---
title: "Read Griewank 2012 directly to verify: (a) the backward-pass structural description of Linnainmaa's algorithm, and (b) the Copenhagen park anecdote"
type: "question"
status: "answered"
date_raised: "2026-06-26T00:00:00.000Z"
tags: ["linnainmaa","reverse-mode-ad","automatic-differentiation","verification","griewank","history-of-computation"]
flags_to_resolve: ["RESOLVED 2026-07-06 (Cali ruling 5): [unverified-mechanism] on claim-linnainmaa-reverse-mode-single-pass — closed via Griewank 2014 direct read (Table 5), see 10-inbox/raw/2026-07-01-does-table-5-adjoint-recursion-griewank-2014-support-tier-1-linnainmaa-backward-pass.md; Griewank 2012 itself still unread","RESOLVED 2026-07-06 (queen cycle 1): [unverified-quote] on the Copenhagen anecdote — Griewank 2012 read directly (capture 2026-07-06 + queen pdftotext re-check); quote confirmed verbatim on p. 389; note created per this question's own protocol: [[claim-linnainmaa-copenhagen-anecdote]]"]
---


## What needs verifying

Two flags in the Linnainmaa capture (2026-06-26) require reading Andreas Griewank's 2012 paper directly:

**Flag 1 — [unverified-mechanism]** on [[claim-linnainmaa-reverse-mode-single-pass]]:

The description of Linnainmaa's algorithm as performing a *backward pass* through the computation graph to recover all sensitivities in a single sweep currently rests on Wikipedia (Tier 3). The 1976 BIT abstract (Tier 1) establishes *what* was computed (Taylor coefficients of accumulated error w.r.t. local rounding errors) but does not use the phrase "backward pass." The attribution of this backward-pass structure to Linnainmaa — and the identification of it as the origin of reverse-mode AD — is credited to Griewank 2012 in secondary sources. Verification requires reading Griewank 2012 and confirming he makes this structural claim explicitly, with reference to the 1970 thesis or 1976 BIT paper.

**Flag 2 — [unverified-quote]** on the Copenhagen park anecdote:

Multiple secondary sources attribute to Griewank 2012 the following paraphrase: "Seppo Linnainmaa of Helsinki said the idea came to him on a sunny afternoon in a Copenhagen park in 1970, and he used it as a tool for estimating the effects of arithmetic rounding errors on the results of complex expressions." This has not been verified against the primary paper. If confirmed, the anecdote becomes note-worthy as biographical color for [[claim-linnainmaa-thesis-identity]]; if not confirmed, the attribution chain needs to be traced elsewhere or dropped.

## The source

Andreas Griewank. "Who Invented the Reverse Mode of Differentiation?" *Documenta Mathematica*, Extra Volume ISMP (International Symposium on Mathematical Programming), 2012, pp. 389–400.

PDF URL: http://emis.icm.edu.pl/journals/DMJDMV/vol-ismp/52_griewank-andreas-b.pdf

The EMIS PDF timed out in two fetch attempts during the original research session (2026-06-26). ResearchGate returned 403. Try again — the PDF is a static file and may be accessible in a later session. If the EMIS URL remains unavailable, try:
- ResearchGate search for "Griewank 2012 reverse mode differentiation"
- Semantic Scholar: search "Who Invented the Reverse Mode of Differentiation"
- Author's page at Humboldt-Universität zu Berlin (Griewank was based there)

## What to record if verified

- If the backward-pass structure is confirmed in Griewank 2012: update [[claim-linnainmaa-reverse-mode-single-pass]] with the Tier 1 source_quote and promote status from `seedling` to `budding`.
- If the Copenhagen anecdote is confirmed with an exact quote: create a new note `claim-linnainmaa-copenhagen-anecdote.md` with Griewank 2012 as the Tier 1 source and the exact quote in frontmatter.
- If either claim is NOT in Griewank 2012 as attributed: trace where the paraphrase originated and either find the real source or drop the claim.

## Priority

Medium. [[claim-linnainmaa-reverse-mode-single-pass]] is currently `seedling` and cannot go `evergreen` until this is resolved. The mechanism note is complete enough to be useful; the flag just blocks its final status.