Let X be a locally topologically noetherian scheme. In their paper on the proétale topology, Bhatt and Scholze defined the proétale fundamental group π1proét(X). The profinite completion of π1proét(X) recovers the usual étale fundamental group. Moreover, π1proét(X) agrees with π1ét(X) when X is normal, but π1proét(X) has the better property that it classifies Qp-local systems. In a completely different setting, given a complete first-order theory T, Lascar defined a topological group GalL(T) that plays the role of the absolute Galois group of T. The original definitions of these two topological groups are very different; in this talk, we’ll explain why they’re both essentially special cases of the same construction. Namely, these invariants are both fundamental groups of a naturally-arising condensed homotopy type. In the algebra-geometric setting, this is joint work with Holzschuh, Lara, Mair, Martini, and Wolf. The relationship to the Lascar group is joint with Damaj and Zhang.