Dynamical systems & ergodic theory
Poincaré's qualitative theory of the three-body problem: deterministic systems can be unpredictable.
Founded: 1890 — Poincaré's corrected prize memoir on the three-body problem
The claim
No credible dismissal found. No named dismissal, but treated as a narrow celestial-mechanics curiosity by nearly everyone — obscure enough that Stephen Smale rediscovered the same ideas independently in the late 1950s.
What happened
Chaos theory & weather-forecast limits (1963) — Lorenz independently rediscovers sensitive dependence on initial conditions in a weather model — founds the modern predictability-limit theory.
73 years — founding (1890) to Lorenz (1963)
Verdict: Never dismissed, applied anyway.
Confidence: high.