At 17, Hannah refuted conjecture at the age of 40 – and shocked the world of mathematics

A brilliant teenager, who at age 11 already dominated differential and integral calculation, chose as a hobby during the pandemic perfecting his mathematical abilities. Six years later, he solved one of the most mysterious problems in mathematics-and became a rising star.

The Young Mathematics Hannah Cairo was only 17 years old when he refuted the evasion Mizohata-takehata’a theory of several decades, related to the behavior of waves on surfaces, which until then no one had managed to counteract successfully.

In advanced mathematics, it is common for an observation -based assumption to become the target of formal refutation attempts – but in 40 years no one had managed to prove – or refute – the mysterious conjecture.

However, in February this year, a pre-published Arxiv left the world of mathematics half stunned, half enchantedand ready to welcome a new prodigy: Hannah had solved the problem about the behavior of the functions that the conjecture had launched.

Born and raised in the Bahamas, and polite at home, at the age of 11 Hannah already dominated the differential and integral calculation, which learned alone from University level manualsand studied remotely with teachers hired by parents as tutors, tells.

When confinements began in 2021, Hannah did what millions of other people in the world also did: arranged a hobby. In his case, he joined the Math Circles de Chicago group, which brings together teachers and students to solve mathematical problems.

At just 14 years old, in 2022 Hannah decided to widen horizons and applied for the prestigious summer program at the University of Berkeley, California. Wrote in the candidacy that already had knowledge equivalent to an advanced degree in mathematics – And, of course, it was accepted.

“Hannah is far above ordinary,” says Zvezdelina StankovaMathematics of the University of Berkeley and founder of the city’s Math Circle, Quanta. “Whenever you are running for a school or program, It is several levels above.”

After completing the program, Hannah began to consider obtaining a formal higher education To complement the knowledge you had already acquired on your own.

Stankova guided her to a U. Berkeley program that allows endowed students, such as Hannah, attend university classes while still completing secondary education.

Once again, Hannah was accepted – And that’s when he met the mathematician and teacher Ruixiang Zhangwhich presented him with the conjecture of Mizohata-Takeuchi. Despite his exceptional intelligence, Hannah had huge difficulties with the problem.

When Zhang proposed A simplified version of the conjecture to their students, encouraged them to explore their reasoning more deeply and see if they could apply them to more complex versions of the problem. Hannah accepted the challenge – but saw her first ideas repeatedly rejected.

Frustrated, but not unmotivatedHannah continued to mentally explore the problem until discovered an innovative approachwhich involved a strange set of waves to propagate on a single curved surface.

Instead of annullingas the original theorem predicted, these waves amplified themselves -Something that the conjecture of Mizohata-Takeuchi considered impossible. Surprised by his own discovery, Hannah simplified the test as much as possible – and, This time, Zhang was convinced.

After his article was published, the world of mathematics was upset – especially when they learned the age of Hannah.

“We all got absolutely shocked”Says the mathematician Itamar Oliveiraresearcher at the University of Birmingham, the United Kingdom, who spent years AA Mizohata-Takeuchi. “I don’t remember seeing anything like that”.

Tony Carberymathematician of the University of Edinburgh, who studies this conjecture has decades, It was also stunnedespecially when he learned the age of Hannah when he wrote the article.

“I was absolutely… wow“Said carryy to Quanta. “This is my favorite problem for almost 40 years, and She left me completely open”.

While the world of mathematics greeted her latest star, the young woman changed her scenario again – this time to the University of Maryland, where she starts classes in the fall. And when finished, this will be the first academic diploma of the self-taught teenager who refuted the conjecture of Mizohata-Takeuchi.