Human concepts can be placed under mathematical interfaces.

Inversion for gender

   ~male = female

Ordinality for human hierarchies:

   CEO > manager > worker

Commutativity for human action:

   Punch human + kick human = damaged human
   Kick human + punch human = damaged human

Mathematical interfaces are different from mathematical primitives which I believe you have mistakenly combined into a singular concept in your response.

By fitting human concepts into mathematical interfaces you develop a sort of algebra dsl for the language allowing you to apply all mathematical theorems of the equivalent algebra to the domain. Those theorems are the generalities that improve design by improving modularity.

Suddenly for ordinal concepts I can use a general min or max function across all domains. By using mathematical interfaces I am in the realm of the ultimate generality. Normally people would be writing some form of equivalent logic to derive the lowest ranking human in a hierarchy when really the concept of min covers it.

These basic mathematical interfaces that apply to basic numerical logic are found to be expandable across domains. There's no proof or logic as to why these interfaces happen to be more universal. It's just a gut feeling after using this interfaces more that they happen to be extremely universal. Thus there's no way I can prove to you what I'm saying is correct, you ultimately have to try it.