  We review the recently discovered connection between the
Belinsky-Khalatnikov-Lifshitz-like ``chaotic'' structure of generic
cosmological singularities in eleven-dimensional supergravity and the ``last''
hyperbolic Kac-Moody algebra E(10). This intriguing connection suggests the
existence of a hidden ``correspondence'' between supergravity (or even
M-theory) and null geodesic motion on the infinite-dimensional coset space
K(E(10)). If true, this gravity/coset correspondence would offer a new view of
the (quantum) fate of space (and matter) at cosmological singularities.
