Group theory & Lie groups
The algebra of symmetry, and its continuous (Lie) generalization.
Founded: 1854 — Cayley's abstract definition of a group
The claim
No credible dismissal found. Weaker than it's often told. Burnside's 1897 preface to Theory of Groups of Finite Order explains an omission — given the results then known to him, he found it hard to name a result more directly reached via linear-transformation groups than via substitution groups — which is a narrow, time-qualified editorial judgment, not a forecast that the topic would never produce anything. Scholarship also cautions he may not even have meant Frobenius's brand-new representation theory: the relevant Frobenius paper connecting character theory to linear substitutions appears to have followed Burnside's preface within the same year. By the 1911 second edition, new results had changed Burnside's assessment. Separately, physicists in the late 1920s coined “Gruppenpest” (the group-plague) for group-representation methods arriving in quantum mechanics, commonly traced to Paul Ehrenfest's circle in Leiden (1928) — but Ehrenfest himself did not reject the theory and ran seminars on it; the episode was a mix of enthusiasm, skepticism, fashion, and pedagogical frustration, not a clean dismissal.
What happened
37 years — founding (1854) to crystallography (1891)
Verdict: Never dismissed, applied anyway.
Confidence: medium.