We guide you through an exciting recent breakthrough in the world of topology, involving something called the telescope conjecture.

This collection of articles explores a recent, exciting breakthrough in the field of topology.

We continue our exploration of the telescope conjecture.

Topologists famously think that a doughnut is the same as a coffee cup because one can be deformed into the other without tearing or cutting. Topology doesn't care about exact measurements of quantities like lengths, angles and areas. Instead, it looks only at the overall shape of an object, considering two objects to be the same as long as you can morph one into the other without breaking it. But how do you work with such a slippery concept? One useful tool is what's called the fundamental group of a shape.