Why can't a system spread across the world be both always consistent and always available?

Because networks break, and when the link between two copies of your data is cut, the copies cannot compare notes. The CAP theorem, also named Brewer's theorem after Eric Brewer, says a distributed data store can provide at most two of three guarantees: consistency, availability and partition tolerance. Consistency means every read receives the most recent write, or an error. Availability means every request to a working node gets a response, without a guarantee it holds the latest data. Partition tolerance means the system keeps operating even when the network drops or delays messages between nodes.

No distributed system is safe from network failures, so partitions generally have to be tolerated, which leaves two options. When a partition happens, a system can cancel the operation, lowering availability but ensuring consistency, or proceed, providing availability but risking inconsistency. Say you save a change on one side of a cut network and someone reads it on the other. The system can only return an error or return the old value.

Notice the limit of the claim. In the absence of a partition, both availability and consistency can be satisfied. Brewer himself clarified in 2012 that "two out of three" can be misleading: designers only need to sacrifice one of them in the presence of partitions, and partition management and recovery techniques exist.

The idea has a founder with a story. Brewer says the theorem first appeared in autumn 1998, and he presented it as a conjecture at a major conference in 2000. In 1996 he had co-founded Inktomi and became a paper billionaire during the dot-com bubble. In 2002 Seth Gilbert and Nancy Lynch of MIT published a formal proof, which elevated the conjecture to a theorem.