Both of the experts in the video are physicists, and in my experience physicists play fast and loose with mathematics. I think this is often because the mathema

Both of the experts in the video are physicists, and in my experience physicists play fast and loose with mathematics. I think this is often because the mathematics that makes their arguments rigorous comes long after the sloppy methods are entrenched in the physics literature. In any case, I have talked to many physicists who have expressed to me their desire to better understand a topic like, say, differential geometry, but abhor the idea of actually reading a proof or studying a precise definition. In their words, "I only want an intuition for the subject." An understandable desire, but now my bar for believing a physicist when they make a mathematical claim is quite high. This video isn't helping them any. To be sure, there is a right way to do it, a simple practice that the men in the video could have employed to appease everyone: when you do something egregiously false, mention that strictly speaking you're not allowed to do it, and that you're actually sweeping a lot of complexity under the rug, and then continue anyway. This is the opposite of the blind appeal to authority in the video, and maintains their integrity.