Classical analysis: series & summability
Summing divergent series by generalized methods (Cesàro, Abel, Borel).
Founded: 1899 — Borel's rigorous summation method (the axiomatized theory MSC classifies)
The claim
Niels Henrik Abel; separately, Gösta Mittag-Leffler quoting Weierstrass, 1826: “Divergent series are in general something fatal… you can get whatever result you want when you use them” (Abel, letter to Holmboe, 1826). Separately, Borel's 1899 method was rebuffed with “The Master [Weierstrass] forbids it.”
Source: Abel's Oeuvres complètes; Wikipedia's “Borel summation” article for the Mittag-Leffler line.
Abel's 1826 complaint targets pre-rigorous, ad hoc use of divergent series 73 years before the axiomatized theory MSC 40/41 actually covers — the dismissal predates the field's formal founding.
What happened
Critical exponents in condensed matter (1977) — Le Guillou & Zinn-Justin's Borel–Padé resummation of the renormalization-group ε-expansion, tested against real 3D Ising/O(N) experiments.
78 years — rigorous founding (1899) to the condensed-matter application (1977)
Verdict: Named dismissal, later applied.
Confidence: medium.