Maths: Do we discover or invent it?

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ChaoticButterfly
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Do we discover mathematics or do we invent it?

:holmes:
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lemonlikelime
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My friend did her EPQ on this! Her conclusion (I think) was that the concepts in Maths were discovered, but the way we understand them (numbers, methods etc) was invented :-)
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Welshstig
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We invent the symbols, but we discover the maths and its axioms!
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TheMightyAugur
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elekro
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Or maybe we invented a concept bigger than we expected and now we discover its aspects/functions?
Just a thought that probably doesn't even make sense...
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ChaoticButterfly
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(Original post by lemonlikelime)
My friend did her EPQ on this! Her conclusion (I think) was that the concepts in Maths were discovered, but the way we understand them (numbers, methods etc) was invented :-)
This seems sensible to me. But it leads to the conclusion that the concepts exist outside our heads and are "real" which I find confusing.

How can you empirically find the existence of math concepts? Sure we can find how maths concepts fit in describing nature, see physics etc, fractals describing how plants grow is an example. But does that prove that there is an underlying maths that controls the plants growth on a deeper level? Is mathematics the fabric made by a deistic god who set the universe in motion? Is the universe made of maths?
:confused::argh:
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Kallisto
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Whenever people find a mathematical relationship to considerations about natural things out, they have discovered it in my view. If they are able to create things based on the mathematical relationships, they have invented something thanks to mathematics.
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fergijane88
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This is something that really stresses me out. Like maths is so real, but at the same time just a concept???? Mind=Blown.
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NotNotBatman
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Some discovered some invented perhaps.

Things like exponential growth exists in nature, so that would mean it's discovered, then equations are made to represent it, such as exponential growth being the limiting factor of (1+1/n)^n as n approaches infinity.
If I've remembered correctly, trigonometry comes from the study of astronomy, so it definitely exists in nature, but the ways of representing it are invented.
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lemonlikelime
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(Original post by ChaoticButterfly)
This seems sensible to me. But it leads to the conclusion that the concepts exist outside our heads and are "real" which I find confusing.

How can you empirically find the existence of math concepts? Sure we can find how maths concepts fit in describing nature, see physics etc, fractals describing how plants grow is an example. But does that prove that there is an underlying maths that controls the plants growth on a deeper level? Is mathematics the fabric made by a deistic god who set the universe in motion? Is the universe made of maths?
:confused::argh:
Ooooh ... those are some intense questions. About the "concepts exist outside our head" thing, I know it's a bit confusing but I love that idea. It's basically Kant's (Immanuel Kant, philosopher) idea of the phenomenal and noumenal worlds.
There's the world that we know through our senses and our experiences (the phenomenal world), and that's the one in which we discover maths and invent a way to interpret it. The phenomenal world can never be anything more that what we experience - the limits of this world/reality (I guess you could call it) are the limits of our senses.
(e.g. a dog can smell a bigger variety of smells than a human. We'll never know what a dog smells, because we literally do not have the capability to smell that = we're restricted by our senses)
On the other hand, the noumenal world is what there actually is. E.g. atoms exist, and we know that, but we will never be able to experience them because they're too small. The only way we can detect them is using machines (I mean individual atoms lol i know everything is made of atoms so we can feel them right now). So noumenally speaking, they might be completely different to what we imagine, because all we have are models. (but pretty accurate ones hopefully)
If you look at Plato's cave analogy - we're like the prisoners in the cave, but we can never leave the cave.
Spoiler:
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I'm sorry I dived into philosophy there! but if you're interested, here are videos which do a much better job of explaining it than i do:
https://www.youtube.com/watch?v=E3xGDTn-Fcw
https://www.youtube.com/watch?v=IV-8YsyghbU&t=303s
highly recommend ^^^^^^!!!


