What Is The Mizohata-Takeuchi Conjecture Solved By 17-Year-Old Math Prodigy Hannah Cairo?
Hannah Cairo, a 17-year-old from the Bahamas, had solved a 40-year-old math puzzle called the Mizohata-Takeuchi conjecture, which had stumped mathematicians worldwide.
Cairo, a homeschooled teen, mastered calculus by the age of 11 and studied advanced university math at Berkeley. As a child, Hannah Cairo learned math by taking online classes from Khan Academy. At 14, she taught herself the equivalent of an advanced undergraduate math degree.
Her parent found a couple of math tutors for her remotely, including Martin Magid of Wellesley College and then Amir Aazami from Clark University. At the age of 17, she had solved a long-standing math problem that had remained unresolved for decades, which mathematicians had tried to prove but failed.
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The Mizohata-Takeuchi Conjecture, a long-standing math problem, predicted that wave energy on curved surfaces always concentrates along a specific line-like pattern. It guides how scientists understand waves in physics, engineering, and quantum mechanics.
However, mathematicians failed to prove this conjecture. It was believed to be true because of its elegant simplicity, but no one could fully understand it mathematically how complicated wave patterns behave on curved shapes.
Hannah built a special function combining waves whose frequencies lie on the curved surface. Unlike usual cases, their combined energy spread out unevenly in fractal-like patterns, defying the conjecture’s predictions.
She transformed the problem into an abstract ‘frequency space,’ making wave patterns easier to analyze. This allowed her to simplify and refine her counterexample, presenting a clear and convincing proof.
