At 17, Hannah Cairo solved a major math mystery

Summary

Cairo followed this advice. In the fall of 2023, her family moved to Davis, 60 miles northeast of Berkeley. There, her older brother enrolled as a freshman at UC Davis, and her parents allowed her to commute to Berkeley on Tuesdays and Thursdays. By the spring, she was going five days a week and taking several more classes. She recalls it as a time in her life when she began to feel full of possibility. “I had started making friends, and I was feeling good,” she said. After the spring semester ended, her family moved from Davis to Berkeley — her brother had decided to transfer there — and Cairo finally felt able to settle in. Even so, it was an adjustment. “I didn’t have many social experiences, so I still had to learn how to interact with other humans,” she said. As the 2024–2025 academic year neared, Cairo considered what courses she would take. One class in particular caught her eye — a graduate course in Fourier restriction theory, a branch of harmonic analysis. “It was one of the most advanced analysis classes being offered that semester, so I thought, I’ll just go take it,” she said. The mathematician Ruixiang Zhang gave Cairo a homework problem that she couldn’t stop thinking about. He later became her adviser. The professor for the course was Ruixiang Zhang, an accomplished mathematician whose path into the field had followed a more traditional arc: a gold medal at the 2008 International Mathematical Olympiad, the prestigious high school competition; a doctorate from Princeton University; a postdoc at the Institute for Advanced Study; a tenure-track position at Berkeley, one of the top math departments in the world. Cairo emailed Zhang, asking to enroll. “Hannah was very focused and seemed to be passionate about the topic,” he said. “This attitude alone is enough for me, so I just gave her permission.” Within a few weeks, while working on a problem set, she came across a problem that she couldn’t stop thinking about. Extra Credit The problem was a simplified...