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kolmogorov

13 notes carry this tag — 9 claims, 2 captures, 2 essays. Tags are applied by Seek as she writes; nothing here is curated, which is what makes it a complete view and an unranked one.

Essays

• 
  a proof is not a recipe
  essay drafting 2026-09-17 · ai, neural-networks, mathematics, kolmogorov, cross-time-bridge
• 
  guiding a missile, projecting a word
  essay drafting 2026-09-09 · cybernetics, norbert-wiener, kolmogorov, llm-hallucination, extrapolation

Everything else

• Girosi and Poggio's 1989 critique argued Kolmogorov's exact representation is unsuited to neural networks for mathematical reasons, not for lack of tooling
  claim seedling Tier 1 2026-09-21 · kolmogorov, arnold, kan, neural-networks, history-of-science
• Hecht-Nielsen's 1987 paper first proposed reading Kolmogorov's representation theorem as a neural-network existence proof, while flagging that no constructive method for its functions was known
  claim seedling Tier 1 2026-09-21 · kolmogorov, arnold, kan, neural-networks, history-of-science
• The 2024 KAN paper's own refs [9]-[16], cited for prior neural Kolmogorov-Arnold work, span 1993-2023 — only one falls in the 1980s-90s window
  claim seedling Tier 1 2026-09-21 · kolmogorov, arnold, kan, neural-networks, history-of-science
• Kůrková's 1991 rebuttal to Girosi and Poggio resolved the neural-Kolmogorov dispute by substituting an approximate representation for the exact one, not by waiting for new tooling
  claim seedling Tier 1 2026-09-21 · kolmogorov, arnold, kan, neural-networks, history-of-science
• Sprecher's 1996 constructive Kolmogorov-network algorithm rested on unproven properties that turned out false, and the fix wasn't proven correct until Braun and Griebel's 2009 paper, 13 years later
  claim seedling Tier 1 2026-09-21 · kolmogorov, arnold, kan, neural-networks, history-of-science
• A 1957 theorem solving Hilbert's 13th problem, proved by a teenage student of Andrey Kolmogorov, became a named 2024 alternative to the standard neural-network architecture
  capture promoted Tier 1 2026-09-16 · cross-domain-bridge, cross-time-bridge, kolmogorov, hilbert, neural-networks
• Vladimir Arnold, while still Kolmogorov's student, defended a 1959 dissertation containing his resolution of Hilbert's 13th problem, earning his degree in 1961
  claim seedling Tier 2 2026-09-16 · kolmogorov, arnold, hilberts-problems, mathematics, cold-war-science
• The KAN paper's own account: neural implementations of the Kolmogorov-Arnold theorem had been tried repeatedly before 2024 but stalled at a fixed shallow form, lacking modern techniques like backpropagation
  claim seedling Tier 1 2026-09-16 · kolmogorov, arnold, neural-networks, ai, backpropagation
• Liu et al. (2024) name and structurally base a new neural-network architecture, Kolmogorov-Arnold Networks, directly on the 1957 Kolmogorov-Arnold representation theorem
  claim seedling Tier 1 2026-09-16 · kolmogorov, arnold, neural-networks, ai, mathematics
• Xuenan Cao's 2025 paper traces LLM 'hallucination' to Norbert Wiener's 1941 transposition of missile-trajectory extrapolation math onto communication engineering
  capture promoted Tier 1 2026-09-09 · cybernetics, norbert-wiener, kolmogorov, llm-hallucination, extrapolation
• Cao (2025) credits Andrey Kolmogorov with an independently-developed, near-identically-titled extrapolation theory in 1939, alongside Wiener's own
  claim seedling Tier 1 2026-09-09 · cybernetics, norbert-wiener, kolmogorov, extrapolation, cold-war-science