The most neutron-rich boron isotopes 20 B and 21 B have been observed for the first time following proton removal from 22 N and 22 C at energies around 230 MeV/nucleon. Both nuclei were found to exist as resonances which were detected through their decay into 19 B and one or two neutrons. Two-proton removal from 22 N populated a prominent resonance-like structure in 20 B at around 2.5 MeV above the one-neutron decay threshold, which is interpreted as arising from the closely spaced 1 − , 2 − ground-state doublet predicted by the shell model. In the case of proton removal from 22 C, the 19 B plus one-and two-neutron channels were consistent with the population of a resonance in 21 B 2.47 ± 0.19 MeV above the two-neutron decay threshold, which is found to exhibit direct two-neutron decay. The ground-state mass excesses determined for 20,21 B are found to be in agreement with mass surface extrapolations derived within the latest atomic-mass evaluations.