Partial differential equations
Equations involving unknown functions of several variables and their partial derivatives.
Founded: 1747 — d'Alembert's wave equation
The claim
No credible dismissal found. Born from 18th/19th-century physics. The one documented case is neglect, not dismissal: Courant's 1943 piecewise-linear variational method went unrecognized for over a decade until independently rediscovered by structural engineers (1954–56).
What happened
Finite element method (1956) — Argyris, Turner, Clough, Martin & Topp's engineering rediscovery of Courant's 1943 method — standard in structural, aerospace and civil simulation.
0 years — applied from inception for the classical theory; Sobolev's 1938 abstract reformulation to FEM engineering deployment (1956) is an 18-year pocket
Verdict: Never dismissed, applied anyway.
Confidence: medium-high.