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At 17, She Disproved a 40-Year-Old Conjecture
It began with an optional question on a graduate mathematics assignment.
Ruixiang Zhang had given his graduate students a problem to practise some advanced mathematical techniques. Hannah Cairo completed it, but one part of the assignment stayed with her.
The question concerned a simplified version of the Mizohata–Takeuchi conjecture, a problem in harmonic analysis that mathematicians had been trying to solve for roughly forty years. Zhang had also included an optional extension: could the argument used for the simpler case be pushed further?
Cairo wanted to find out.
She spent months thinking about the problem, trying approaches that didn’t work and discussing her ideas with Zhang during office hours at the University of California, Berkeley. Eventually, her investigation took an unexpected direction. She found a mathematical construction that contradicted the original conjecture.
On February 10, 2025, Cairo submitted a paper titled A Counterexample to the Mizohata–Takeuchi Conjecture to arXiv. She was seventeen years old. [1, 2]
The news attracted attention partly because of her age, but the mathematics deserved attention of its own. Cairo had found a way for waves to behave in a manner that a long-standing conjecture said should be…
