We discuss tree level scattering of any number of massless open superstring states on a worldsheet of disk topology. The entire state dependence of the tree amplitude can be expressed in terms of gauge theory subamplitudes from the point particle limit. The string corrections entering through momentum dependent integrals over the disk boundary can be disentangled from the YM seeds and analyzed separately. Their power series expansion in the string length and momenta involves multiple zeta values (MZVs). We review some mathematical background on MZVs and the network of relations between them. The explicit form of any tree level string correction to YM theory is derived from the generating function of MZVs -- the Drinfeld associator. It interpolates between the worldsheet integrals in N-point and (N-1)-point scattering and leads to a recursive formula for the momentum expansion of any disk amplitude. Our results apply for any number of spacetime dimensions or supersymmetries and chosen helicity configurations.