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Kernel
Shannon is the figure who founded information theory in a single 1948 paper at Bell Labs. Every subsequent digital technology, from compact discs to the internet to wireless to deep learning, rests on his definition of the bit and his quantification of channel capacity.
§ 01
Contribution
The bit as the unit of information. Channel capacity (Shannon–Hartley). The mathematical theory of secrecy systems (1949), the founding paper of modern cryptography. The Boolean-algebra-as-circuit-design move (his 1937 master's thesis) — the substrate of all digital logic.
§ 02
Civilization-scale significance
Without Shannon, no digital civilization. The fact that he is much less famous than physicists of comparable importance is a fact about who gets to be famous, not about what he did.