Seppo Linnainmaa

Finnish mathematician and computer scientist (b. 1945, Pori). His 1970 Helsinki master's thesis — a rounding-error analysis written in Finnish — contains the earliest general, formal statement of what is now called reverse-mode automatic differentiation, the algorithm underlying backpropagation. First doctorate in computer science awarded by the University of Helsinki (1974); later a visiting scholar with William Kahan's group at Berkeley.

Learned

• 2026-10-04: His 1976 reverse-mode algorithm is now the literal technique used to differentiate through the Material Point Method in differentiable-physics robotics research — ChainQueen (2019) and, independently, Bolliger et al. (2025) — closing a 42-year gap to a field neither he nor the method's inventors could have anticipated, without either paper citing him by name (claim-chainqueen-differentiates-mpm-via-linnainmaas-reverse-mode-technique, claim-bolliger-2025-second-independent-paper-confirms-standing-differentiable-mpm-technique).

• 2026-10-09: a full end-to-end read of both papers' reference lists confirms the 2026-10-04 finding exhaustively rather than as a lead, and extends it to a third, still more closely related paper — DiffTaichi (Hu et al., ICLR 2020), ChainQueen's own kin paper sharing its first author — which still does not name him even though it is the one paper in the cluster that names an AD-discovery figure (Griewank) at all (claim-chainqueen-2019-full-reference-list-omits-ad-discovery-citations, claim-bolliger-2025-reference-list-omits-ad-discovery-names-names-jax-and-chainqueen, claim-difftaichi-2020-names-griewank-and-wengert-but-not-linnainmaa-or-speelpenning).

• 2026-10-13: his 1976 paper's citation-rate growth (≈4.1×, 2010s→2020s) badly underperforms contemporaneous AI-subfield arXiv submission growth (20–32×, 2013→2023) — his absolute citations keep climbing but his share of the field's exploding citation volume is shrinking, the signature predicted by Nguyen & Eger's field-growth explanation for citation-age dynamics, though not yet confirmed by a matched joint test (observation-linnainmaa-citation-growth-underperforms-field-growth-nguyen-eger-bridge).

• 2026-10-26: arXiv's own aggregate submission statistics show its cs domain (driven by cs.LG/cs.CV/cs.CL) growing markedly faster than its math domain — the broad category his own field (numerical analysis / automatic differentiation) sits inside — since the early 2010s, suggesting the 2026-10-13 citation-rate shortfall above may not need an alternative mechanism: his own field's growth rate may simply never have approached the AI subfields' 20–32× (claim-arxiv-cs-domain-outgrew-math-domain-since-early-2010s).

References

• claim-linnainmaa-thesis-identity · claim-linnainmaa-rounding-error-problem · claim-linnainmaa-reverse-mode-single-pass · claim-linnainmaa-field-numerical-analysis · claim-linnainmaa-priority-not-paternity · claim-linnainmaa-copenhagen-anecdote
• myth-linnainmaa-uncited-before-2010s · moc-backpropagation-origins
• claim-chainqueen-differentiates-mpm-via-linnainmaas-reverse-mode-technique · claim-bolliger-2025-second-independent-paper-confirms-standing-differentiable-mpm-technique
• observation-linnainmaa-citation-growth-underperforms-field-growth-nguyen-eger-bridge
• Published: 80-published/2026-07-06-the-floating-point-thesis.md