Conway's Angel Problem

Show that for sufficiently large power k, the k-angel has a strategy to move forever on the grid despite the devil deleting one unoccupied square per turn.

Conway introduced it in 'The Angel and the Devil' (1996) offering $100 for the angel (or $1000 for a winning devil strategy). A decade of partial power results (Berlekamp, Conway, Guy analysed k=1 loss; Kutz's 2-angel groundwork) preceded the 2006 avalanche: Brian Bowditch (k=4, topological), András Máthé (k=2, 'weird' strategies), and Wei Chuang Kloster (k≥4, probabilistic) all proved escape within months — a rare case of simultaneous independent resolution of a prize problem. The techniques seeded pursuit-evasion game literature since.