A pair of identical particles swapping places sounds like a small move. In quantum physics, it is a defining one. In everyday ...

In our three-dimensional space, elementary particles neatly filter into either bosons or fermions. But in lower dimensions, that distinction gets a bit murky.

For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them. In geometry and the closely ...