How a High School Student Overturned a Famous Conjecture

By Quanta Magazine

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When Hannah Cairo was a 17-year-old high school student, she did something mathematicians had been unable to do for four decades: she overturned the Mizohata-Takeuchi conjecture, a famous prediction about how wave energy behaves. In this video, Cairo and the mathematicians she worked with explain how she found the counterexample and what it means for the field. Read Cairo's paper: https://arxiv.org/abs/2502.06137 00:00 - Introduction to Cairo 01:06 - A big question in Fourier restriction theory 02:20 - Tubes and what the Mizohata-Takeuchi conjecture predicted 04:08 - Cairo's process 05:54 - A key object, the hypercube 06:37 - The result and its significance 07:53 - Cairo's creative approach to mathematics --------- Quanta Magazine is an editorially independent publication supported by the Simons Foundation. We focus on developments in mathematics, theoretical physics, theoretical computer science, and the basic life sciences.

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