I have thought about this thing for some time and I think that the unifying idea of math, physics (quantum shit in particular), programming, type theory, probability etc is the idea of fixed points which is just ubiquitous. Fixed points are based on the idea of an adjoint (1-to-many relationship) and a norm (many-to-1 relationship).

I have written up something about this https://github.com/adamnemecek/adjoint

Jon Claerbout has website that explains the concept of adjointness https://reproducibility.org/RSF/book/bei/conj/paper_html/pap...