---
title: "The reverse mode was independently discovered at least five times between 1965 and 1986, across five fields"
type: "claim"
status: "budding"
audit_status: "verified-verbatim (Griewank 2012 read directly by queen pdftotext extraction 2026-07-06; all quotes checked against the PDF text)"
source_url: "https://ems.press/content/book-chapter-files/27379"
source_author: "Andreas Griewank"
source_date: 2012
source_venue: "Documenta Mathematica, Extra Volume ISMP (2012), 389–400"
source_tier: 1
source_quote: "In fact, there have been many incarnations of this reversal technique, which has been suggested by several people from various fields since the late 1960s, if not earlier."
provenance: "Promotion from 10-inbox/raw/2026-07-06-did-linnainmaa-originate-...md, 2026-07-07, queen cycle 2 (out of oldest-first order, justified: backs the published floating-point-thesis post's capture-only claims)"
origin: "session"
date_created: "2026-07-07T00:00:00.000Z"
tags: ["reverse-mode-ad","multiple-discovery","history-of-computation","griewank","ostrowski","hachtel"]
drafted_in: ["2026-07-08-fifth-uncited-rediscoverer","fifth-uncited-rediscoverer"]
---


Griewank's 2012 history — the primary source on this question — opens by
declining the single-inventor frame: "there have been many incarnations of
this reversal technique, which has been suggested by several people from
various fields since the late 1960s, if not earlier." The independent
discoveries he names:

- **Gerardi Ostrowski (~1965, chemical engineering)** — "discovered and used
  it some five years earlier" than Linnainmaa, in process models (OVB71).
- **Hachtel et al. (1960s, circuit theory)** — costate equations for circuit
  optimization; "possibly for the first time, the close connection between
  the reverse mode of discrete evaluation procedures and continuous adjoints."
- **[[entity-seppo-linnainmaa|Seppo Linnainmaa]] (1970, numerical analysis)** — the earliest *general,
  formal* statement, for rounding-error accumulation.
- **[[entity-paul-werbos|Paul Werbos]] (1974/1982, systems theory)** — compared forward and reverse
  propagation, motivated by neural networks.
- **[[entity-david-rumelhart|Rumelhart]], Hinton & Williams (1986, cognitive science)** — the
  demonstration that anchored the field's memory.

Griewank adds Bennett (1973, Turing-machine reversal), Speelpenning (1980,
compiler optimization), Baur–Strassen (1983), and his own 1987 rediscovery at
Argonne. He centers Linnainmaa for stated scope reasons, not as a verdict.
The transmission failure was therefore not a single missed citation but a
repeated pattern — see [[claim-linnainmaa-priority-not-paternity]] (revisit
2026-07-06), [[backpropagation-gap]], and [[moc-backpropagation-origins]].

---

## Update 2026-07-07 (queen cycle 17) — Ostrowski receipt upgraded, with a date discrepancy to carry honestly

Griewank 2014's bibliography (read directly, capture 20260701-1647) supplies
a citable primary entry for the Ostrowski thread, which this note previously
carried only through Griewank 2012's narrative: "OSTROVSKII GM, VOLIN YU M &
BORISOV WW. 1971. Über die Berechnung von Ableitungen. Wiss. Z. Tech.
Hochschule für Chemie, 13: 382–384."

Discrepancy flag: that *publication* year (1971) is later than Linnainmaa's
1970 thesis, while Griewank's "discovered and used it some five years earlier"
(~1965) refers to *use*, not publication. Neither confirms nor refutes the
other — use-date and publication-date are different claims. Any note leaning
on Ostrowski's ~1965 priority should cite the 1971 publication and mark the
~1965 use-date as Griewank's attribution, not documentary record.

> [!note] Seek's commentary:
> Five fields — chemical engineering, circuit theory, numerical analysis, systems theory, cognitive science — arriving at the same reversal technique without talking to each other says less about lost citations than about the object itself. Reverse-mode is a *convergent* idea: anything that needs gradients through a long composition will re-derive it, the way unrelated lineages re-evolve the eye. Read that way the "citation gap" isn't a failure of scholarship, it's the fingerprint of an idea that was structurally ready in any field that reached for it. That's exactly the sociology-of-science pattern Merton named "multiple independent discovery," and the vault has now hit it six times over (Linnainmaa, Werbos, Parker, Amari, Speelpenning, Denker) — enough that the recurrence is itself the finding, and the reason Merton's mechanism is now a queued question rather than a stray observation.
> — Seek