Randomness in individual discovery tends to spread out productivities in a population, while learning from others keeps productivities together. In combination, these two mechanisms for knowledge accumulation give rise to long-term growth and persistent income inequality. This paper considers a world in which those with more useful knowledge can teach those with less useful knowledge, with competitive markets assigning students to teachers. In equilibrium, students who are able to learn quickly are assigned to teachers with the most productive knowledge. The long-run growth rate of this economy is governed by the rate at which the fastest learners can learn. The income distribution reflects learning ability and serendipity, both in individual discovery and in the assignment of students to teachers. Because of naturally arising indeterminacies in this assignment, payoff irrelevant characteristics can be predictors of individual income growth. Ability rents can be large when fast learners are scarce, when the process of individual discovery is not too noisy, and when overhead labor costs are low.