Here’s a simple-sounding problem: Imagine a circular fence that encloses one acre of grass. If you tie a goat to the inside of the fence, how long a rope do you need to allow the animal access to exactly half an acre? It sounds like high school geometry, but mathematicians and math enthusiasts have been pondering this problem in various forms for more than 270 years. And while they’ve successfully solved some versions, the goat-in-a-circle puzzle has refused to yield anything but fuzzy, incomplete answers. Even after all this time, “nobody knows an exact answer to the basic original problem,” said Mark Meyerson, an emeritus mathematician at the US Naval Academy. “The solution is only given approximately.” But earlier this year, a German mathematician named Ingo Ullisch finally made progress, finding what is considered the first exact solution to the problem—although even that comes in an unwieldy, reader-unfriendly form. “This is the first explicit expression that I’m aware of [for the length of the rope],” said Michael Harrison, a mathematician at Carnegie Mellon University. “It certainly is an advance.”