Stefan Banach

Banach was one of the founders of functional analysis. Spaces now called Banach spaces are more general than Hilbert spaces, in that the norm might not be derivable from a scalar product. In fact, a norm is so derivable if and only if it satisfies Appollonius's equality. Whereas Hilbert spaces have a simple classification (up to isomorphism) in terms of their dimension, the search for a classifying space for Banach spaces has been perhaps a waste of time.