Probability theory
The mathematics of randomness, later axiomatized via measure theory.
Founded: 1654 — Pascal & Fermat's correspondence on gambling problems
The claim
No credible dismissal found. Not at any level of abstraction, including Kolmogorov's 1933 measure-theoretic axiomatization, which “became the mostly undisputed axiomatic basis” essentially immediately. Invented to solve a practical problem and never stopped being applied.
What happened
Actuarial science & statistical mechanics (1654) — Applied from the field's origin.
Black–Scholes options pricing (1973) — Itô calculus, built on measure-theoretic probability, underlies modern derivatives markets.
0 years — applied from inception — the clean control case: never even a candidate for the myth
Verdict: Never dismissed, applied anyway.
Confidence: high.