The two XIXth century mathematicians R. Dedekind and G. Cantor contributed to the development of set theory. They, for example, constructed different versions of the continuum, or the real numbers. Their approach to set theory, however, is quite different. Dedekind used set theory to build a system of natural numbers whereas Cantor formulated a transfinite set theory, a foundation of set theory and - in part - constructed a proof against infinitesimals. It can be thus said that Dedekind and Cantor dealt with similar problems and objects in the foundations of mathematics, but that their solutions and constructed structures were quite different.

The purpose of this talk is to consider why two mathematicians working on seemingly similar problems and mathematical objects at the same time could end up with introducing very different types of mathematical theories. We propose in the considered case that there are different factors that influence the intuition of the mathematicians and that these intuitions shape their mathematical contributions. We consider in particular the role of visual aspects and how they affect the intuition of mathematicians.

Coffee, tea, cake and fruit will be served before the colloquium @ 2 pm.