A Mathematical Theory of Communication

Published in two parts in the Bell System Technical Journal in 1948, Claude Shannon's A Mathematical Theory of Communication transformed communication from an engineering craft into a mathematical science. The paper established three foundational results: that information has a precise quantitative measure (the bit), that every channel has a maximum capacity above which reliable transmission is impossible, and that noise does not preclude arbitrarily reliable communication provided sufficient redundancy is employed. The paper's abstractions — source, encoder, channel, decoder, destination — proved general enough to describe every communication system from telephone wires to biological signaling to, seventy-seven years later, the exchange between a human being and a large language model. The framework explicitly excluded semantic meaning from its mathematical treatment, a methodological choice that both enabled the mathematics and left a gap subsequent generations have tried to close.