Unweaving the Fabric of the Universe: The Interplay between Mathematics
  and Physics
  Our conventional understanding of space-time, as well as our notion of
geometry, break down once we attempt to describe the very early stages of the
evolution of our universe. The extreme physical conditions near the Big Bang
necessitate an intimate interplay between physics and mathematics. The main
challenge is the construction of a theory of quantum gravity, the long-sought
unification of Einstein's general relativity with quantum mechanics. There are
several attempts to formulate such a theory; they can be tested against
experimental and observational results coming from high energy physics and
astrophysics, leading to a remarkable interplay between gravity, particle
physics and cosmology.
