The Gopakumar-Vafa conjecture predicts that the Gromov-Witten invariants of a Calabi-Yau 3-fold can be canonically expressed in terms of integer invariants called BPS numbers. In this talk, based on joint work with Tom Parker, I describe the proof of this conjecture, coming from a more general structure theorem for the Gromov-Witten invariants of symplectic 6-manifolds.