At the International Congress of Mathematicians in Rio de Janeiro this past August, the algebraic geometer Carolina Araujo was difficult to track down.

As a member of the organizing committee, she was overseeing the women-in-mathematics file and working on several files behind the scenes, plus refining her own lecture — non-trivially, she was among the first Brazilian women to deliver an invited lecture in the history of the congress (four Brazilian-based women delivered invited lectures at the ICM in Rio).

She’d also been leading the charge in planning the inaugural World Meeting for Women in Mathematics — (WM)2 — a satellite event held the day before the congress at which both women and men were welcome.

Or if not “leading,” since Araujo herself might dispute that term, she was a key member of the (WM)2 team. “I’m a bit of an anarchist,” she said recently in a Quanta interview. “I don’t like hierarchy. What we had in mind when we organized the (WM)2 meeting was that it be very inclusive and as horizontal as possible.”

Born and raised in Rio and having earned a Ph.D. in mathematics from Princeton, Araujo is the lone female permanent researcher at the Institute for Pure and Applied Mathematics (a second was recently hired and will join IMPA by the end of the year). Founded in 1952, IMPA is the most prestigious center for mathematics in Brazil, a country that in 2018 was promoted by the International Mathematics Union to the elite “Group 5” tier of the most developed nations in mathematics research. Araujo is also a Simons associate at the International Center for Theoretical Physics (a position supported by a grant from the Simons Foundation, which also funds Quanta).

Araujo started her career as a postdoc at IMPA after she finished her Ph.D. in 2004. Having not yet solved the problem that motivated her thesis, she persevered, continuing to work almost exclusively on that same problem — about the algebraic characterization of projective space.

Over the years, during her Ph.D. and afterward, she developed techniques that had to do with families of rational curves of minimal degree passing through a fixed point — very generally, imagine yourself tracing lines from a fixed point on the ground and leading off in all directions to the horizon line. This theory of rational curves of minimal degree was introduced by the Japanese mathematician Shigefumi Mori, who was awarded a Fields Medal in 1990.

Araujo disregarded advice that this single-minded strategy was risky, that she should be publishing papers to build up her CV. But by 2008, Araujo and two collaborators had found a solution and published their result (generalizing an important result of Mori’s from 1979). This accomplishment likely earned her the tenure-track job at IMPA.