Teen Math Genius Discovered

17-year-old Hannah Cairo disproved the 40-year-old Mizohata-Takeuchi conjecture.

From Quanta:

At 17, Hannah Cairo Solved a Major Math Mystery

By Kevin Hartnett

After finding the homeschooling life confining, the teen petitioned her way into a graduate class at Berkeley, where she ended up disproving a 40-year-old conjecture.

August 1, 2025

It’s not that anyone ever said sophisticated math problems can’t be solved by teenagers who haven’t finished high school. But the odds of such a result would have seemed long.

Yet a paper posted on February 10 left the math world by turns stunned, delighted and ready to welcome a bold new talent into its midst. Its author was Hannah Cairo, just 17 at the time. She had solved a 40-year-old mystery about how functions behave, called the Mizohata-Takeuchi conjecture.

“We were all shocked, absolutely. I don’t remember ever seeing anything like that,” said Itamar Oliveira of the University of Birmingham, who has spent the past two years trying to prove that the conjecture was true. In her paper, Cairo showed that it’s false. The result defies mathematicians’ usual intuitions about what functions can and cannot do.

So does Cairo herself, who found her way to a proof after years of homeschooling in isolation and an unorthodox path through the math world.

Cairo grew up in Nassau, the Bahamas, where her parents had moved so that her dad could take a job as a software developer. She and her two brothers — one three years older, the other eight years younger — were all homeschooled. Cairo started learning math using Khan Academy’s online lessons, and she quickly advanced through its standard curriculum. By the time she was 11 years old, she’d finished calculus.

Soon she had consumed everything that was readily available online. Her parents found a couple of math professors to tutor her remotely — first Martin Magid of Wellesley College, then Amir Aazami from Clark University. But much of her education was self-directed, as she read and absorbed, on her own, the graduate-level math textbooks that her tutors recommended. “Eventually,” Cairo recalled, Aazami “said something like, he feels uncomfortable being paid, because he feels like he’s not really teaching me. Because mostly I would read the book and try to prove the theorems.”

But Cairo found homeschooling confining.

“There was this inescapable sameness, in a way. No matter what I did, I was in the same place doing mostly the same things,” she said. “I was very isolated, and nothing I could do could really change that. I’d wake up on certain days and realize, I’m just older.” …

In 2023, after a second summer with the Berkeley Math Circle, Cairo wondered what her next step should be. She had already applied to several universities, and while most schools rejected her — she hadn’t finished high school yet — she was accepted by the University of California, Davis. Should she start her undergraduate studies three years early? Or should she pursue educational opportunities elsewhere?

Stankova encouraged her to instead participate in Berkeley’s concurrent enrollment program, where she could take graduate-level math courses from leading researchers in the field. …

Over the decades, mathematicians made limited progress on a few special cases of the Mizohata-Takeuchi conjecture. But the general problem remained wide open. None of the standard methods seemed able to touch it. That imperviousness made some mathematicians suspect that the conjecture was false; others felt that its elegance made it more likely to be true.

“Some mornings, I’d wake up with the idea that because it’s so simply and elegantly stated, and it’s so broad, in the end it had to be true,” said Tony Carbery, a mathematician at the University of Edinburgh who worked on the problem for decades. “Other mornings, I’d wake up and say … it can’t possibly be true in any simpleminded way.”

Mathematicians found themselves at an impasse. …

The proof, and its unlikely author, have energized the math community since Cairo posted it in February. “I was absolutely, ‘Wow.’ This has been my favorite problem for nigh on 40 years, and I was completely blown away,” Carbery said. “When I found out [Cairo] was much younger than I previously thought, I was much more impressed. The elegance with which the paper is written is quite extraordinary.”

Mathematicians are excited about how Cairo’s work will inspire new research. “I am certain that, from now on, whenever we come upon a problem of similar flavor, we will try to test it against Cairo-like constructions,” Oliveira said. …

The math world is also adjusting to the fact of Cairo herself. After completing the proof, she decided to apply straight to graduate school, skipping college (and a high school diploma) altogether. As she saw it, she was already living the life of a graduate student. Cairo applied to 10 graduate programs. Six rejected her because she didn’t have a college degree. Two admitted her, but then higher-ups in those universities’ administrations overrode those decisions.

Only the University of Maryland and Johns Hopkins University were willing to welcome her straight into a doctoral program. She’ll start at Maryland in the fall. When she finishes, it will be her first degree.

An interesting question is: What are the odds these days that a teen math genius who uses feminine pronouns is female?

Paywall here.