This paper studies the dynamics of fundamental research. We develop a simple model where researchers allocate their effort between improving existing fields and inventing new ones. A key assumption is that scientists derive utility from recognition from other scientists. We show that the economy can be either in a regime where new fields are constantly invented, and then converges to a steady state, or in a cyclical regime where periods of innovation alternate with periods of exploitation. Our analysis provides a rigorous foundation to the Kuhnian theory of scientific evolution. We show that scientists' care for reputation has a strong impact on research dynamics and tends to favor innovation. Especially, innovation fads may emerge. We also study welfare and find that the academic reputational reward system can help align scientists' short-term incentives with society's long-term interests.