Mizohata-Takeuchi Conjecture
17-year-old found a counterexample to the 40-year-old conjecture about Fourier restriction estimates.
The Mizohata-Takeuchi conjecture (1985) proposed that certain weighted Fourier restriction estimates should always hold for positive Borel measures on spheres. Hannah Cairo, at age 17, found an explicit counterexample that disproved it. She went directly into a PhD program, skipping undergrad.
Formula
The Mizohata–Takeuchi conjecture predicted that a single condition on the measure μ would control Fourier restriction.
The Mizohata–Takeuchi norm measures concentration of μ along thin tubes — necessary but not sufficient for restriction.
Disproved by exhibiting a measure with bounded MT norm but unbounded Fourier restriction — showing the conjecture was too optimistic.
Summary
The Mizohata-Takeuchi conjecture (1985) proposed that certain weighted Fourier restriction estimates should always hold for positive Borel measures on spheres. Hannah Cairo, at age 17, found an explicit counterexample that disproved it. She went directly into a PhD program, skipping undergrad.