Mathematics is a playground. Its game is a game of games. Various kinds of games with rulesets (theorems) bound by a greater set of rules (axioms). You can either learn a few rulesets and see where they take you or even reject the entire shebang and build your own game(s).
One needs to be careful when rejecting an entire set of rules as that entails throwing away the indexical qualities of correspondence the rejected rules have to inside (other games) or outside (reality). If they are met better one is free to construct one's own mathematics.
What we know now as "Mathematics" in singular is a set of (sometimes) mutually consistent games which got formed as a result of stochastic wavefronts of changes drastically different from existing ones that got incorporated continuously and sporadically to give a stable body.
The diffs (like git diffs) of these changes are invisible and lost to history now and are considered part and parcel of the game network. This canon is taught in schools implicitly as a single thing but nothing could be further from the truth:
Relevance of certain things are appreciable only with enough context: Ideas like cardinality (size) vs. ordinality (order) seemed remote and not worthy of much attention but as I built up a historical context I got to see how it undergirded many concepts I engaged with daily.
An advantage of reading widely different works on a subject matter by authors in different fields is that you get acquainted with abstractions/analogies you yourself hadn't considered before which these authors gained after hard work in their field(s) of inquiry.
To illustrate such an instance: Just learnt about an idea called "integuments" in a logic system employed by Bertrand Russell. These are constituents that form a proposition. This I think in computer speak is analogous to arguments of functions.
Source: ncatlab.org/nlab/show/Logi…
Source: ncatlab.org/nlab/show/Logi…
