We establish a version of Poincaré duality for a class of (topological) groups called profinite groups, which provides isomorphisms from the cohomology groups to certain homology groups of a profinite group. The main goal of the talk is to outline the proof techniques for this result, namely condensed mathematics and derived categories. The former is a novel theory promising to act as an alternative fundament of geometry while the latter constitutes an approach of doing homological algebra. The talk will conclude by a rough sketch of the main argument of the proof.