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Hannah Cairo

Hannah Cairo

2025 Davidson Fellow Laureate
$100,000 Scholarship

Age: 18
Hometown: Berkeley, CA

Mathematics: “A Counterexample to the Mizohata-Takeuchi Conjecture”

About Hannah

Hello! I’m Hannah, an incoming Ph.D. student at the University of Maryland studying harmonic analysis, a branch of mathematics. I was born and raised in the Bahamas.

Outside of my career as a mathematician, I enjoy teaching at mathematics enrichment programs for youth, running, playing piano, spending time with friends, meeting new people, and trying new things. I am also beginning to get involved in animal rights activism.

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"I am honored to become a Davidson Fellow; the scholarship will open doors for me and allow me to spend more time on research."

Project Description

If you drop two stones into a pond, you might notice a pattern called an interference pattern: instead of forming separate circles, the ripples overlap. What kinds of shapes can we build if we are only allowed to use certain ripples? You cannot form just any object; in fact, you can only produce a relatively small family of shapes. The Mizohata-Takeuchi conjecture states that the shapes we get should be concentrated along lines. I proved that they do not need to be concentrated along lines.

Deeper Dive

My project consisted of disproving the Mizohata-Takeuchi conjecture, a conjecture in harmonic analysis. I began exploring harmonic analysis in fall 2024 when I took a class on Fourier restriction theory taught by Ruixiang Zhang. I decided to study the MT conjecture when it was mentioned in a homework problem in his class.

During my research, I encountered several challenges. Many times, I thought I could prove or disprove the conjecture, only to realize the next day that my idea did not work. My mentor helped me understand why some of my ideas were flawed.

It is difficult to say exactly how mathematical research will impact quality of life for others. In mathematics, as well as in certain areas of physics and other sciences, the applications of a specific project are often unclear. As a whole, harmonic analysis is a central tool in many technologies used in daily life, with applications in telecommunications, biomedical imaging, electrical engineering, and data compression.

Q&A

If you could have dinner with the five most interesting people in the world, living or dead, who would they be?

  • Johann Sebastian Bach
  • Greta Thunberg
  • Fred Hampton
  • Ingrid Newkirk
  • My friends 🙂

What is your favorite tradition or holiday?

Pride month! 🌈

What is your favorite hobby?

I love to go for walks on outdoor trails.

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In The News

Three Bay Area teens have been named 2025 Davidson Fellows, one of the nation’s most prestigious honors for students 18 and younger. Hannah Cairo of Berkeley, Ethan Yan of Burlingame, and James Gu of Newark will share $175,000 in scholarships as part of the program’s 25th anniversary year, which is awarding a record $825,000 to 21 students nationwide.

Download the full press release here

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