I would trust a math professor to have an intuitive and abstract understanding of the kind algebraic or notational concerns you have. Math people reuse symbols

I would trust a math professor to have an intuitive and abstract understanding of the kind algebraic or notational concerns you have. Math people reuse symbols and invent new algebras all the time, so they don't hold these symbols (or their syntax) sacred at all. There is in fact a healthy professional irreverence. Perhaps you may have benefited from a constructionist approach to mathematics, which is far less "magical", but most math is for engineering so its understandable why math professors teach differently. * https://en.wikipedia.org/wiki/Church_encoding https://en.wikipedia.org/wiki/Church_encoding