I will discuss three different contexts in which commutative
rings of functions and modules over them are replaced by their
non-commutative versions. One is the ring of differential operators, where
the modules correspond to systems of differential equations. The second
setting is geometric quantization which provides a baby version of the
Hilbert space in quantum mechanics. The third setting is deformation
quantization in symplectic geometry. I will explain a relation between these
three versions, although the reasons behind the relations are not quite well
understood.