Yes, I saw that! Inspired me to look at the original paper. The video takes a slightly different approach from the paper and uses a retraction on the möbius st

Yes, I saw that! Inspired me to look at the original paper. The video takes a slightly different approach from the paper and uses a retraction on the möbius strip to its boundary as a contradiction. That particular argument doesn’t generalize as well in higher dimensions (in particular, the symmetric product won't always have a boundary to retract to), so I followed the original paper’s one instead. I'll add a link to that video as well