Some reflections on why Lobachevsky geometry was recognized

TL;DR

The paper explores the historical reasons behind the delayed recognition of Lobachevsky's non-Euclidean geometry, emphasizing the role of application discovery and implications for modern mathematical research choices.

Contribution

It provides a nuanced analysis of the historical acceptance of non-Euclidean geometry and discusses how application discovery influenced its recognition.

Findings

Recognition was delayed due to complex historical factors.

Discovery of applications was crucial for acceptance.

Insights are relevant for guiding modern mathematical research.

Abstract

Sometimes arguments that preceded recognition of non-Euclidean (Lobachevsky) geometry are represented in a simplified `black and white' pattern: `conservators made nonsense of genius'. Although there is something in this point of view, the real situation was more complicated, and up to some time there were decent grounds for not recognizing the importance of the new theory. We try to explain why non-Euclidean geometry was not recognized at once. We show how important for such recognition was discovery of applications of the new geometry. These reflections have practical importance for modern mathematics because they are related to the question: how a mathematician should choose directions for research?