John Nash became famous by solving the Riemann Embedding Problem. Shortly thereafter, he fell into a profound schizophrenic psychosis. The Riemann Embedding Problem: Is it possible to embed every surface, and more generally every manifold with a metric in the Riemannian sense, into some n-dimensional Euclidean space such that the metric (and hence the distance) on the manifold is the same as the one inherited from the Euclidean ambient space?
