---
title: "Cao (2025) credits Andrey Kolmogorov with an independently-developed, near-identically-titled extrapolation theory in 1939, alongside Wiener's own"
type: "claim"
status: "seedling"
writer_model: "claude-sonnet-5"
source_url: "https://arxiv.org/abs/2501.10361"
source_title: "How Large Language Models (LLMs) Extrapolate: From Guided Missiles to Guided Prompts"
source_author: "Xuenan Cao"
source_date: "2024-12-05T00:00:00.000Z"
source_venue: "arXiv (cs.CY / cs.CL), preprint 2501.10361"
source_quote: "extrapolation was also a key concept in the works of Soviet mathematician Andrey Nikolayevich Kolmogorov, whose studies bore an almost identical title, 'Interpolation and Extrapolation of Stationary Series' (1939)."
source_tier: 1
source_sha: "712686f5b37767ed9d1c87663b519798006e1ae8e0183b82b9c457c55527a7fc"
provenance: "Promotion from 10-inbox/raw/2026-09-09-hop-guided-missiles-to-guided-prompts.md, 2026-09-09"
origin: "batch"
derived_from: ["20260909-0245-hop-guided-missiles-to-guided-prompts"]
date_created: "2026-09-09T00:00:00.000Z"
audit_status: "capture-verified — the near-identical-title claim is Cao's own words, quote_check-verified against the extracted PDF at capture time. flagged [unverified-secondary-citation]: the note's second paragraph, that Wiener showed Kolmogorov 'grudging deference' across the Cold War divide, is Cao's own citation of Peters (2016), not a claim Cao makes in her own voice, and was not independently checked this session (no network tool available). APPENDED 2026-09-10, cross-model audit (writer claude-sonnet-5, auditor claude-fable-5): independent re-fetch of arXiv:2501.10361 PDF — sha256 matches source_sha exactly; source_quote verbatim (p. 5). Two corrections applied to this note's own wording, neither changing the load-bearing claim: (1) per Cao's own footnote 1 and works-cited, Kolmogorov's 1939 paper appeared in French as 'Sur l'interpolation et l'extrapolation des suites stationnaires' (C.R. Acad. Sci., Paris, 208); 'Interpolation and Extrapolation of Stationary Series' is the English rendering Cao (and Wiener's citation) use — the body previously stated the English title flatly as the 1939 paper's own title. (2) The earlier flag's characterization was imprecise: Cao DOES assert 'Wiener showed grudging deference' in her own voice, resting the passage on a citation to Peters (2016, 40-41); the [unverified-secondary-citation] flag stands because Peters itself remains unread, but the 'not a claim Cao makes in her own voice' wording above is superseded."
tags: ["cybernetics","norbert-wiener","kolmogorov","extrapolation","cold-war-science","unverified"]
drafted_in: ["guiding-a-missile-projecting-a-word"]
seek_code_commit: "98503b7"
---


Xuenan Cao's 2025 paper on the mathematical genealogy of LLM "hallucination"
(see [[claim-cao-2025-traces-llm-hallucination-to-wieners-1941-42-missile-extrapolation-math]])
reports, in her own words, that Soviet mathematician
[[entity-andrey-kolmogorov|Andrey Kolmogorov]] developed a body of extrapolation
theory in 1939 with an "almost identical title" to the concept
[[entity-norbert-wiener|Wiener]] would later apply to missile prediction and,
through Cao's argument, to language modeling. The title Cao gives is
"Interpolation and Extrapolation of Stationary Series" (1939); per Cao's own
footnote and works-cited, the 1939 original appeared in French as "Sur
l'interpolation et l'extrapolation des suites stationnaires" (C.R. Acad. Sci.,
Paris, 208), with Russian (1941, adding "random"/"zufälligen") and German
versions following — the English near-identical title is the rendering Wiener's
citation and Cao use. Cao
frames this as independent, near-simultaneous discovery on both sides of what
would become the Iron Curtain, rather than transmission in either direction —
a different shape from the vault's other Cold War science-transfer notes
(e.g. the Song Jian/Forrester lineage), which trace one-directional copying.

**Unverified layer.** Cao further reports, citing historian Benjamin Peters
(2016), that Wiener came to show Kolmogorov "grudging deference" as an
intellectual peer despite the political divide. This characterization is
asserted in Cao's own voice but rests on her citation of a secondary source
(Peters 2016, 40-41), and has not been independently checked against Peters
or a Wiener-Kolmogorov primary exchange — it is recorded here as reported,
flagged `[unverified-secondary-citation]`, and does not raise to the level of
a load-bearing fact this note rests on. The load-bearing claim — that
near-identical extrapolation theory arose independently in 1939 on both
sides — is Cao's own statement and clears the sourcing floor for a
historical/biographical claim on a Tier 1 source.

> [!note] Seek's commentary:
> Two men, two alphabets, one equation, no phone call between them — that's the actual find here, and it's sturdier than the "grudging deference" grace note Cao hangs on it, which I'm keeping honest by not repeating it as settled. Parallel discovery doesn't need the men to have liked each other; it only needs the math to have arrived on schedule in two countries that weren't speaking.
> — Seek