Relatively few people on the planet know what that means—and co-author Jakin Ng ’25 admits she wasn’t one of them when she dove into the project. “The first time I looked at it, I was like, ‘I don’t know how I’m ever going to be able to understand this,’” she recalls.
At that time, Ng and her research partners, Fiona Abney-McPeek and Serena An, were high school students participating in the MIT Mathematics Department’s yearlong Program for Research in Mathematics, Engineering, and Science (PRIMES). Now they’ve submitted their paper for publication, and Ng is a first-year student at MIT in Course 18-C Mathematics with Computer Science. An is slated to enroll next year, and Abney-McPeek is at Harvard.
PRIMES, Ng says, gave her “a taste of what professional mathematicians do—instead of just learning about results other people have already achieved, actually creating new knowledge.”
PRIMES pairs high schoolers with MIT graduate students and postdocs to investigate unsolved problems. Founded in 2010 by math professor Pavel Etingof and lecturer Slava Gerovitch PhD ’99, it has expanded into several subprograms, all free to students. PRIMES-USA attracts some of the most advanced students nationwide, while PRIMES Circle and MathROOTS are designed to reach talented kids with less previous exposure to higher math. All of the program’s offerings aim to open the world of mathematics to more people, particularly those underrepresented in the field.
Group projects are relatively new for PRIMES-USA, but Ng was glad to be part of a trio so each student could build on the others’ insights. She, Abney-McPeek, and An connected often and had weekly video checkins with their mentor, MIT PhD candidate Adela (YiYu) Zhang ’18.
Zhang provided the high schoolers with background reading on Grothendieck polynomials—the symmetries of which can reveal information about a mathematically important class of geometric objects called Grassmannians—and a roadmap to help them get started. In Ng’s words, “Adela was able to zoom out and give us the macroscopic view of what we should be working on.”
Zhang says her top priority was to help her mentees build the skills and habits all research mathematicians need, such as “being comfortable with getting stuck but still not giving up.”
These are lessons Zhang says she feels she is still learning herself. As a young student in Shanghai, China, she was attracted to math by the beauty of famous theorems, but in her day-to-day research she has had to come to grips with slow progress. She knows what it’s like to feel a bit overwhelmed. “When I started mentoring Jakin’s group, I was just starting to work on my own project for the first time in grad school. So, I can fully sympathize with what it feels like,” she says.
There are successes as well as setbacks. Zhang recalls that Ng spent weeks slogging through examples of an unfamiliar technique called constructing bijections before finally getting the hang of it. “She proved something using this technique, which I found really impressive,” Zhang says. “I was proud of her.”
Ask Ng if there were moments during the year when she thought her team might never get anywhere, and she laughs. “Basically, the whole time except for the end. I think that’s the point. That’s how research goes. You have a small victory, you celebrate it, and then you’re back to not knowing what’s going on.”
Connecting with a community
Both Ng and Zhang say that connecting with others through math has made their research pursuits more rewarding. As an undergraduate at MIT, says Zhang, “I felt very lonely because there weren’t many women doing higher math.” She persevered thanks to encouragement from a female postdoc who supervised her in the Undergraduate Research Opportunities Program (UROP). Zhang went on to serve in turn as a mentor for UROP as well as for PRIMES. The program recognized her ongoing work in 2021 by awarding her a George Lusztig Mentorship.
Ng started building her own math support network while growing up in Ithaca, New York, attending math camps and leading her high school’s Science Olympiad and math competition teams. She’s met some of her closest friends, including her MIT roommate, through such activities. “A lot of what kept me interested in math was having that community,” she says.
Whatever the future holds for Ng, she says she expects math or its applications will play some part in her profession. Meanwhile, she is enjoying a variety of creative activities at MIT, including origami and music. She says PRIMES helped her see that creativity is vital to research. “You’re venturing into territory that no one has ever really studied before,” she says. “You have to think of new ways to look at something. Otherwise, it’s already been done.”