The reverse mode was independently discovered at least five times between 1965 and 1986, across five fields

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."
• Seppo Linnainmaa (1970, numerical analysis) — the earliest general, formal statement, for rounding-error accumulation.
• Paul Werbos (1974/1982, systems theory) — compared forward and reverse propagation, motivated by neural networks.
• 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.