The problem of machine teaching is considered. A new formulation is proposed under the assumption of an optimal student, where optimality is defined in the usual machine learning sense of empirical risk minimization. This is a sensible assumption for machine learning students and for human students in crowdsourcing platforms, who tend to perform at least as well as machine learning systems. It is shown that, if allowed unbounded effort, the optimal student always learns the optimal predictor for a classification task. Hence, the role of the optimal teacher is to select the teaching set that minimizes student effort. This is formulated as a problem of functional optimization where, at each teaching iteration, the teacher seeks to align the steepest descent directions of the risk of (1) the teaching set and (2) entire example population. The optimal teacher, denoted MaxGrad, is then shown to maximize the gradient of the risk on the set of new examples selected per iteration. MaxGrad teaching algorithms are finally provided for both binary and multiclass tasks, and shown to have some similarities with boosting algorithms. Experimental evaluations demonstrate the effectiveness of MaxGrad, which outperforms previous algorithms on the classification task, for both machine learning and human students from MTurk, by a substantial margin.