On the history of the Hopf problem

TL;DR

This paper provides a historical overview of the Hopf problem, an unsolved question in mathematics about the existence of a complex structure on the 6-sphere, highlighting its significance and recent discussions.

Contribution

It offers a historical context and summarizes recent discussions on the longstanding open problem regarding complex structures on the 6-sphere.

Findings

The Hopf problem remains unsolved.

Recent conferences have focused on its non-existence.

Historical insights into the problem's development.

Abstract

This short note serves as a historical introduction to the Hopf problem: "Does there exist a complex structure on $S^6$?" This unsolved mathematical question was the subject of the Conference "MAM 1 $-$ (Non-)Existence of Complex Structures on $S^6$", which took place at Philipps-Universit\"at Marburg, Germany, between March 27th and March 30th, 2017.