The Mathematics of the Telephone – Shannon’s Theorem

Claude Shannon’s 1948 paper ‘A Mathematical Theory of Communication’ founded information theory. He defined the bit as the unit of information, derived the formula for channel capacity: C = B log₂(1 + S/N). For a telephone line with 3 kHz bandwidth and 30 dB signal‑to‑noise ratio, capacity ≈ 30 kbit/s. This sets the ultimate limit on data transmission. Shannon’s work made digital communication possible – every modem, DSL line, and wireless network uses his mathematics.