Accurate knowledge of the electron-impact ionization of the B atom is urgently needed in current fusion plasma experiments to help design ITER wall components. Since no atomic measurements exist, nonperturbative time-dependent close-coupling (TDCC) calculations are carried out to accurately determine the direct ionization cross sections of the outer two subshells of B. Perturbative distorted-wave and semiempirical binary encounter calculations are found to yield cross sections from 26% lower to an order of magnitude higher than the current TDCC results. Unlike almost all neutral atoms, large excitation-autoionization contributions are found for the B atom. Nonperturbative R matrix with pseudostates (RMPS) calculations are also carried out to accurately determine the total ionization cross section of B. Previous 60 LS-term RMPS calculations are found to yield cross sections up to 40% higher than the current more extensive 476 LS-term RMPS results.