Geometry in the twentieth century: A return to Euclid -- The work of Herbert Busemann

TL;DR

This paper reviews Herbert Busemann's work, highlighting its focus on classical Greek geometry and its significance within the history of mathematical practice, emphasizing its philosophical and historical context.

Contribution

It offers a comprehensive perspective on Busemann's approach, framing it as a modern revival of ancient Greek geometric principles within 20th-century mathematics.

Findings

Busemann's work emphasizes classical Greek geometry.

The paper discusses the historical significance of Busemann's contributions.

It situates Busemann's approach within the broader context of mathematical history.

Abstract

This is a point of view of the work of Herbert Busemann (1905-1994), seen as a return to the geometry of Ancient Greece. The importance of this work, its recognition and its relation with other works are discussed. The final version of this paper will appear in the Handbook of the History and Philosophy of Mathematical Practice, ed. Bharath Sriraman, Springer, 2024.