Thirty years after: insights on the cultural origins of Kolmogorov's 1954 theorem from a short conversation with Arnold

TL;DR

This paper explores the historical and biographical context of Arnold's reflections on Kolmogorov's 1954 invariant tori theorem, revealing insights into its cultural origins through a detailed analysis of Arnold's accounts.

Contribution

It provides a comparative analysis of Arnold's two different accounts of his conversation with Kolmogorov, enriching the historical understanding of the theorem's development.

Findings

Arnold's two accounts differ in details and emphasis.

The paper situates the theorem within its cultural and historical context.

It offers new perspectives on the origins of Kolmogorov's 1954 theorem.

Abstract

Among the impressive contributions of Andrej N. Kolmogorov's to mathematics in the 20th century, his 1954 invariant tori theorem is still little understood from a historical point of view [Dumas 2014]. Vladimir I. Arnold, who entered Moscow State University that same year and would became a student of Kolmogorov, 30 years after asked him about the origin of a research program to which Arnold himself gave a big contribution. In this paper we compare and put in historical and biographical context two different account's by Arnold on this conversation.