# 2022 Student Essay Contest: Grand Prize Winner

## “Community and Commutative Algebra”

### by: Sunmin Eom (Albany High School)

### Interviewee: Juliette Bruce (University of California, Berkeley)

Envision a mathematician: what tends to come to mind is someone who locks themselves in a room, scribbles chaotically on a blackboard in isolation, and comes out years later with an elegant proof, a la Good Will Hunting, Rain Man, or A Beautiful Mind. Yet, for Dr. Juliette Bruce, math has always been about finding and building communities.

Although Dr. Bruce had always been involved in STEM, she and math didn’t tie the knot until college. An advanced freshman math course at the University of Michigan–Ann Arbor unexpectedly kickstarted the journey that would transform her life. As someone who didn’t have a strong background in math, she was totally unprepared for the fast-paced, rigorous, theoretical Honors Mathematics I with Professor Karen Smith – a smorgasbord of calculus and topology. Dr. Bruce recalls the first exam she took as any student’s nightmare: “The professor handed it back, and on the back, it didn’t have a score. It just said ‘see me.’”

She would have dropped the course and run away if it hadn’t been for her teacher Dr. Smith, who became her close mentor and helped her figure out how to approach advanced math. With Smith’s support and a strong community of peers, she started diving deeper into the world of math—and, later, declared it as her major.

As an undergraduate, Dr. Bruce developed her interest in commutative algebra and algebraic geometry, the same areas that Smith studies. Those areas gave her a newfound appreciation of math: “The high school math that I learned a number of years ago about lines and parabolas and systems of equations all made sense in this kind of really beautiful way.” She especially loved how “systems of many polynomials with many unknowns can be simultaneously approached using techniques from geometry that have these gorgeous shapes in it.”

Another appeal of these areas was their particularly—and surprisingly—inclusive community. Dr. Bruce explains that “each area of math has its own culture and feeling for how people approach it,” and, as it turns out, commutative algebra has an unprecedentedly large number of women and gender minorities. For Dr. Bruce, a member of the LGBTQ+ community, the welcoming atmosphere was exactly what she was looking for. This tight-knit group helped her overcome challenges that she faced as a woman: “There were different incidents where I was harassed or not represented. They didn’t form great moments, but I was lucky enough to find a support system,” Dr. Bruce elaborates. “When I came out as LGBTQ+ in graduate school, my colleagues had my back and supported me unconditionally.” Captivated by these aspects, she went on to obtain a Ph.D. with a focus on algebraic geometry and commutative algebra at the University of Wisconsin–Madison.

Her work since graduate school can be divided into three categories—outreach, mentoring, and research—all of which come down to different ways to build community.

To further build gender equality in math, she works to create and strengthen communities that she wishes she had seen earlier in her career. For Dr. Bruce, maintaining visibility is imperative—it helps marginalized students just to know there is someone like them studying math. She has been a board member of Spectra, an association for LGBTQ+ mathematicians, for years, working to promote LGBTQ+ mathematicians and build structures that make math more inclusive and welcoming. She also organizes multiple conferences for women and gender minorities in math, aiming to create communities that “recognize everyone’s entire identity as a human being, not just as a mathematician” and “transform math so others don’t face challenges that [she] faced.”

In addition to supporting gender minorities, Dr. Bruce also ignites a love for math amongst grade school students. Since her college years, she’s collected math circles like some people collect stamps. She became a student organizer of the University of Michigan Math Circle—teaching bright, young students is her passion. At the University of Wisconsin, she started as a volunteer, but she soon became the lead organizer of the Madison Math Circle, too.

At UW, she recognized the obstacles to accessibility far too many students face: “The people coming to the evening math circle that takes place at the university don’t represent the whole community of students interested in math.” So, she decided to organize traveling math circles. Under her watch, mathematicians visited local schools—both to give lectures and to connect with previously untapped mathematical minds.

Today, she is a National Science Foundation postdoctoral fellow at UC Berkeley. Her work involves collaborating and communicating with fellow mathematicians and promoting research conducted by others in the mathematical community, especially ones from people who are part of underrepresented groups, so that those would be recognized more. When her fellowship at UC Berkeley ends this coming spring, she’s planning to embark on a new postdoc at Brown University, where she’ll continue working on her two key focuses: algebraic geometry and commutative algebra. Afterwards, she’s planning to apply to work at a university where she can continue researching, organizing community, and mentoring as many students and other math enthusiasts as possible.

To young mathematicians, Dr. Bruce promises that math is about collaborating and exploring, not competing and finding the right answer: “As I progressed in my career, I came to realize that we as mathematicians often get to define what it means to have the right answer. I think the right answer is something [where] myself and others walk away saying, ‘wow, that was really interesting.’”

She urges students not to be discouraged when they find a particular area of math difficult—even if one theorem or proof isn’t for them, there are thousands, and potentially infinitely many, others to choose from. She asserts, “For anyone who is interested in math, there’s a way you are able to do mathematics and there will always be someone who can guide you in the process.” Plus, math can intersect with other fields like fashion, athletics, art, and political science, enriching the field a hundredfold.

Above all, Dr. Bruce encourages young mathematicians to find a community where they can always seek support. She reflects on how her spheres helped shape her, saying, “I feel like I am where I’m at as a mathematician only because I found those people who could say, ‘We are here to support you. We see you,’ when I failed an exam, when I faced discrimination, and when I felt like I was the only woman or LGBTQ+ person in my math classes or in my area.”

Of course, pursuing a career in math brings its own challenges, but Dr. Bruce emphasizes that they will face the same gauntlets in any other area of life. Those challenges may be more extreme for underrepresented mathematicians like women and the LGBTQ+ community, the crossroads of Bruce’s experience, but she hopes those additional barriers won’t dissuade members of these communities from joining the field.

On the contrary, she believes they can change it for the better. After all, for Dr. Bruce, math is about building supportive and equitable systems and “applying what [she] is doing to change the world for people”—and, most importantly, doing so together.