Functional analysis & operator theory
Infinite-dimensional vector spaces, studied for their own analytic properties.
Founded: 1904 — Hilbert's papers on integral equations
The claim
David Hilbert (on his own work), 1904: “I developed my theory of infinitely many variables from purely mathematical interests, and even called it ‘spectral analysis’ without any presentiment that it would later find application to the actual spectrum of physics.”
Source: Widely attributed via Lynn Steen, American Mathematical Monthly 80(4), 1973; primary provenance unconfirmed.
What happened
Quantum mechanics (1932) — Von Neumann's Mathematical Foundations of Quantum Mechanics — quantum states are vectors in Hilbert space.
28 years — founding (1904) to von Neumann (1932)
Verdict: Named dismissal, later applied.
Confidence: medium-high.