How to think about dimensions beyond our own. What if we could move in a new direction, along a new dimension? Maybe not. Because we live in three dimensions, we have access to one- and ...

In a hypertorus model of the Universe, motion in a straight line will return you to your original location, even in an uncurved (flat) spacetime. The Universe could also be closed and positively ...

Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere. In a burst of work ...