What is the connection between reading the fifth act of Peer Gynt and doing Mathematics?

Here I want to briefly recall the entertaining and inspiring talk given by Dagfinn Føllesdal on Similarities and Differences in Methodology between the Natural Sciences, the Social Sciences and the Humanities. This talk held place on 5th of December 2012 at the University of Hamburg in the course of the Carl Friedrich von Weizsaecker-Vorlesungen.

Føllesdal distributed parts of the fifth act of Peer Gynt in the audience. The piece is written by his famous Norwegian compatriot Henrik Ibsen (1867). In the excerpt, Peer Gynt is on the sea on a little boat in a heavy storm. Suddenly, a strange person appears (“the passenger”) and involves Peer into a an Ibsen-typical and absurd conversation about drowning. Føllesdal faced us with the question: Who is this passenger?

Apparently, in linguistics and literary studies, there are a lot of interpretations which try to explain “the passenger”. Here are a five hypotheses:

  • Is he Peer’s fear?
  • The death?
  • Ibsen himself?
  • The devil?
  • The phantom of Lord Byron?

Or does the passenger comprise all of these types or some combination?

Well, I am quite sure that you already anticipate the concise key point of Føllesdal‘s lecture:

All scientists develop hypotheses and then try to support their hypotheses argumentatively. There is no basic methodological division.

Et voilà, this is the link between Maths and Peer Gynt. Føllesdal wants to stress the fact that there are less differences between the disciplines than it might appear. From my perspective, this is a very wise and forward-thinking message. It is also true, for example regarding the artificial divisions in many universities: Does it really make sense to clearly draw a line between philosophy and natural sciences and maths? (I passionately do not think so!)

There are further remarks by Føllesdal which I kept in mind, for example on Kant and hypotheses:

Kant believed that Newton’s laws were ‘a priori’. Then he blundered into the question how the human being can have a free will if everything happens according to fixed laws. Kant did not believe that Newton’s laws were hypotheses which need to be tested with observations.

On the distinction between quantitative data versus amorphous observation:

Numerical data is popular because most of the people read them quite similarly.

On the education of social scientists:

All social scientists should learn game theory and decision theory.

Concluding, from my part, I want to thank Dagfinn Føllesdal for his inspiring visit in Hamburg. His calm, clear, surprising and consistent series of lectures has taught me a lot, not only concerning the content but also the style of lecturing.

Thank you!

All of those who will have the chance to hear a talk by Føllesdal: Enjoy it!