Will artificial intelligence (AI) help poorer countries catch up? This paper argues that the answer depends less on access to AI than on the capacity to use new knowledge productively. We show that countries have narrowed gaps in capital and schooling more readily than gaps in productivity. Technology can diffuse widely without producing productivity convergence. Measured human capital explains only a modest share of productivity differences in levels, but is associated with sharply different mobility regimes. The estimated transition processes imply an expected time to exit the lowest-productivity state of about 65 years for economies below the estimated human-capital threshold, compared with about 25 years for those above it. This reconciles development accounting with the view of human capital as absorptive capacity. If AI mainly augments skilled workers and capable firms, it may reinforce existing gaps. If it lowers the costs of learning, adaptation, and implementation in weaker-capability economies, it could instead promote convergence. The Intelligence Divide is therefore not simply about access to AI, but about the capacity to turn knowledge into productivity.