[en] The most neutron-rich boron isotopes ²⁰B and ²¹B have been observed for the first time following proton removal from ²²N and ²²C at energies around 230 MeV/nucleon. Both nuclei were found to exist as resonances which were detected through their decay into ¹⁹B and one or two neutrons. Two-proton removal from ²²N populated a prominent resonance like structure in ²⁰B 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 ²²C, the ¹⁹B plus one-and two-neutron channels were consistent with the population of a resonance in ²¹B 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 ^20,21B are found to be in agreement with mass surface extrapolations derived within the latest atomic-mass evaluations. (authors)