Potential theory
Harmonic functions — solutions of Laplace's equation.
Founded: 1828 — Green's essay on electricity and magnetism
The claim
No credible dismissal found. Born directly from physics (Newtonian gravitation, electrostatics) and never abstracted away from application before being taken seriously. One aside: Green's own 1828 essay was neglected (51 subscribers) until Kelvin rediscovered it in the 1840s — obscurity, not a “useless” verdict.
What happened
Electrostatics & gravitational modeling (1828) — Applied essentially from the moment of its rigorous formulation.
0 years — applied from inception — no meaningful gap
Verdict: Never dismissed, applied anyway.
Confidence: medium.