Field theory & Galois theory
Which polynomial equations are solvable by radicals — and the finite-field arithmetic this required.
Founded: 1830 — Galois's “Sur la théorie des nombres,” developing finite-field arithmetic — published in his lifetime, in the Bulletin des sciences mathématiques, without much incident
The claim
No credible dismissal found. No dismissal attaches to this specific paper. A separate, related work fared worse: Galois's 1831 memoir on solvability of equations by radicals was rejected by Siméon Poisson for the Paris Academy (“neither sufficiently clear nor sufficiently developed to allow us to judge its rigour”) and published only posthumously in 1846. That memoir became foundational to group theory through Serret, Betti, and Jordan across the rest of the 19th century — actively developed, not shelved — but its influence runs through group theory broadly, not through the specific finite-field arithmetic that Reed–Solomon codes use. The two papers are often run together; they shouldn't be.
What happened
130 years — founding (1830) to Reed–Solomon (1960)
Verdict: Never dismissed, applied anyway.
Confidence: medium.