mathematics discovered or invented?

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What is Jitro?

The jury on that is still out.

You missed some:
Is discovery discovered or invented?
Is invention invented or discovered?
Are differences real?
Is real real?
Is "is" is?
Just what is the difference between a duck?

logic > discovered (two-state systems are as old as night and day)
physics > invented as a description of the natural universe
biology > invented as a description of the natural universe
language > invented to map labels to concepts

Most of the other questions about "is" etc are subsumed under language.

Math is different from these in the sense that it has an independent existence about it. Math is so abstract that it doesn't need anything real to exist. You can't be, say, a biologist without something biological. You measure animals from nose to tail or look at plants, but biology wouldn't exist otherwise. Same for physics. Without things taking up space, having mass, and moving, physics wouldn't exist. Math, though, could exist per se without anything else.

Math is understood by people because we have a facility (which some like Kant and Plato think is innate; others like Locke and Hume don't seem to think so) to think abstractly. An animal might be taught to do math on some level, but they do not have the ability to abstract from this and come up with, say, commutative rings. Only people can do this, which connects people to an abstract world. (Which may or may not exist depending on how Platonic your concept of ontology is.)

That's what makes the question so fascinating with regard to math, and why it is so hard to answer. We both apply math to everyday life, making it a descriptive thing that depends on what exists to be useful, but we also abstract our math into structures which don't actually exist in the physical world. (Other than the tesseract I made out of toothpicks in junior high. I'm working on a paper mache commutative ring next. After that, I may do a non-commutative one.)

That sounds fascinating. Could you provide something of verbal description of this model. My favorite commutative rings are vector spaces.

ruveyn

Physics - discovered.
Maths - invented.

The principles of math and the principles of phenomena which they describe have been discovered.

You can prove the ridiculous with incorrectly applied math.
A mathematical prove is usually only born out when it describes or predicts an observed phenomena correctly.

That was sort of a joke, trying to poke fun at reifying abstract concepts by making it seem so easy a child could do it in paper mache.

I think it can be argued that everything is discovered and nothing is invented.

Physics is the study of naturally phenomena, same with chemistry, biology and the other natural sciences.

Physics - discovered
Biology - discovered

Mathematics is an invented language used to describe natural phenomena.
The phenomena which human language describes is discovered, but the language itself is invented.
Logic is also a language, but the phenomena to which it applies is discovered.

Mathematics - invented
Logic - invented
Language - invented

The reason why you can't consider mathematics simply as a language is because a language such as english is only created when necessary (a posteriori), while mathematics is discovered for its own sake and things that are entirely abstract and not related, by the discoverer, to the real world end up being applied to phenomena previously unknown to man with remarkable results.

I believe all of them was invented.

The methodology was invented. The content was mostly discovered.

ruveyn

Which in my belief is a disovering of an imaginary content constructed by the language which made it possible to exist.

Scientists can create neutrons, but they certainly didn't invent them.
Newton was the author of calculus, but he certainly didn't discover it in some dusty drawer.

Mathematics come from ideas and are developed.
Its rigor prohibits arbitrary facts that don't work.

The problem is that a change in language can make the neutrons disappear; making them only visible and existing to scientists who use a given language.