I browsed a book by Byron & Fuller "Math. Physics" and read the following: Algebra, Geometry & Analysis are joined when functions are treated as vectors in a vector space. This makes Hilbert spaces extremely useful in QM.(paraphrased but that's the jist of it) Comments on this? If it's true than I am interested in studying Hilbert spaces to better understand QM. When I took QM my teacher was asked "What good is this stuff on Hilbert Spaces?". His reply was that every space & every function used in QM is a Hilbert Space so don't worry about it - it's of no consequence at all.