Around 50 years ago, physicists Belinski, Khalatnikov and Lifshitz provided heuristics describing the behaviour of near-singularity solutions to the Einstein equations as spacelike, local and oscillatory. Vaguely speaking, they suggest that dynamics corresponding to different spatial points on the singularity decouple and resemble a chaotic cascade of so-called “Kasner epochs”. In this talk, we present a mathematical formulation of this “BKL Conjecture” and progress towards the conjecture in the case of Gowdy symmetric spacetimes.