Is more novel research always desirable? We develop a model in which knowledge shapes society's policies and guides the search for discoveries. Researchers select a question and how intensely to study it. The novelty of a question determines both the value and the difficulty of discovering its answer. We show that the benefits of discoveries are non-monotone in novelty. Through a dynamic externality, moonshots---research on questions more novel than myopically optimal---can improve the evolution of knowledge. Incentivizing moonshots requires promising ex-post rewards. However, even a myopic funder combines rewards with ex-ante cost reductions to increase research effort.