Mathematical cosmology is defined, informally speaking, as the study of whole universes. It started in 1917, when Albert Einstein showed how to build the first universe as a solution of his equations of general relativity. Since then it has developed into a vast mathematical science that aims to study possible universes, solutions of Einstein’s and other gravity theories, and confront with the latest observations.
Mathematical cosmology uses differential geometry to construct novel theories of gravity, and topological and dynamical methods to study their implications for the possible models of the Universe that emerge – the universes. It has freed us from prejudices about our Universe, by separating the always unknown and unknowable Universe, from the many different universes-the possible constructions of mathematical and physical models of the Universe that we can build, study and compare!
Mathematical cosmology has also triggered new developments in both theoretical physics and modern mathematics, and has led to definite theoretical predictions that are being tested observationally.