"Completed infinities" are at the center of modern mathematics. Their existence is taken as a foundational axiom. I must admit: I think this is an error - a logical mistake. Infinity, by definition, cannot be completed, right? I am joined by Dr. Gary McGuire, the head of Mathematics and Statistics at the University College Dublin. To my surprise, Gary also expresses skepticism about completed infinities. Get full access to Steve Patterson's Substack at stevepatterson.substack.com/subscribe