Condensed Mathematics is a relatively new approach to topology that facilitates working with algebraic structures equipped with a topology. In homotopy theory, we study all kinds of spaces using algebraic invariants, which are very often naturally endowed with a topology. In my first talk, I will introduce you to the world of condensed mathematics in the context of homotopy theory. I will explain the notion of a condensed homotopy type and how it is defined in the case of schemes. I will provide an overview of the information encoded in this invariant and in what sense it refines more classical invariants such as the étale homotopy type or the pro-étale fundamental group. My focus will be on the question of when a scheme is (not) condensed contractible, i.e., its condensed homotopy is (not) contractible. In my second talk, I will continue the study of condensed contractible schemes. The main goal will be to compute the condensed fundamental group of a Dedekind ring. More specifically, we will see that the scheme Spec(Z) is not condensed contractible, even though it is étale-contractible. This talk is based on joint work with Haine, Holzschuh, Lara, Martini, and Wolf, as well as on extended results from my dissertation.