We present a method for computing the 3-point genus zero Gromov–Witten invariants of the complex flag manifold $G/B$ from the relations of the small quantum cohomology algebra $QH^\ast G/B$ ($G$ is a complex semisimple Lie group and $B$ is a Borel subgroup). In [3] and [9], at least in the case $G={\rm GL}_n{\bf C}$, two algebraic/combinatoric methods have been proposed, based on suitably designed axioms. Our method is quite different, being differential geometric in nature; it is based on the approach to quantum cohomology described in [7], which is in turn based on the integrable systems point of view of Dubrovin and Givental.