Title : The mathematical theory of
general relativity
Abstract : In 1915, when Einstein revealed the gravitational nature of spacetime, a new language was needed to express this
groundbreaking concept. Remarkably, the necessary mathematics had already been developed 50 years prior by Riemann. In
terms of Riemannian geometry, spacetime could be described as a Lorentzian manifold satisfying the now-famous Einstein
equation. It was later discovered that the evolution of spacetime itself could be formulated as an initial value problem of a nonlinear
system of hyperbolic partial differential equations. This is the foundation of what we now call the mathematical theory of general
relativity, placing it squarely at the crossroads of differential geometry and partial differential equations. Today, this field remains
vibrant and dynamic, with recent discoveries and renewed interest constantly pushing the boundaries of our understanding.