This is an incarnation of the https://en.wikipedia.org/wiki/Functor_represented_by_a_scheme#Functor_of_points https://en.wikipedia.org/wiki/Functor_represented_

This is an incarnation of the https://en.wikipedia.org/wiki/Functor_represented_by_a_scheme#Functor_of_points https://en.wikipedia.org/wiki/Functor_represented_by_a_schem... perspective on https://en.wikipedia.org/wiki/Scheme_(mathematics) https://en.wikipedia.org/wiki/Scheme_(mathematics), the fundamental object of study in modern algebraic geometry. This perspective could be interpreted as treating equations as recipes and number systems, (fields/rings) as ingredients. It turns out to be extremely fruitful to study the "R-points" of an equation for all sorts of rings R, even more exotic ones like p-adic numbers or finite fields. Algebraic geometry and the study of schemes is a truly beautiful field of mathematics, linking number theory to theoretical physics, and much more.