Is math invented or discovered? I've heard several of you saying that "math doesn't exist in the real world", but I have the feeling that "it's out there".

# Is math invented or discovered? I've heard several of you saying that "math..."

Shhhhh little animu...

No more questions...

You've asked too much...

Only sleep now...

here's the deal with math, my dude, you cannot prove its own existence through math.

That's okay though, because there are plenty of things in the world which we know are true, but cannot prove them to be so.

This might sound like "faith" but it isn't. These ideas do not follow through to a clearly inconsistent holy text. We know this by math itself. We simply cannot prove math's existence by using itself to prove it.

Mathematical facts are discovered, but mathematical techniques and algorithms are invented.

I'd say it's invented. Like you could invent a million different ways to build a working door, you could build a bunch of different ways to count (the naturals, reals etc.).

there is a problem with all statements like this that I don't know quite how to phrase

but it has something to do with the assumption that consciousness is either the "real" or not when the "real" is a concept formulated by consciousness as a boundary

Math helps us explain shit, it isn't really anything of value on its own. It is a language we use. It was invented by people. It's value and existence lies in when and how it is used.

math was discovered. our system to describe math (numbers for example) was invented.

aliens who have discovered math too could have invented a different system to describe it.

is this clear now?

Invented in the case of new formalisms and methods, discovered in the case of fundamental laws

So you can invent calculus but then discover the laws governing it, eg that d/dx (x^n) = n x^(n-1)

But that's just my opinion

Discovered.

Every alien species would have the exact same math we do. They may write it differently but it would be the exact same stuff. It does not come from within us, we just got smart enough to figure it out and 'mine' it from the Platonic realm.

not it is not. it applies strictly to a system which is known to be internally consistent, and has been used by brainlets with regards to a blatantly inconsistent religious text to try and defend some form of spiritual nature. quite literally, there are things in this world which we know are true, but cannot prove them to be so. we know this by "proving" it.

Yeah that's what I like to think too. That we're uncovering something beyond physical reality yet intimately connected to it.

If you are looking for examples, Ramsey Theory has a rich history of statements which we know are true but not "proveable".

If you're not a Platonist you're literally retarded, discovered for sure. The part that's "invented" is all the culture specific syntax crap and that's not the same thing as mathematics itself. Just because the same tree is called "arbre" by a Frenchman and "baum" by a German doesn't mean they each invented their own separate tree. The language used to work with an object is not the object itself. And there absolutely are mathematical abstract objects which exist independent of cultural differences. Numbers are a good example, there are many different names for numbers, but we all generally understand my "four" is your "cuatro." The approaches a culture takes to working with the mathematical reality that's out there can be super-convoluted and even just outright wrong, but that doesn't mean they have a different mathematics, it just means they have a different attempted approach to working with the one true mathematical reality. Same deal with axioms, you can pick different axioms to work with, but what truly works or not given those axioms is out of your hands, you can only either discover the answers or make up non-answers, and if you do the latter others will eventually find out you're wrong.

Godel was a Platonist too FYI. A lot of people don't realize he only meant the Incompleteness Theorem to say something about the limits of systems like Principia Mathematica, not to say something about mathematics in itself. He actually considered the fact these systems were limited an argument in favor of Platonism because all the truths of mathematics are independent of and greater than the truths that can be proven by PM alone.

Sure, but I'm not talking about Godel - he has alluded to this though. For many, what he was talking about was incomprehensible and has been used in a dramatically "u can't no nuthin" incorrect manner.

Math is just a way on how to describe things in nature. So it's neither invented or discovered, more like translated from nature, call it the language of the universe.

Thing you have to realize about math is that it is universal; merely a language to describe nature, but with concepts for humans, by humans. If we ever are to find other civilizations, it would be quite interesting to see their own "interpretation" of math.

the only difference between invention and discovery is the intent of the researcher.

If you unwittingly stumble upon a finding, then its a discovery.

If you intentionally build an argument then its invented.

If the axioms of a mathematical system attempt to say something about reality as we perceive it, and its axioms are consistent with reality, then in a fundamental sense it is discovered; in a superficial sense it is invented (symbols, etc.). In addition, obviously, many mathematical entities are purely constructs of our own (e.g. complex numbers), yet they are able to describe reality very effectively.

here's the deal with math, my dude, you cannot prove its own existence through math.

You mean mathematical systems cannot prove their own consistency. Of course they can't, because mathematical systems cannot talk about themselves; rather, they can only tell us about truths within those systems.

If you're alluding to anything Godel said, note that he didn't prove what you claim. He proved that the consistency of certain mathematical systems (which are consistent) cannot be proved using first-order logic.

What is the scientific consensus on "why anime has sidemouths 9 times out of 10"?