Casey Rodriguez is an assistant professor in the Department of Mathematics within the UNC College of Arts and Sciences. He uses mathematics to describe and predict the behavior of materials, from everyday objects to advanced metamaterials engineered with properties not found in nature.

“Whether it is a pencil, a sheet of paper, or an engineered metamaterial, every object bends, twists, and stretches according to the same underlying mechanical principles,” Rodriguez says. “My research develops the mathematics needed to describe those behaviors and predict them accurately.”

How did you discover your specific field of study?

When I was in high school, I read a popular account of an unsolved math problem called the Riemann hypothesis. It alternated between chapters on the history of the problem and the mathematicians behind it, including Carl Gauss and Bernhard Riemann, and chapters that gradually introduced the mathematics itself. Around the same time, I also read a biography of John Nash, who won the Nobel Prize for his contributions to game theory. Those books opened my eyes not only to the richness of mathematics, but also to the very human stories of the people who devote their lives to it.

Inspired by those books and by several wonderful professors I had as an undergraduate at Texas A&M University, I decided to pursue analysis and applied mathematics. That’s when I was first introduced to continuum mechanics, which describes the behavior of large materials like solids and fluids.

Academics are problem-solvers. Describe a research challenge you’ve faced and how you overcame it.

Deciding to move into a field that was largely unrelated to my graduate research. I went from studying questions in partial differential equations to working on applied problems in continuum mechanics. None of my previous advisors or collaborators specialized in this area, so I had to learn the foundations largely on my own without knowing whether the investment would ultimately lead anywhere.

Fortunately, I reached out to one of my undergraduate professors, who shared papers with me and introduced me to new collaborators. The encouragement and guidance I received from those professors, together with the mentorship of my PhD and postdoctoral advisors, have shaped my career ever since. They also instilled in me a deep appreciation for the profound difference that dedicated teachers and mentors can make in a student’s life.

Looking back, the transition opened the door to an exciting new research direction and ultimately led to my first National Science Foundation grant. More importantly, it taught me that some of the most rewarding opportunities begin by stepping outside your comfort zone and into the unknown.

Describe your research in five words.

Stretching, bending, and twisting mathematics.

Who or what inspires you? Why?

Books and articles on the history and philosophy of science. Learning about the people who came before me, the questions they struggled with, and the dead ends they encountered reminds me that discovery is rarely a straight path. There is something comforting about knowing that even the greatest mathematicians and scientists wrestled with conceptual and technical challenges. Research can often be a solitary endeavor, and those stories make me feel connected to a much larger community that stretches across generations.

I also think there is much to learn from how great scientists developed new ideas, not just from the ideas themselves. I have been fortunate to collaborate with several researchers who have spent their careers challenging long-held assumptions in continuum mechanics. Their example has reinforced the importance of questioning conventional wisdom and remaining open to entirely new ways of thinking about old ideas.

If you could pursue any other career, what would it be and why?

One of the things that has always fascinated me is that nature can be understood through systems of language, whether it is the language of mathematics or the four-letter alphabet of DNA. As Albert Einstein famously remarked, “The most incomprehensible thing about the universe is that it is comprehensible.” I have spent much of my life trying to understand that order through mathematics.

If I were to pursue another career, I would probably study philosophy and theology. Mathematics has led me to appreciate the intelligibility of the natural world (the laws), and I think I would enjoy spending more time exploring the deeper questions about truth, meaning, and the source of that order (the lawgiver). Whether in academia or within the Catholic Church, I would find that work deeply fulfilling.