When Corina Tarnita was a budding mathematician, she found her interest in mathematics flickering, about to burn out. As a girl she had stormed through Romania’s National Mathematical Olympiad — where she won a three-peat from 1999 to 2001 — then on to Harvard University as an undergraduate and straight into its graduate school to study questions in pure mathematics.

Then suddenly, around a decade ago, it wasn’t so fun anymore. “I would still get a kick out of solving a problem,” she said. “The question is whether it was just kind of an ego kick.”

Facing a crisis of faith, Tarnita felt her future narrow to just a few paths. She had been offered a cushy “quant” job working for a bank. She could take time off. And then she found in the library an intriguing book with a colorful cover called Evolutionary Dynamics: Exploring the Equations of Life. The book’s author, the mathematical biologist Martin Nowak, was, conveniently, also at Harvard. The same week she had to decide on the job, she sent him an email asking to meet.

The meeting changed her life. Tarnita turned down the job and finished her doctorate with Nowak. (She completed her Ph.D. just a year after earning her master’s degree.) She began a project with him and the legendary biologist Edward O. Wilson that led to a 2010 Nature paper on the evolution of cooperative insects like ants and termites. Since 2013, she has continued to study biology using mathematical tools as a member of the faculty at Princeton University.

Since switching fields, Tarnita has focused her work on how living things orchestrate themselves itself into patterns on different scales. Sometimes the forces of natural selection bear down on individuals. Other times, they act on a unit such as an ant colony. Other collective organisms such as slime molds must contend with evolutionary pressures both on the whole and on individuals. And in still larger systems like the African savanna, evolution shapes the component parts, but not the whole. “From the small scale to the large scale,” she wonders, “does nature use the same rules?”

Of all the patterns Tarnita explores, one of the most enchantingly enigmatic are fairy circles: barren round patches that dot the grasslands of Namibia like pepperoni slices on a pizza. They can persist as long as 75 years, but their cause has been hotly debated. Some scientists argue that termite colonies build and maintain the bare circles, while others blame them on plants battling for water across the arid landscape. In January, Tarnita and her colleagues published an article in Nature that suggested a compromise: that both processes together, acting on different scales, could imprint the observed pattern on the ecosystem.

Among her other projects, Tarnita is still working on understanding the fairy circles, which may someday allow environmental scientists to tell from satellite imagery if an ecosystem is on the verge of collapsing into a desert (or if it’s especially resilient). Quanta caught up with her to ask about her early forays into mathematics, her career arc and her current research. The interview has been condensed and edited for clarity.