FLP impossibility Fischer–Lynch–Paterson
Proved in 1985 that no deterministic asynchronous consensus algorithm can guarantee both liveness and safety if even a single node can crash.
Fischer, Lynch, Paterson. "Asynchronous" = no guarantees on message delivery time. Practical consequence: every real consensus algorithm (Paxos, Raft, PBFT) sidesteps FLP by (a) relying on timing assumptions (partial synchrony — messages get delivered eventually within some bound), (b) using randomness (randomised consensus), or (c) using failure detectors. Together with the CAP theorem one of the heavyweight theoretical foundations of distributed systems design.