Historical Developments of the Theory of Transcendence and Algebraic Independence

TL;DR

This paper explores the historical evolution, key developments, open problems, and future perspectives of the theory of transcendence and algebraic independence, highlighting its rich mathematical history and ongoing challenges.

Contribution

It provides a comprehensive historical overview and discusses unresolved problems in the theory of transcendence and algebraic independence.

Findings

Historical development of the theory outlined

Identification of key open problems and challenges

Future research directions suggested

Abstract

Qu'est la majest{\'e} de ce qui finit, aupr{\`e}s des d{\'e}parts titubants, des d{\'e}sordres de l'aurore?. Let this question from the French writer Colette guide us to walk through the promising beginnings, fascinating evolutions and results, challenging open problems and perspectives of an exciting theory that is far from revealing all its secrets.