The issue of disagreements amongst human experts is a ubiquitous one in both machine learning and medicine. In medicine, this often corresponds to doctor disagreements on a patient diagnosis. In this work, we show that machine learning models can be successfully trained to give uncertainty scores to data instances that result in high expert disagreements. In particular, they can identify patient cases that would benefit most from a medical second opinion. Our central methodological finding is that Direct Uncertainty Prediction (DUP), training a model to predict an uncertainty score directly from the raw patient features, works better than Uncertainty Via Classification, the two step process of training a classifier and postprocessing the output distribution to give an uncertainty score. We show this both with a theoretical result, and on extensive evaluations on a large scale medical imaging application.