[AndrewC]

Can you point to an implementation of any of them that is purely non-physical? Can you point to anything that does mathematics that is not physical?

What do you think interacting with physical means? Are you now changing your question to not interacting with the physical?

[js1138]

Mathematics is an activity of humans. Humans are physical.

This is not something that will be decided here. People have differing opinions as to whether mathematics is discovered or invented. I say invented, though there is little hope of convincing anyone who doesn't share my opinion.