Welcome to Quantum Magazine's podcast.

Each episode, we bring you stories about developments in science and mathematics.

I'm Susan Vallett.

What does it take to solve a centuries-old question about some of the most basic objects in geometry?

A young couple, and a decade of chipping away at the question.

That's next.

Explore science mysteries in the Quanta book, Alice and Bob Meet the Wall of Fire,

published by the MIT Press.

Available now at Amazon.com, Barnes & Noble.com, or your local bookstore.

A basic fact of geometry known for millennia is that you can draw a line through any two points in the plane.

Any more points, and you're out of luck, it's not likely that a single line will pass through all of them.

But you can pass a circle through any three points, an iconic section,

like an ellipse, parabola, or hyperbola, through any five. More generally, mathematicians want to know

when you can draw a curve through arbitrarily many points and arbitrarily many dimensions.

It's a fundamental question known as the

interpolation problem. It's a question about algebraic curves, one of the most central objects

in mathematics. Ravi Vakil is a mathematician at Stanford University. So this is really about

even just understanding what curves are.

Curves that live in higher dimensions may have been studied with state-of-the-art tools for hundreds of years,

but they're tricky beasts.

In two-dimensional space, a curve can be cut out by a single equation.

A line might be written as y equals 3x minus 7.

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