Despite satellite mapping and GPS, a few spots on Earth are defined entirely by how hard they are to reach, and pinning them down is a mathematical nightmare. This episode explores the poles of inaccessibility, the points farthest from any coastline, and the obsessive explorers and mathematicians who chase a target that keeps moving as our coastline data improves.

We start with Point Nemo, the oceanic pole nearly 2,688 kilometers from the nearest land, used as a spacecraft cemetery and so remote the closest humans are often astronauts overhead. Then we journey to Antarctica's southern pole, marked by a buried plastic bust of Lenin, and explore why the continent has two poles depending on how you measure the ice. We also cover the shifting Arctic pole and the contested Eurasian pole.

• How a pole of inaccessibility is the center of  ...