In introductory functional analysis one learns that every normed linear space with a Schauder basis is separable. The converse of this was a famous question raised by Banach- does every separable Banach space have a Schauder basis? Since almost all known separable Banach spaces had been shown to possess a Schauder basis it was believed that this must be true. But in 1972 Enflo constructed a counterexample to this.

For this achievement of his Enflow was awarded a live goose by Stanislaw Mazur.

See [this][1].


  [1]: http://en.wikipedia.org/wiki/Per_Enflo#Enflo.27s_solution