When you look at your surrounding environment, it might seem like you're living on a flat plane. After all, this is why you can navigate a new city using a map: a flat piece of paper that represents all the places around you. This is likely why some people in the past believed the earth to be flat. But most people now know that is far from the truth. You live on the surface of a giant sphere, like a beach ball the size of the Earth with a few bumps added. The surface of the sphere and the plane are two possible 2D spaces, meaning you can walk in two directions: north and south or east and west. Through a field called geometric topology, mathematicians like me study all possible spaces in all dimensions. Whether trying to design secure sensor networks, mine data or use origami to deploy satellites, the underlying language and ideas are likely to be that of topology. When you look around the universe you live in, it looks like a 3D space, just like the surface of the Earth looks like...
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