Math: Discovered or Invented?

[iff]

Maths wasn't invented, just the words and terms we use to articulate maths were invented

 

Saying maths was invented is like saying physics or biology was invented, they weren't. They were there from the start, working in the background but we then became more aware of these as our knowledge and understanding of the world increased. 

[WonkyQuadratic]

I absolutely adore this question. I don't have a concrete answer and I think that this is the beauty of it. If I was to put an argument forward it'd go something like this:

- Mathematics is made of axioms, definitions, proofs and lemmas / theorems.

- Axioms are named fundamental laws, these cannot be created, in fact I would argue they are discovered, in the most fundamental sense.

- From here what is created is the path to a theorem, there are many ways to a theorem, I would argue infinitely many, so we create one for future mathematicians to use.

- We also create the names and the problems that Mathematics is discovered off. Because we didn't discover the millennium problems, we created them.

- Once a set of axioms is set, all of mathematics is so as well, so it's just out there to discover, much like a forest. It is to be discovered, we just create a path.

[WoodwindWhistler]

Mathematical properties exist, objectively. 

The tree that falls in the forest does make a sound, the widdle shockwaves just don't hit any earbones. 

 

If your question is over whether the sum total of mathematical equations that we have written down are "mostly" abstract algebra or "mostly" derived from concrete problem solving about building or observations of nature, I would lean towards the latter.