Machine learning methods are increasingly used to model risk in criminal justice, banking, healthcare, and other high-stakes domains. These new tools promise gains in accuracy and raise challenging statistical, legal, and ethical questions but common mathematical definitions of fairness can lead to discriminatory outcomes in practice. In this talk, Sharad Goel, professor of public policy at Harvard Kennedy School, will describe the dominant axiomatic approach to fairness in machine learning, and argue that common mathematical definitions of fairness can, perversely, lead to discriminatory outcomes in practice.