Important mathematical competences for students in the age of generative artificial intelligence: proof comprehension and evaluation, and ChatGPT

The rapid growth and popularity of generative artificial intelligence has influenced all aspects of life and education, including mathematics education. Specifically, generative Large Language Models (LLMs), notably ChatGPT, are becoming increasingly popular among students and are changing the landscape of what mathematical competences students need in order to function effectively in the age of generative artificial intelligence and interact productively with the new technologies. We contend that educational systems must adapt to the new realities by resetting priorities, reorganizing curricula, and retraining teachers. In this paper, we call attention to the increased importance gained by two competences in the area of proof, proof comprehension and proof evaluation, as students interact with ChatGPT. We view our discussion of these proof competences as a case in point of the pressing need for mathematics education researchers and practitioners to reflect on what constitute important mathematical competences for students in the age of generative artificial intelligence. This is a foundational step that can serve as the basis for discussions about reimagining the future shape and role of mathematics education in society, including the training of teachers.