduate research you produce.
3. Attend Professional Development and Conferences
Every Friday, PRiME would have professional development days where they brought in outside speakers. These speakers exposed us to opportunities in Number Theory such as the Preliminary Arizona Winter School, connected us with other REUs such as Park City, RIPS, and MSRI-UP, and gave us useful tips on improving our CV and applying for other opportunities. Particular highlights were Bobby Wilson’s presentation on the Kakeya Problem, Caroline Turnage-Butterbaugh’s presentation on Small Gaps Between the Zeroes of the Riemann Zeta Function, and Stephan Garcia’s presentation on Giving Effective Mathematical Presentations. PRiME also gave us the opportunity to attend LatMath and MAA MathFest. Conferences are a critical part of the profession. They allow you to connect with people from different institutions and can reinvigorate your enthusiasm for mathematics by hearing others speak.
4. Learn to Redefine Success in Research
Research is difficult. Math is unique in the sense that doing meaningful research requires a high barrier of foundational knowledge. Therefore, finding questions that undergraduates can contribute to is also difficult. It’s important to have a fluid definition of success when you enter an REU. When you participate in an REU, you should aim to understand the topic you’re researching and not be too focused on obtaining results. In addition, you should become comfortable with partial results; you may not always prove what you originally set out to do, but that doesn’t negate all of the work that you’ve done. Learning where the pitfalls and dead ends are in your problem will help you understand the subject in the future. Given how fast you are learning advanced topics, don’t be discouraged when you don’t understand something.
At an REU, it will likely be your first time reading papers as well. There is an art to reading papers that you will become acquainted with when you enter your REU. This is a great time to learn before you enter graduate school. At an REU, You want to develop some sense of independence. Although mathematics is collaborative, it is important to learn how to test your own understanding, ask the right questions, and become more creative. The only way one is able to develop these skills is by time and acquaintance with the literature of your field. REUs provide a low-stakes environment to develop these skills.
5. Explore and Have Fun!
Finally, have fun! You may never again find yourself in such a unique experience. PRiME had weekly Saturday outings for the sake of community bonding. Whether it was riding Splash Mountain at Disneyland nine times, seeing the Hollywood sign, or walking along Santa Monica Pier, I’m thankful for all the opportunities PRiME provided for students to connect with one another. In addition to this, the Pomona College campus was beautiful. The late night walks to In-N-Out Burger were the best memories of the program. On these walks, we spoke of math, we spoke of our cultures, and most importantly, we spoke of our dreams. When you dream together, those dreams begin to become reality. As I hugged everyone goodbye, I couldn’t help but feel I had chanced upon something special.
Barry Henaku is a current senior majoring in Mathematics and Classics at Washington University in St. Louis. He hopes to become a professor and help mentor students from underrepresented communities.