Mathematics has long assumed a central place in the curriculum, but its warrant is under scrutiny. Both social demands and psychological assumptions have changed; the core purpose of education is deeply contested, powerful new models of teaching and learning are being proposed, and mathematics is in need of a new rationale. This article reflects on how the world around mathematics has changed, and what implications and possibilities arise. The article discusses what the author sees as three main challenges for mathematics education: (1) It is not clear that much of mathematics is as directly useful as it has claimed to be; (2) It is not clear that mathematics is the new Latin--in the sense of providing any kind of effective, generic "training of the mind"; and (3) Mathematics has achieved its high status in the curriculum not through its utility, either specific or generic, but because it forms a closed, elegant, timeless domain, capable of being neatly turned into an apparently logical succession of curriculum packages that require clear expository teaching, and that can be assessed objectively, unambiguously, and rigorously. The author unpacks the metaphor: minds are like "bodies; and schools are like "gymnasia" for developing fitter minds.