The thesis examines how critical AI literacy can come to be in mathematics education. This is explored in relation to steering documents, pre-service teacher education, and classroom context. The results indicate that mathematics education with critical and ethical perspectives on AI technology is didactically possible, in the sense that teacher education and mathematics lessons can be shaped around such goals. However, the results also indicate that the traditions of mathematics education and expectations about what mathematics and mathematics education are and should be, are characterized by notions that contrast with such learning about AI technology.