“We often have this sort of vision, like a mathematician sitting off in the dark, alone, scribbling on a sheet of paper,” says Dana Paquin, when asked about what math research truly is like, “and I think it’s definitely not that.”

Dr. Paquin is a Math Instructor at OHS, and currently teaches Discrete Mathematics and Geometry of Numbers. Dr. Paquin completed her undergraduate work at Davidson College, a small Liberal Arts College in North Carolina, and earned her PhD. at Stanford in 2007.

She says, “I’ve always loved doing math. And I definitely enjoy pure math research, and I still do research in number theory, combinatorics and discrete math. But I’m also interested in looking at the ways in which math can be applied to problems in other fields.”

As a doctoral student, she started working in abstract algebra and number theory, specifically representation theory, an area combining the two fields. While taking a class on partial differential equations in graduate school, she became interested in the applications of math to other fields, joining her instructor’s work on medical imaging to understand the role mathematics plays in deciphering MRI and CT images to more effectively treat cancer.

Now, Dr. Paquin focuses her attention on applying the basics of mathematics to other fields. She says her journey really started when she realized how interesting it was that math could be used in cancer/biology related problems.

Dr. Paquin’s research demonstrates the immense potential mathematics has for making an impact on a variety of fields and its potential to improve lives, yet, accessibility to mathematics and its benefits remains a challenge for many.

Dr. Paquin believes that math research can be made more accessible to high school students. She says that the most important part is “helping students become aware of the broad range of opportunities that are available.” For example, at the end of her two classes, Discrete Mathematics and Geometry of Numbers, the class talks about a variety of unsolved problems to help students become aware of areas open for math research. Behind the scenes as an instructor, Dr. Paquin works on instilling curiosity with questions like “What are people working on? What does it mean to be a mathematician in real life? What does it look like?”

But, even as a high schooler, Dr. Paquin believes that you can get into research without these degrees and further study, by finding a question and field that really peaks your interest as “it’s really a matter of finding the right questions to ask, and the right fields to get into.”

“I think another misconception about math research is that it is often done alone.” To address this misconception, Dr. Paquin talks about her work in math research being very collaborative, involving immunologists, medical practitioners, statisticians, and scientists – people from so many other fields. She says, “I think that mathematics research is collaborative. Just like other areas of scientific research.”

Dr. Paquin believes that it is “mostly a matter of just helping integrate an awareness of math research into existing courses and other similar settings.” She adds that OHS’s math curriculum does a really good job of something she calls vertical development of mathematics, “helping students see where math can go beyond the standard curriculum through calculus,” while also having connections with other disciplines, building exposure to unsolved problems and open areas in research. As an instructor, she thinks that one of the best things about being at OHS is that the students are so inquisitive and innovative. She adds that courses like Geometry of Numbers “have confirmed her belief that high school students really can contribute in meaningful ways to high level mathematics,” where it is a matter of framing the questions and backgrounds in the right way, so high school students can become engaged.

As a teacher, Dr. Paquin’s biggest obstacle is finding the time and academic space to do research, balancing research with teaching and thinking about ways to integrate research and teaching. She says that one way she has worked to overcome this obstacle is “find ways for research problems to be a part of courses, introducing problems for students to work on.”

When getting started with research in Math, Dr. Paquin suggests reaching out to teachers willing to supervise high school students or refer you to books that you could start with for research, or even just a class. She also suggests, maybe forming a small group of students and “thinking like, okay, we solved this particular problem in class, how could we extend this to another more challenging problem, like what if we are working in 7 dimensions instead of 2 or 3.”

“Expect to work hard and sometimes not be sure what the next step is, and to have to reference or talk to other people. Collaborate.” She notes that math research can be much different from solving a problem for a class, where often the answer is known, but for math research, the answers aren’t known, and that “being willing to engage in problems, for where the answer isn’t known, may mean that you might get stuck.”

One final piece of advice Dr. Paquin offers: “Explore a broad range of different fields, and explore a lot of different areas of research and collaboration with different people and learn about it. There is a full spectrum of areas of mathematics research out there.”