We introduce the role that productivity plays in scientific success by describing Paul Erdös’ exceptional productivity. How does Erdös’ productivity measure up to other scientists? Is the exponential increase in the number of papers published due to rising productivity rates or to the growing number of scientists working in the discipline? We find that there is an increase in the productivity of individual scientists but that that increase is due to the growth of collaborative work in science. We also quantify the significant productivity differences between disciplines and individual scientists. Why do these differences exist? To answer this question, we explore Shockley’s work on the subject, beginning with his discovery that productivity follows a lognormal distribution. We outline his hurdle model of productivity, which not only explains why the productivity distribution is fat-tailed, but also provides a helpful framework for improving individual scientific output. Finally, we outline how productivity is multiplicative, but salaries are additive, a contradiction that has implications for science policy.