The advent of ChatGPT, and the subsequent rapid improvement in the performance of what has become known as Generative AI, has led to many pundits declaring that AI will revolutionize education, as well as work, in the future. In this paper, we argue that enthusiasm for the use of AI in tertiary education is misplaced. A proper understanding of the nature of the outputs of AI suggests that it would be profoundly misguided to replace human teachers with AI, while the history of automation in other settings suggests that it is naïve to think that AI can be developed to assist human teachers without replacing them. The dream that AI could teach students effectively neglects the importance of ‘learning how’ in order to ‘learn that’, that teachers are also role models, and the social nature of education. To the extent that students need to learn how to use AI, they should do so in specialized study skills units. Rather than creating a market for dodgy educational AI by lowering their ambitions about what they can offer, universities should invest in smaller class sizes and teachers who are passionate about their disciplines. To flourish in the future, just as much as they do today, societies will need people who have learned to think and not—or not just—intelligent machines.