Is mathematics invented or discovered ?

[Ero]

I challenge all of you to work long enough on a math problem until you start hallucinating.

The degree of imagination you need to comprehend higher levels of mathematics is not one accessible to normal humans.

[AION]

Everything is i-magi-nation but not all imagination is the same.

[Natasha Tori Maru]

Both? 

Deep structures appear to exist whether we're here or not..  pythag, primes, geometry, limits. They appear to behave the way they do regardless of human opinion. 2 bananas + 2 bananas = 4 bananas long before anyone counted... Or so it would seem.

But also invented in the sense that the language is ours. I like to think of mathematics as a universal language. Symbols, axioms, co-ordinate systems - human made tools. Calculus didn't 'exist' until someone framed it. Even though change and motion always did.

So I think we built a map to help navigate what was always there... So there was always constraints and patterns & we supplied the formal systems to describe them.

 

[UnbornTao]

16 hours ago, Salvijus said:

 As far as I'm concerned, I see no problems with my definition of what language is. I'm open to hearing opposite views than my own but so far I found none of it more convincing than mine. That's my side of the story at least. Perhaps your experience is different. It's okay. We can just agree to disagree. 

That's the thing, it's just a definition. Ironically, without language, we couldn't come up with any of the things that we think are language. Without language, what's language? 

I ran out of synonyms this morning.