t’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 (opens a new tab) left the math world by turns stunned, delighted and ready to welcome a bold new talent into its midst. Its author was Hannah Cairo (opens a new tab), 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 (opens a new tab) 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.

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The math world was taken aback when Cairo announced her counterexample to the Mizohata-Takeuchi conjecture — both because it settled a major open problem, and because Cairo was still in high school at the time.

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