The last half-dozen years have seen The American Statistician publish well-argued and provocative calls to change our thinking about statistics and how we teach it, among them Brown and Kass, Nolan and Temple-Lang, and Legler et al. Within this past year, the ASA has issued a new and comprehensive set of guidelines for undergraduate programs (ASA, Curriculum Guidelines for Undergraduate Programs in Statistical Science). Accepting (and applauding) all this as background, the current article argues the need to rethink our curriculum from the ground up, and offers five principles and two caveats intended to help us along the path toward a new synthesis. These principles and caveats rest on my sense of three parallel evolutions: the convergence of trends in the roles of mathematics, computation, and context within statistics education. These ongoing changes, together with the articles cited above and the seminal provocation by Leo Breiman call for a deep rethinking of what we teach to undergraduates. In particular, following Brown and Kass, we should put priority on two goals, to make “fundamental concepts accessible” and to “minimize prerequisites to research.” [Received December 2014. Revised July 2015]