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Hannah Cairo Refuted a Mathematical Theory Over 40 Years Old. The Story of a Brilliant Young Woman Who Surprised the Scientific World.
During the pandemic, millions of people sought new hobbies. In the case of Hannah Cairo, a 17-year-old teenager, this new interest led her to achieve an impressive feat in mathematics.
Homeschooled and self-taught, she mastered calculus by the age of 11, read graduate-level books on her own, and had tutors hired by her parents.
The young woman became involved with the Math Circles club in Chicago, which promotes meetings between students and teachers to solve mathematical problems.
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Curious, she also decided to participate in the summer program of the club’s branch in Berkeley, California.
At age 14, she wrote in her application that she had knowledge equivalent to an advanced degree. She was accepted without difficulty.
Advancement Beyond The Expected
Zvezdelina Stankova, a mathematician at the University of Berkeley and founder of the local Math Circles, praised Hannah’s performance.
According to her, the student consistently stands out, surpassing expected levels in any program she joins.
After repeating the summer course, Hannah was advised by Stankova to enroll in the university’s concurrent enrollment program.
This program allows high school students to take college-level courses.
The young woman was accepted and began taking more advanced subjects. There, she met Professor Ruixiang Zhang, who introduced her to the Mizohata-Takeuchi conjecture, one of the most intriguing problems in modern mathematics.
Challenges and Persistence
The conjecture, proposed decades ago, deals with specific behaviors of waves on curved surfaces.
Although several mathematicians have tried to refute it, all have failed. When Zhang presented a simplified version of the problem to his students, he encouraged them to go beyond and seek generalizations.
Hannah accepted the challenge. However, in her initial attempts, her ideas did not work.
She sought out the professor during office hours to present new approaches, but always received the same response: it was not enough. Even so, she did not give up.
“I went to office hours and asked him: ‘Do these ideas work?’. It turned out they didn’t because they were silly“, she told Quanta. Persistent, she continued reformulating hypotheses until she found something truly promising.
The Unexpected Discovery
After much effort, Hannah had a vision. She proposed a new way to look at the problem, using a peculiar set of waves over a curved surface.
Contrary to expectations, these waves amplified, something the conjecture claimed was impossible.
She then simplified her proof to make it as clear as possible. Zhang, who had previously refuted all ideas, this time agreed with the reasoning presented.
The result was an unprecedented paper, published in February, even before undergoing peer review.
Repercussions in the Academic World
The publication generated surprise among specialists in the field. The most striking aspect was the astonishment at the author’s age.
Tony Carbery, from the University of Edinburgh, stated that he has been studying the problem for nearly 40 years and was completely impressed to see the solution coming from a teenager.
Itamar Oliveira, from the University of Birmingham, also expressed surprise. “We were all shocked, absolutely,” he commented to Quanta. For him, Hannah’s work was something unprecedented.
New Step Towards The Future
Despite all the recognition, Hannah decided to continue expanding her horizons. She was accepted by the University of Maryland, which, along with Johns Hopkins, was one of the only institutions to allow her entry without a formal high school diploma or degree.
Now, Hannah is preparing to begin this new chapter later this fall. When she completes her course, it will be her first official diploma — a symbolic achievement for someone who has already shown the world that talent and dedication know no age.
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