Loke Lagerkvist: Rigour in mathematics: A historical perspective

Abstract:

In this essay, we shall be investigating the rigorisation process that occured in Europe during the 19th century, particularly within analysis. The norms of the period regarding the sciences and within the profession of a mathematician will be examined, followed by a deep dive into the mathematical discoveries that brought this change along, namely continuity, the limit and epsilontics and the real numbers. This will be done by looking at the advancement of these topics, as made by some key mathematicians in France and in Prussia/Germany. Sub- sequently, the societal factors will be explored to further analyse what brought said development along, mentioning revolutions, the birth of some European countries, the industrial revolution and the technological advancements that followed as well as some other topics.