Complex analysis
Holomorphic functions of a complex variable: Cauchy's theorem, residues, conformal mapping.
Founded: 1825 — Cauchy's integral theorem
The claim
No credible dismissal found. Cardano's “as subtle as it is useless” (1545) and Descartes coining “imaginary” (1637) as an insult both target complex numbers, roughly two centuries before complex analysis existed as a field — conflating the two would misattribute the dismissal.
What happened
AC circuit analysis (1893) — Charles Steinmetz's complex-impedance/phasor method for electrical engineering.
68 years — founding (1825) to Steinmetz (1893)
Verdict: Never dismissed, applied anyway.
Confidence: medium.