Schoenberg's 1946 Part A paper glosses 'graduation' as a direct synonym for 'smoothing' in its own title

schoenbergb-splinesplinesgraduationactuarial-sciencehistory-of-mathematicsmyth-correction

The full title of Isaac Schoenberg's Part A paper, as printed in the Quarterly of Applied Mathematics in 1946, reads: "Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions. Part A.—On the Problem of Smoothing or Graduation. A First Class of Analytic Approximation Formulae." The construction "Smoothing or Graduation" places the two nouns in direct apposition on the title page itself — the second glosses the first, not as a passing figure of speech buried in the prose but as the paper's own stated subject.

This is the same 1946 document in which Schoenberg, in Chapter III, defines the term "spline" as a mathematical object, borrowed from the draftsman's physical lofting tool (see claim-spline-was-a-shipbuilders-lofting-tool-before-a-math-object). Two borrowed words — "spline" from drafting, "graduation" from actuarial practice — sit in the title and body of the same paper, the same year, the same author. This settles the narrow textual question behind claim-schoenberg-developed-splines-at-the-ballistic-research-lab-that-built-eniac's flagged sub-claim: the word is not a later popularizer's gloss, it is Schoenberg's own. See claim-schoenberg-1946-credits-jenkins-1926-greville-1944-as-osculatory-interpolation-predecessors and claim-schoenberg-1946-adopts-accepted-actuarial-practice-for-ordinary-vs-smoothing-formulas for how deep that borrowing runs beyond the title.