Thought Experiments in Mathematics: Anything but Proof.

It is apparently not an easy task to understand what thought experiments (TEs) could be, what they are, how they function, and so on. There are many, quite different definitions around that seem to be in conflict with one another (as the contributions to this volume will no doubt illustrate). Usually all examples of TEs come from the natural and, more exceptionally, the social sciences: Galileo' s falling bodies experiment, Newton's bucket, Einstein's light ray, Maxwell's Demon, are the prototypical cases. Occasionally, authors talk about mathematical thought experiments (MTEs). There the situation becomes even more complex: first, few authors actually believe that there are such things as MTEs and those that do believe so, put forward nearly contradictory definitions. Nevertheless, the aim of this paper is to suggest that, first, MTEs do exist, second that there is a wide class of such MTEs, and finally, that is necessary. to have MTEs in order to understand a major part of mathematical practice. The core thesis of this paper is this: if it is so that what mathematicians are searching for are proofs within the framework of a mathematical theory, then any consideration that (a) in the case where the