But this then sounds like that math or logic is a "thing", and then I must ask where that does thing reside? Either in physical reality out there, or in people's minds.

It doesn't have to be either or. You can learn maths from books, .ir record your knowledge in them.

Consider Vaniver on Harari on cultural artefacts:-

There are no gods in the universe, no nations, no money, no human rights, no laws, and no justice outside the common imagination of human beings.People easily understand that 'primitives' cement their social order by believing in ghosts and spirits, and gathering each full moon to dance together around the campfire.

What we fail to appreciate is that our modern institutions function on exactly the same basis.But, of course, those modern institutions (as well as the 'primitive' ones) function. One division Harari discusses that I found useful was objective, subjective, and inter-subjective:

An objective phenomenon exists independently of human consciousness and human beliefs. ... [Radioactivity is his example.]The subjective is something that exists depending on the consciousness and beliefs of a single individual. ... [A child's imaginary friend is his example.]The inter-subjective is something that exists within the communication network linking the subjective consciousness of many individuals. If a single individual changes his or her beliefs, or even dies, it is of little importance. However, if most individuals in the network die or change their beliefs, the inter-subjective phenomenon will mutate or disappear. ...Many of history's most important drivers are inter-subjective: law, money, gods, nations.