Most professional mathematicians weren't what we consider prodigies, doing advanced math at a young age or powering through college and graduate school, while most of the rest of us are trying to figure out what to do with our lives.

But there's also people like Paul Erdoche and Terry Tao, or Blaise Pascal, Everest Galois, or John

von Neumann.

They were all prodigies who went on to prodigious careers.

With that tradition in mind, we will all be watching the career of another prodigy named

Hannah Cairo.

And that's not because she's starting a doctoral program

without either an undergraduate or even a high school degree, which she is, but because at just

17 years old, she's already rewritten the rules of a subfield of mathematics.

Welcome to the Quantum Podcast, where we explore the frontiers of fundamental science and math.

I'm Samir Patel, editor-in-chief of Quantum Magazine.

We've noticed that some of our most popular math stories are ones about big findings in math that come from unexpected places, often from young people or students.

Even in that illustrious group, Hanna Cairo stands out. Contributing writer Kevin Hartnett wrote about this for us in the story called

At 17, Hannah Cairo solved a major math mystery, and here to talk about it with us is our math editor,

Jordana Seppelowitz. Welcome back to the show, Jordana. Thank you. It's nice to be back.

So, as we always start, what is the big idea of this story? So as you've previewed, in this piece,

Kevin tells about a surprising mathematical result that comes from a very surprising place.

This 17-year-old girl who was homeschooled in the Bahamas basically came out of nowhere and solved this really important conjecture.

She proved it false, actually.

And so, yeah, he tells the story about who she is and how that happened.

What do you know about the tradition of math prodigies?

This is a very powerful myth in mathematics, this idea that you have to have very

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