Thirty years after: insights on the cultural origins of Andrej N. Kolmogorov’s 1954 invariant tori theorem from a short conversation with Vladimir I. Arnold

The paper documents, via Arnold’s recollections, that Kolmogorov explicitly denied Landau’s turbulence ‘tori’ as the origin and instead traced his 1954 work to a long-standing fascination with celestial mechanics and a decisive resurgence of “hope” in 1953; it quotes Kolmogorov’s own words about Flammarion and sustained reading (Charlier, Birkhoff, Whittaker, Krylov–Bogolyubov, Chazy, Schmidt), plus repeated pre‑1954 attempts and the 1953 turning point . It situates the 1954 Doklady note and ICM talk as inaugurating the KAM program in direct dialogue with celestial-mechanical stability questions . The candidate solution states the same core claims and even the same names and the 1953 ‘hope’ phrasing, while correctly ruling out the Landau-tori origin . Minor issues in the paper (e.g., an apparent date slip “November 31, 1953”) do not affect these conclusions . Overall, both accounts align on sources, chronology, and causation.