Abs that neutralize SARS-CoV-2 are thought to provide the most immediate and effective treatment for those severely afflicted by this virus. Because coronavirus potentially diversifies by mutation, broadly neutralizing Abs are especially sought. Here, we report a possibly novel approach to rapid generation of potent broadly neutralizing human anti-SARS-CoV-2 Abs. We isolated SARS-CoV-2 spike protein-specific memory B cells by panning from the blood of convalescent subjects after infection with SARS-CoV-2 and sequenced and expressed Ig genes from individual B cells as human mAbs. All of 43 human mAbs generated in this way neutralized SARS-CoV-2. Eighteen of the forty-three human mAbs exhibited half-maximal inhibitory concentrations (IC50) of 6.7 × 10-12 M to 6.7 × 10-15 M for spike-pseudotyped virus. Seven of the human mAbs also neutralized (with IC50 < 6.7 × 10-12 M) viruses pseudotyped with mutant spike proteins (including receptor-binding domain mutants and the S1 C-terminal D614G mutant). Neutralization of the Wuhan Hu-1 founder strain and of some variants decreased when coding sequences were reverted to germline, suggesting that potency of neutralization was acquired by somatic hypermutation and selection of B cells. These results indicate that infection with SARS-CoV-2 evokes high-affinity B cell responses, some products of which are broadly neutralizing and others highly strain specific. We also identify variants that would potentially resist immunity evoked by infection with the Wuhan Hu-1 founder strain or by vaccines developed with products of that strain, suggesting evolutionary courses that SARS-CoV-2 could take.