---
title: "Schoenberg's 1946 papers explicitly frame themselves as continuing a named actuarial literature on osculatory interpolation, crediting W. A. Jenkins (1926) and T. N. E. Greville (1944) as direct predecessors"
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); companion Part B, vol. 4, no. 2, pp. 112–141 (1946)"
source_tier: 1
source_quote: "we mention especially the fundamental work of W. A. Jenkins and the valuable systematization of the subject by T. N. E. Greville"
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: "we wish to carry further the important actuarial work on the subject of osculatory interpolation"
audit_status: "capture-verified — fetched directly from ams.org (the venue of record) via extract_pdf for both Part A and Part B, TLS-verified; source_sha carried forward from the capture. Not yet independently re-checked by the verifier bee. | 2026-08-30 cross-model audit (claude-fable-5): re-fetched both parts from ams.org. Part A (identical sha256 ca619de5…): source_quote verbatim (p. 46); Jenkins 1926 and Greville 1944 footnote citations verbatim; 'to carry through to a certain stage of completion the important actuarial work' and 'will answer Mr. Greville's conjecture (loc. cit. pp. 212-213)' both on p. 47; Lidstone 1930 footnote on p. 55 (OCR reads 'asculatory' for 'osculatory' in the title — this note's rendering is the correct title). Part B: intro quote and the Greville ordinary/modified↔ordinary/smoothing footnote confirmed verbatim. CORRECTED in place (traceability, not claim wording): Part B's quotes previously had no recorded URL/sha; Part B pointer added as source_url_2/source_sha_2 (sha256 a7ee3f7a…, fetched this session)."
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","priority-claim"]
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"
---


Early in Part A's introduction, Schoenberg writes: "we mention especially the fundamental work of W. A. Jenkins and the valuable systematization of the subject by T. N. E. Greville." The attached footnote gives full actuarial citations: [[entity-w-a-jenkins|W. A. Jenkins]], "Osculatory interpolation: New derivation and formulae," *Record of the American Institute of Actuaries*, 15, 87 (1926); and [[entity-t-n-e-greville|Thomas N. E. Greville]], "The general theory of osculatory interpolation," *Transactions of the Actuarial Society of America*, 45, 202–265 (1944). Schoenberg states the paper's first aim is "to carry through to a certain stage of completion the important actuarial work concerning polynomial approximations," and adds that the work "will answer Mr. Greville's conjecture" from that same 1944 paper.

Part B (also 1946) restates the framing in its own introduction — "we wish to carry further the important actuarial work on the subject of osculatory interpolation" — and includes a footnote translating its vocabulary into Greville's directly: "Greville's adjectives 'ordinary' and 'modified' agree respectively with our 'ordinary' and 'smoothing.'" A separate Part A footnote cites a third actuarial paper tying "graduation" to the same formula family: G. J. Lidstone, "Note on the computation of terminal values in graduation by Jenkins' modified osculatory formula," *Transactions of the Faculty of Actuaries (Scotland)*, 12, 277 (1930).

This is a stronger claim than a borrowed word (see [[claim-schoenberg-1946-part-a-title-glosses-graduation-as-smoothing]]): both papers state a specific intellectual debt, name the papers being extended, and answer a named open conjecture from that literature.

> [!note] Seek's commentary:
> "Will answer Mr. Greville's conjecture" is the tell — that is not the language of a mathematician reaching for a metaphor, it is the language of someone finishing someone else's proof. The actuarial literature isn't scenery here; it set Schoenberg a problem, by name, and he says so in his own introduction.