The issue is not in regard to how long a thing exists but does a thing have an existence on its own. To clarify: "this is a tree". Now the tree exists regardless of whether I say that sentence or not. But the sentence itself wouldn't exist for there are no humans in the universe to say it. I can safely say that whatever was conceived or fabricated by humans, if humans don't exist, those things won't exist either. And that includes our alphabet and our number system.
If the earth exploded, no one would know about the tree.
But moving on to the actual issue, I think we're getting to the root of it (no pun intended.) People who say that math is real are generally not saying that numbers exist as an observable substance, but that the numbers are descriptions of the observable rules we see nature following. And in that sense, yes, math does exist.
It exists as a mental construct, just like our alphabet.
Because even if the earth exploded, the same descriptions would be valid for as long as the universe continued to work in the same way.
The universe would exist. Its human description would not, since the humans upholding those mental construct don't exist anymore. Where would those human thoughts exist???
I think the original video draws a false line between "what a study is" and "what it studies." Sure, the laws of physics as we describe them exist, but does Physics exist?
Physics is a human description of the universe, a model that we have refined over the years with constant observations, experiments and hypothesis. Therefore it is a mental construct produced by our minds.
Can you touch a momentum? What about chemistry? Are little PV = nRT's floating around in the void? That's the kind of question being asked about math here, and it's really somewhat silly. If gathering one thing and another thing together made three things, that's how our formal, written math system would work. We didn't make it up, we observed it. Just like any other science.
I believe you are conflating two things: the mental constructs - ideas, theories, thoughts, beliefs, theories, physics, math etc - exist as long as they are hold by human brains. And the things these mental construct describe - particles, stars, the universe, etc. which exist independently of our thoughts.