Exotic sphere discoverer wins mathematical 'Nobel': Imagine splitting an ordinary sphere into two halves along the middle, so that each half has a copy of every point on the equator. Now rejoin the two halves so that the southern copy of a point doesn't join its northern counterpoint. In two dimensions, there's only one way to do this: by twisting the sphere. But in seven dimensions the points can be mixed up with respect to each other in multiple different ways...
It turns out there are a total of 28 exotic spheres in seven dimensions, and they also exist in other dimensions. Dimension 15 has as many as 16,256, while others like dimensions five and six only have the ordinary sphere. Mathematicians don't yet know whether exotic spheres exist in four dimensions – a problem known as the smooth Poincaré conjecture, and related to the generalised Poincaré conjecture, which was solved in 2003.
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