To demonstrate that impossible manifolds could be coaxed into living in Euclidean space is counterintuitive and pretty exciting.
Impossible manifolds could never be coaxed into living in Euclidean space. 
mnli hypothesis: Impossible manifolds could never be coaxed into living in Euclidean space.  premise: To demonstrate that impossible manifolds could be coaxed into living in Euclidean space is counterintuitive and pretty exciting.