Third places are places to congregate with semi-strangers without invitation/previous agreement with acquaintances. They are separate from work or home. In the UK, traditionally that would be a pub.
Math is considered a non-empirical, deductive discipline.
However, it "maps" onto reality, which gives it an empirical feedback.
For example, N is proven useful for counting sheep among many things, and Z for temperatures or debt/income among many things. It is designed to fit reality. At least a part of math finds a reality counterpart.
So is math considered non-empirical as a whole?
Why isn't any Non-empirical Mathematics Department that competes for funds against the Empirical Mathematics Department?