At the very same time that Hairer introduced his theory of regularity structures, Gubinelli-Imkeller-Perkowski (GIP) devised a simpler approach to handle a number of so far ill-posed PDEs, based on tools from harmonic analysis, mainly Bony's paraproducts. The classical formulation of these tools does not allow to consider problems outside the realm of Euclidean space, or the flat torus, though. After explaining GIP's approach to singular PDEs, I will explain how the use of heat semigroups allows to construct a functional calculus and define a paraproduct in much more general settings than the Euclidean space and allow to consider stochastic singular PDEs on manifolds for instance. No prior knowledge of PDEs or harmonic analysis is required.