Rod in a train: a mechanical problem of H.Whitney, or Much Ado About Nothing

TL;DR

This paper examines the historical and mathematical debates surrounding a 1941 problem about a rod in a moving train, analyzing the validity of various objections and the continuity argument used in its solution.

Contribution

It provides a detailed analysis of the problem's history, the objections raised, and the mathematical reasoning, clarifying misconceptions and the problem's significance.

Findings

The problem has generated extensive discussion among mathematicians.

Continuity arguments played a central role in the solution.

Objections to the solution were partially justified, leading to deeper understanding.

Abstract

In 1941 a mechanical problem about a rod in a moving train (there is a initial position such that rod does not touch the floor while train is moving) was published by R.Courant and H.Robbins in their popular book "What is mathematics?" and attributed to H.Whitney. Many mathematicians, including G.E.Littlewood, A.Broman, T.Poston, I.Stewart, V.Arnold, commented on this problem and its solution based on a continuity argument, and created a lot of confusion. In this paper we follow these developments and discuss at what extent the objections were justified. (In Russian)