We design a method to compute the full inelastic neutron cross section from first principles in polyatomic systems, and validate it by achieving a remarkable match of experimental data for silica by using ab-initio-generated structural models of silica. We thus challenge and dispel the idea, upon which all current interpretations of inelastic scattering spectra are based, that the multiphonon contributions are small enough to be neglected at low temperatures. Instead, we show that, due to zero-point quantum fluctuations, significant and even dominant multiphonon contributions exist for scattering vectors Q≽Q*≃1 A-1 , at arbitrarily low temperatures.