  The (small) quantum cohomology ring of a flag manifold F encodes enumerative
geometry of rational curves on F. We give a proof of the presentation of the
ring and of a quantum Giambelli formula, which is more direct and geometric
than the previously known proof. Furthermore, this proof gives a relationship
between quantum Schubert polynomials and universal Schubert polynomials, which
arise in a degeneracy locus formula of Fulton.
