---
title: "Schoenberg names 'accepted actuarial practice' as the direct source of his own 'ordinary' vs. 'smoothing' interpolation-formula distinction"
type: "claim"
status: "seedling"
source_url: "https://www.ams.org/journals/qam/1946-04-01/S0033-569X-1946-15914-5/S0033-569X-1946-15914-5.pdf"
source_sha: "ca619de588086bb02b4b74d304de6f8fee252059b3ac1bf4076bc0885cb7017b"
source_author: "I. J. Schoenberg"
source_date: "1946"
source_title: "Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions. Part A."
source_venue: "Quarterly of Applied Mathematics, vol. 4, no. 1, pp. 45–99 (1946)"
source_tier: 1
source_quote: "We shall follow the accepted actuarial practice of referring to (3) as an ordinary interpolation formula if (3) reproduces exactly the given ordinates {y,, ]. Otherwise we call (3) a smoothing interpolation formula."
source_url_2: "https://www.ams.org/journals/qam/1946-04-02/S0033-569X-1946-16705-2/S0033-569X-1946-16705-2.pdf"
source_sha_2: "a7ee3f7aca7243afa3aed5a76586503538d728b9d5a6bf04d232d9148700746e"
source_title_2: "Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions. Part B."
source_venue_2: "Quarterly of Applied Mathematics, vol. 4, no. 2, pp. 112–141 (1946); doi:10.1090/qam/16705"
source_quote_2: "Greville's adjectives \"ordinary\" and \"modified\" agree respectively with our \"ordinary\" and \"smoothing.\""
audit_status: "capture-verified — fetched directly from ams.org (the venue of record) via extract_pdf, TLS-verified; source_sha carried forward from the capture. The bracket in the quote is an OCR artifact of the scanned PDF, preserved verbatim rather than silently corrected. Not yet independently re-checked by the verifier bee. | 2026-08-30 cross-model audit (claude-fable-5): re-fetched Part A from ams.org (identical sha256 ca619de5…) and confirmed the source_quote verbatim, OCR bracket included (Sec. 2.11, pp. 56–57). CORRECTED in place (traceability, not claim wording): the Part B footnote this note leans on had no recorded URL/sha; Part B was re-fetched from ams.org and its footnote 1(ii) confirmed verbatim, and the Part B pointer added as source_url_2/source_sha_2 so the Greville-mapping claim is re-checkable without hunting the URL."
provenance: "Promotion from 10-inbox/raw/2026-08-29-do-schoenbergs-1946-b-spline-papers-actually-use.md, 2026-08-29"
origin: "batch"
derived_from: ["10-inbox/raw/2026-08-29-do-schoenbergs-1946-b-spline-papers-actually-use.md"]
date_created: "2026-08-29T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["schoenberg","b-spline","splines","graduation","actuarial-science","osculatory-interpolation","history-of-mathematics"]
verified_verbatim: "2026-08-30 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
seek_code_commit: "7d6d9ed"
---


Defining the split between formulas that reproduce given data points exactly and formulas that smooth them, Schoenberg writes in Part A: "We shall follow the accepted actuarial practice of referring to (3) as an ordinary interpolation formula if (3) reproduces exactly the given ordinates {y,, ]. Otherwise we call (3) a smoothing interpolation formula." (The bracket is an OCR artifact of the scanned journal PDF; the sentence is otherwise intact.)

This goes beyond borrowing a single word — Schoenberg states outright that he is following existing actuarial convention for a core piece of his own formal apparatus, the ordinary/smoothing split that structures the rest of the paper's formula classification. Part B's footnote mapping his terms onto [[entity-t-n-e-greville|Greville]]'s ("ordinary"/"modified" ↔ "ordinary"/"smoothing") shows the mapping held across both papers, not just as a one-off acknowledgment in Part A. Compare [[claim-schoenberg-1946-credits-jenkins-1926-greville-1944-as-osculatory-interpolation-predecessors]], which documents the same debt at the level of citation rather than terminology.

> [!note] Seek's commentary:
> There's a difference between citing a field and speaking its dialect, and this sentence is Schoenberg doing the second one. He didn't just credit the actuaries in a footnote and move on in his own vocabulary — he kept their two-way split for the rest of the paper's classification scheme. A borrowed taxonomy is a heavier debt than a borrowed noun.