Is mathematics discovered or invented?

[Independent voter]

Is mathematics something that exists in nature and we are somehow extracting that information from nature, or are we coming up with mathematics on our own?

If we met aliens and they had a completely different way of doing math, that would point to us inventing our own math. If the aliens had the exact same math system that we do, that would point to math being something that exists in nature?

[Theodarzna]

Mathematics is a language to describe the universe.

Its neither discovered nor invented, its described.

[Shadowferal]

Math is exactly as physics; it exists independent of our awareness of it.

How it might be translated by different races isn't relevant.

[WintersLegion]

Mathematics is a language to describe the universe.

Its neither discovered nor invented, its described.

it has to be discovered before it can be described.

[Shadowferal]

it has to be discovered before it can be described.

The Catholic Church refused to recognize the integer "0" for the longest time thinking it a heathen thing since it meant "nothingness" and it was utilized by Muslims, which is what is used today "Hindu-Arabic" numeral system.

[Fencers]

Entirely invented. It's a language to describe processes, relations, sums, et cetera.

Calculus, for example, doesn't exist as a thing independent of human thought out in the universe.

[zephid]

Mathematics is a language we use to describe the universe, so you could say that it's both invented and discovered. The mathematical language is invented, but what it describes are discovered.

[PC2]

Is mathematics something that exists in nature and we are somehow extracting that information from nature, or are we coming up with mathematics on our own?

I would say there is fundamental logic that nature follows but we can try to understand it through data, math expressions, equations. Physicist David Deutsche says "without explanation there is no such thing as data".

@Garnier Fructis has a different take, that processes and information or data can be separate stand alone concepts, apparently where neither is extracted from the other?

[Turtel]

I think it depends on what aspect of mathematics that you're talking about. There are certain aspects that are invented, like when you define the rules for what it means to add, multiply or divide, or what an '=' sign means. But once you set up those rules, a lot of things get implied or can be concluded based on those rules, which would be classified as discoveries in my opinion.

[Shadowferal]

*shrugs*

1 + 1 = 2

Symbols may change but the meaning and results don't.

[Deleted]

Mathematics is a language to describe the universe.

Its neither discovered nor invented, its described.

Considering new concepts and ways of approaching calculations are developed ; they are invented.

Just as we can invent words and ways to express things - Math is a evolving thing.

OT: Who the *beep* really thinks Math is a Universal force to be "discovered", lol? Are you so arrogant, to really wish to believe that a random collection of biological blobs that came to sentience, superimpose their understanding to the level of that it's actually a factual truth, that the universe would REMOTELY be connected to us?

Dear lord.

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it has to be discovered before it can be described.

Discovery implies existence since before - Math is a construction.

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*shrugs*

1 + 1 = 2

Symbols may change but the meaning and results don't.

Depends on the axioms ; 1 +1 = 2 is only true on a certain set of subjective constraints.

[Flabberly]

Mathematics is, foremost, a language invented by humans. It is the most advanced language we, as a civilization, created and it can be used to define the Universe as we understand it.

Bear in mind, that mathematics isn't exactly the number system created by the Arabian culture,as 1 equals one unity, but the mental understanding of that numerical system, as 1+1=2. It is absolute and, let's be honest, it makes sense.

Therefore, as an answer to your question, mathematics is something both invented and discovered by humans. It's easier to look at it as something that perfectly describes the Universe but I, and Humanity as a whole, can't say for certainty that it is the sole system capable of such description.

[Deleted]

Mathematics is a language we use to describe the universe, so you could say that it's both invented and discovered. The mathematical language is invented, but what it describes are discovered.

Discovery is still implying previous existence ; Math is created upon the point of invention, thus, never "Discovered".

Even in perspective of "But we figured something we didn't know before" - Still does not imply that math per say, was there to begin with - So, in the grand scheme of math itself, it's invented, for the person in question understanding it - it's discovered.

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Bear in mind, that mathematics isn't exactly the number system created by the Arabian culture,as 1 equals one unity, but the mental understanding of that numerical system, as 1+1=2. It is absolute and, let's be honest, it makes sense.

Nothing in math is absolute, as the theory of it is based on subjective axioms to begin with.

[Shadowferal]

Depends on the axioms ; 1 +1 is only true on a certain set of subjective constraints.

Prove it.
If you can.

And not some thesis length post that merely obfuscates. Something as simple and easy as..say...1 + 1...

[Deleted]

Trust me we know jack shit about world around us. Math and physics as complicated as they look are nothing compared to real truth. Truth that our minds aren't capable of understanding. Nor should we understand it I was to be honest with you.

[zephid]

Discovery is still implying previous existence ; Math is created upon the point of invention, thus, never "Discovered".

Even in perspective of "But we figured something we didn't know before" - Still does not imply that math per say, was there to begin with - So, in the grand scheme of math itself, it's invented, for the person in question understanding it - it's discovered.

Which is why I wrote that the "mathematical language" is invented.

[Deleted]

Prove it.
If you can.

And not some thesis length post that merely obfuscates. Something as simple and easy as..say...1 + 1...

You ask for Mathematical proof, yet dismiss the notion of a thesis.

I don't think you are ready to grasp the concept.

[Shadowferal]

You ask for Mathematical proof, yet dismiss the notion of a thesis.

I don't think you are ready to grasp the concept.

Oh...you mean you can't prove it...
*shrugs*
I already knew it.

[Garnier Fructis]

I don't think it's fair to the history or practice of mathematics to say that it's discovered or invented. It's essentially both.

This duality is sort of built into a lot of abstract mathematics. We invent some new structure by setting down a bunch of rules that it follows, and then it becomes a game of what we can discover about this structure using logic and whatever other structures it depends on.

Though if you really think about it, things like 'group' and 'field' were abstracted from more concrete examples, which were themselves either discovered or abstracted from something else. So in a really roundabout way, one might be able to argue that it all boils down to discovery, and that the only aspect that we invent is how we choose to organize what we know.

Mathematics is a language to describe the universe.

Its neither discovered nor invented, its described.

Most of mathematics started out this way, but a good amount of modern pure mathematics doesn't really describe anything about the real world. That being said, I'm of the belief that we can apply anything if we try really hard:

http://www.smbc-comics.com/comics/14...4-20160603.png

I would say there is baseline logic that exists in nature but we can try to understand it through mathematical expressions and data. The physicist David Deutsche says "without explanation there is no such thing as data".

@Garnier Fructis has a different take, that processes and information or data can be separate stand alone concepts, apparently where neither is more dependent on the other?

I don't necessarily disagree with Deutsche. I'm pretty sure he's getting at the fundamental problem of experiment and data, which is that you can only interpret that data through some theory that is assumed to be valid. Without a theory of electromagnetism, what does the mass of an electron even mean? So in that sense, data is not truly objective in its own right, but dependent on theory for interpretation.

But in general, I do think there is a difference between a mathematical or logical process, and the 'object' on which it acts. This is sort of the underlying philosophy of abstract algebra. We talk about groups, fields, torsors, etc., but all of our theorems in some sense assume that meets our criterion for being one of these objects. Because otherwise, we'd be talking about nothing. The flip side is that our deductions of groups apply to anything that meets the criterion for being a group. Crystal orientations, integers, complex matrices, even functions can be groups. So our abstract algebraic deductions are independent of any specific instance or model.

[Flabberly]

Nothing in math is absolute, as the theory of it is based on subjective axioms to begin with.

Everything we believe as truth is based on subjective axioms.