17-Year-Old Hanna Cairo Disproves Hypothesis in Harmonic Analysis and Impresses Scientific World

Self-taught American student Hanna Cairo, just 17 years old, overturns ideas in the field of harmonic analysis by disproving the Takeuchi hypothesis – a topic mathematicians have been actively working on since 1980. The hypothesis concerns the decomposition of functions into simpler components using sinusoidal waves, limiting the type of waves that form a specific geometric shape.

Hanna manages to construct a counterexample in a new and more elegant way by transforming the task into frequency space. Her achievement causes a sensation in scientific circles – the young mathematician presented her solution at the 12th International Congress on Harmonic Analysis and Differential Equations in Spain, which was her first international appearance.

Born and raised in the Bahamas, Hanna studied through online courses and later independently with graduate-level literature. Her parents support her and hire tutors, with one of them admitting he can no longer help her. During the pandemic, the family moves to the USA, where Hanna joins a mathematics club in Chicago.

Soon she is accepted as a doctoral student at the University of California, Berkeley, where she first encounters the Takeuchi hypothesis. This fall, Hanna will also begin studies at the University of Maryland, despite not having a formal high school diploma or bachelor's degree.