The first measurement of the helicity dependence of the photoproduction cross section of single neutral pions off protons is reported for photon energies from 600 to 2300 MeV, covering nearly the full solid angle. The data are compared to predictions from the SAID, MAID, and BnGa partial wave analyses. Strikingly large differences between data and predictions are observed, which are traced to differences in the helicity amplitudes of well-known and established resonances. Precise values for the helicity amplitudes of several resonances are reported.