Jesper Lützen: A History of Mathematical Impossibility

Professor Jesper Lützen (University of Copenhagen) will deliver a seminar at The Open University on A History of Mathematical Impossibility, focusing especially on Arrow’s Impossibility Theorem (all ranked-choice voting procedures have spoilers).

If you would like to attend, either in-person or via Microsoft Teams, then please contact Dr Brigitte Stenhouse no later than February 25th via: brigitte.stenhouse[at]open.ac.uk.

The History of Impossibility Theorems and Arrow’s impossibility theorem in particular

In modern mathematics, impossibility results occupy a prominent place. Famous examples include Fermat’s last theorem, Gödel’s theorem, the impossibility of squaring the circle with ruler and compass and the impossibility of solving the general quintic equation by radicals. I shall begin my talk by giving a survey of the historical development of such theorems. In particular, I shall argue that such theorems were at first considered as unimportant compared with positive theorems, and that they only gradually obtained the status of real mathematical results within mathematics having earlier been considered a kind of meta results about mathematics. The last part of my talk will deal with the history of Arrow’s surprising impossibility theorem stating that in an election with three or more candidates, it is impossible to design an election procedure satisfying a few desirable and innocent looking requirements. Arrow’s proof (1950) of his impossibility theorem initiated the so-called theory of social choice.