When Hannah Cairo was 17 years old, she disproved the Mizohata-Takeuchi conjecture, a long-standing guess in the field of harmonic analysis about how waves behave on curved surfaces. The conjecture was posed in the 1980s, and mathematicians had been trying to prove it ever since. If the Mizohata-Takeuchi conjecture turned out to be true, it would illuminate many other significant questions in the field. But after hitting wall after wall trying to prove it, Cairo managed to come up with a counterexample: a circumstance where the waves don’t behave as predicted by the conjecture. Therefore, the conjecture can’t be true.

Cairo got hooked on the problem after being assigned a simpler version of the conjecture to prove as a homework assignment for a class she was taking at the University of Ca

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