[kamaal]

>>when it is actually about relations, and numbers are just some of the entities whose relations mathematics studies.

Well no. Math is studying anything at their most atomic machinations. That mostly involves.

- Making hypothesis, that is assumptions about start conditions and rules of play.

- Evolving the system you just created. Such that conclusions are consistent with the rules of play.

The real deal is good math involves lots of paper work, to an extent you could almost say Math is a writing skill than a thinking skill.

Think of it like generating a lengthy changelog.

[SyzygyRhythm]

I would say instead that math is a game. A universal game with no predefined rules at all and only one guideline: if the rules you make up lead to a contradiction, then the rules are probably boring. If your rules say that 1+1=3, then you can prove anything and the whole thing becomes uninteresting.

Mathematicians have come up with various rules (axioms) that seem to work pretty well. And they spend a great deal of time figuring out their consequences. But it may still happen that the rules have a contradiction and they need to come up with a different set.

Sometimes mathematicians add extra rules when they run into a roadblock. And part of the meta-game is to come up with the minimum set of extra rules they need to keep going. Sometimes they spend time figuring out if the existing rules aren't needed.

[kamaal]

>>I would say instead that math is a game.

Yup, and as you keep going the level too go up!

But the core ideas are simple though-

1. Start some where where you understand things enough to make sense.

2. Make the smallest possible, atomic change to some aspect of thing you know at point 1.

3. Test if the change sticks- If yes, repeat steps 1 - 3

4. If the change doesn't stick- Go back to step 1. Now either make a different change to the same thing or make a new change to a different thing. Repeat steps 1 - 3.

As you can see you write a lot. Like really a lot. Math is just writing skills.