Number theory
The study of integers, primes, and modular arithmetic.
Founded: 1801 — Gauss's Disquisitiones Arithmeticae
The claim
G. H. Hardy, 1915: “The Theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics” (1915 lecture, delivered with sustained irony per the annotated edition); echoed, with explicit hedges (“at present at any rate,” “Time may change all this”), in A Mathematician's Apology (1940).
Source: Hardy, A Mathematician's Apology, CUP 1940, §21/§25/§28 (primary text, quoted directly).
Hardy's case wasn't purely empirical: he also argued serious mathematics is justified as art, independent of use, and he explicitly allowed that time might prove him wrong about the applications. He was too pessimistic about scope and timescale — that's the real story, not a flat, unhedged prediction.
What happened
RSA cryptography (1977) — Rivest–Shamir–Adleman; publicly circulated 1977, the canonical paper appeared in Communications of the ACM in 1978. Security rests on the difficulty of factoring large primes.
176 years — founding (1801) to RSA (1977)
Verdict: Named dismissal, later applied.
Confidence: high.