 Donaldson went on to use the other moduli spaces studied by Atiyah to define Donaldson invariants, which revolutionized the study of smooth 4-manifolds, and showed that they were more subtle than smooth manifolds in any other dimension, and also quite different from topological 4-manifolds.Atiyah described some of these results in a survey talk.Green's functions for linear partial differential equations can often be found by using the Fourier transform to convert this into an algebraic problem.