Hannah Cairo has solved the Mizohata-Takeuchi conjecture

Summary

Hannah Cairo was stuck on a math problem. All she could think about during those weeks was a new approach. “After months of trying to prove the result, I managed to understand why it was so difficult. I realized that if I used that information correctly, I might be able to refute the claim. Finally, after several failed attempts, I found a way to construct a counterexample [a case that does not satisfy the studied property and therefore proves it is not universally true].” Ciaro says it required several tools, including fractals, and she had to arrange everything very carefully. “It took me a while to convince Ruixiang Zhang [the professor of the course where the problem had been posed] that my proposal was actually correct,” Cairo says.She was right—and with that, Cairo solved the so-called Mizohata-Takeuchi conjecture, a problem first proposed in the 1980s that had kept the harmonic analysis community had been working on for decades. The conjecture was widely believed to be true — if so, it would have automatically validated several other important results in the field — but the community greeted the new development with both enthusiasm and surprise: the author was a 17-year-old who hadn’t yet finished high school.“When I moved to the U.S. from Nassau [in the Bahamas, where she was born], I entered the educational system as a high school student, although I took classes at UC Berkeley. I wrote to professors, telling them what books I’d read on the subject, and asking if I could attend their classes. Many said yes, including Zhang,” she says. “One day, he proposed proving a special, much simpler case of the conjecture as a homework assignment. As an optional part, he included the original conjecture. And I became obsessed with it,” she adds.The Mizohata-Takeuchi conjecture falls within the field of harmonic analysis, which attempts to break down functions into simpler components, such as sinusoidal functions. Today, it’s a very active area of research and has becom...