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.

Consider a pencil lying on your desk. Try to

spin it around so that it points once in every direction, but make sure it sweeps over

as little of the desk's surface as possible. You might twirl the pencil about its middle,

tracing out a circle, but if you slide it in clever ways, you can do much better. Understanding the

smallest volume that you can create has alluded some of the greatest living mathematicians,

which is why people are hailing a new proof of the so-called Ciccaia conjecture in three dimensions

as a once-in-a-century kind of result. It seems like a problem about how

straight lines intersect with one another, but it's also so much more. 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.

For five decades, mathematicians have sought the best possible solution to the three-dimensional

version of the pencil challenge. Hold a pencil in mid-air, then point it in every direction

while minimizing the volume of space it moves through. This straightforward problem has alluded some of the greatest living mathematicians,

and it lurks beneath a host of open problems.

Now, the hunt for a solution appears to be over.

In a paper recently published on the scientific preprint site Archive.org,

Hong Wong of New York University's Corront Institute and Joshua Zal of the University of British Columbia have proved the three-dimensional

...