zlacker

I think the biggest mistake people make when thinking about mathematics is that it is fundamentally about numbers.

It’s not.

Mathematics is fundamentally about relations. Even numbers are just a type of relation (see Peano numbers).

It gives us a formal and well-studied way to find, describe, and reason about relation.

>>jbande+(OP)
Prime numbers are the queens/kings of mathematics though.

>>jbande+(OP)
The most commonly used/accepted foundation for mathematics is set theory, specifically ZFC. Relations are modeled as sets [of pairs, which are in turn modeled as sets].

A logician / formalist would argue that mathematics is principally (entirely?) about proving derivations from axioms - theorems. A game of logic with finite strings of symbols drawn from a finite alphabet.

An intuitionist might argue that there is something more behind this, and we are describing some deeper truth with this symbolic logic.

>>jbande+(OP)
To form or even to define a relation you need some sort of entity to have a relation with.

My wife would have probably gone postal (angry-mad) if I had tried to form an improper relationship with her. It turns out that I needed a concept of woman, girlfriend and man, boyfriend and then navigate the complexities involved to invoke a wedding to turn the dis-joint sets of {woman} and {man} to form the set of {married couple}. It also turns out that a ring can invoke a wedding on its own but in many cases, it also requires way more complexity.

You might start off with much a simpler case, with an entity called a number. How you define that thing is up to you.

I might hazard that maths is about entities and relationships. If you don't have have a notion of "thingie" you can't make it "relate" to another "thingie"

It's turtles all the way down and cows are spherical.