scroll to 4:40 I like his one argument: if we have finite neurons and thus cannot construct an infinite set in our "map" what makes you think that you can make it correspond to a (hypothetical) infinity in the territory?

I don't really see what this argument comes to. The map-territory metaphor is a metaphor; neural structures do not have to literally resemble the structures they have beliefs about. In fact, if they did, then the objection would work for any finite structure that had more members than there are synapses (or whatever) in the brain.

If he is saying that infinite sets are a mathematical impossibility then he is wrong.

But I'm fairly sure that he is saying they are a physical impossibility. Which is not at all unreasonable. (this is the "territory" I think he is talking about)

I have a feeling we are working with different definitions of the "mathematics". I think your definition of "mathematics" might be "symbols that occur in physics and can be manipulated to give answers about the universe".

My definition is something like "set of axioms => conclusions about the structure of the object generated by the axioms" (which includes things like the real numbers, which gives calculus, so the first version of "mathematics" is included the second).