The Dialectical Theorem: The future of universities, mathematics departments, and training of human mathematicians

We consider the future of mathematics as a profession in a world where artificial intelligence may surpass human mathematicians in essentially every technical task. Through an informal dialogue, we explore why human mathematical expertise might nevertheless remain valuable, what kinds of expertise universities should cultivate, and how graduate education might adapt. We also discuss the institutional and economic uncertainties that threaten the continued existence of a thriving mathematical profession, even if the value of human mathematical understanding endures.