Welcome to the Quanta Audio Edition. In each of these bi-weekly episodes, we bring you a story direct from the Quanta website about developments in basic science and mathematics. I'm Susan Vallett. One German mathematician has dedicated her career to proving one of the biggest unanswered problems in group theory.

And she, along with the partner she fell in love with along the way, has finally succeeded.

That's next.

Check out this feed every Tuesday for the Quanta podcast.

That's where Editor-in-Chief Samir Patel talks to our writers and editors about more of Quanta's most popular, interesting, and thought-provoking stories.

In 2003, a German graduate student, named Br Spate encountered the Mackaye conjecture,

one of the largest open problems in the mathematical realm known as group theory.

At first, her goals were relatively modest.

She hoped to prove a theorem or two that would make incremental progress on the problem, as many other mathematicians had done before her.

But over the years, she was drawn back to it again and again.

Whenever she tried to focus on something else, she says it didn't connect.

There was a risk that such a single-minded pursuit of such a difficult problem could hurt

her academic career. But Schaith dedicated her time to it anyway. It brought her to the office

of Mark Caban, a mathematician now at the Institute of Mathematics of Zyushu in Paris. He was so inspired by her efforts that he became

consumed by the conjecture too. While working together, the pair fell in love and eventually

started a family. The problem that absorbed them takes a key theme in mathematics and turns it

into a concrete tool for group theorists. Math is full of enormously

complicated abstract objects that are impossible to study in their entirety. But mathematicians have

discovered that it's often enough to look at a small fragment of such an object to understand

its broader properties. For instance, in the third

century BCE, the ancient Greek mathematician Eratosthenes estimated the circumference of the earth,

roughly 25,000 miles. He measured shadows cast by the sun in just two cities, about 500 miles apart. Similarly, when mathematicians want to

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