This article examines the historical and contemporary mobilizations of 'Luddism' as a mode of resistance to technological inevitability, particularly in response to the integration of generative AI into education. Tracing three historical 'waves' of Luddism -- the original nineteenth century machine-breakers, the Neo-Luddites of the late twentieth century, and the present day critics of digital automation -- it explores how the term has been mobilized, at different junctures, in service of overlapping (and, at times, competing) political projects. Reading across these 'waves,' the article considers what lessons, and cautions, they hold for how education research and practice might confront generative AI and the challenges it introduces for teaching, learning, and school governance.