  We discuss a particular problem of enumerating rational curves on a
Grassmannian from several perspectives, including systems theory, real
enumerative geometry, and symbolic computation. We also present a new
transversality result, showing this problem is enumerative in all
characteristics.
  While it is well-known how this enumerative problem arose in mathematical
physics and also its importance to the development of quantum cohomology, it is
less known how it arose independently in mathematical systems theory. We
describe this second story.