So! Maths exists outside our limited reality, and the numbers we use are a way of translating the patterns we see in the world. It's like a language :-P

About the other questions... Maybe maths was designed by a deity... maybe not? I'm not sure! Your deduction is as good as anyone's :confused: :awesome:


Lol I just realised I could have linked the videos in directly instead of trying to explain the two worlds thing. Sorry
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TheMightyAugur
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Quarternions were not discovered. They're completely made up. Let's not kid ourselves here
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Kallisto
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(Original post by Welshstig)
We invent the symbols, but we discover the maths and its axioms!
Would rather say we have agreed on symbols, just to give mathematics a language.
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ChaoticButterfly
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Also where the **** do imaginary numbers come into this? :bricks:

There are no physical manifestations of imaginary numbers in nature. Yet they are used "round the back" to calculate physical things (e.g. the wave function in quantum mechanics). We start of with real numbers, then use some imaginary and complex numbers to do some calculations before getting bask to a number we can actually put a physical unit in front of. Is that proof that maths exists on a deeper more fundamental level than which the physical universe exists in?

lemonlikelime
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lemonlikelime
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(Original post by ChaoticButterfly)
Also where the **** do imaginary numbers come into this? :bricks:

lemonlikelime
Hahaha me when I looked up exactly what imaginary numbers are meant to be:
:lolwut:

After some very very superficial reading, in direct reference to your question I'd say imaginary numbers are ... "things/values/quantities" which obviously exist as they're used in electrical calculations etc. but our "math language" isn't sophisticated enough to explain properly since they're not on any number line (???) :nooo:

me trying to figure out an answer :-P
:tumble:

What brought on this question anyway (the maths discovered or invented question)??

in response to your edit: there may not be a physical manifestation of imaginary numbers in the visible nature, but they clearly do work when we're working with the laws of physics. I think Maths has a whole lot more going for it than just what's visible to us - or even what's been discovered so far. We're kinda stumbling in the dark here, making up things and ideas to explain what we come across in Science. If anything it's a proof of how little we know (cliche yes).


Also. My old maths teacher used to be fond of saying that physics is applied maths. If that's the case (physicists may disagree!) then considering physics has helped us establish some fundamental "laws of the universe" it's a fair conclusion to draw that maths exists on a deeper, more fundamental universe than the one we can observe straight away
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ChaoticButterfly
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(Original post by lemonlikelime)

What brought on this question anyway (the maths discovered or invented question)??
I have a physics degree and am interested in those kind of areas of science where maths is the language used, so I always think about these things

I'm also part way though a book entitled "Our Mathematical Universe" by a cosmologist who thinks reality is not just described by mathematics but is reality so it is on the brain a lot at the mo.

I just decide I would make a thread because why not. This section is normally full of tedious "why god does not exist threads" that have been done to death a million times -______-
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lemonlikelime
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(Original post by ChaoticButterfly)
I have a physics degree and am interested in those kind of areas of science where maths is the language used, so I always think about these things

I just decide I would make a thread because why not. This section is normally full of tedious "why god does not exist threads" that have been done to death a million times -______-
You have a physics degree!! Gah!!! In that case you're far better equipped to think about these questions than me lol I had no idea

aha no i think it's a very interesting question, but like all extremely interesting questions, it raises more questions in turn. Science and philosophy ftw!:bl:

in response to edit: Cool book! slightly unrelated but have you read the book "Zero"? on maths
--- reality is not just described by maths.. but IS reality.. you lost me there
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ChaoticButterfly
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(Original post by lemonlikelime)
You have a physics degree!! Gah!!! In that case you're far better equipped to think about these questions than me lol I had no idea
Not really

It's like quantum physics. No one really knows what the wave function actually means, but we know how to use it to do stuff. Let the philosophers worry about that. Same goes with these sorts of questions.

Nope I've not read that. I should read more maths pop books
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oShahpo
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retro_turtles
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oh no Jaden Smith
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lemonlikelime
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(Original post by ChaoticButterfly)
Not really

It's like quantum physics. No one really knows what the wave function actually means, but we know how to use it to do stuff. Let the philosophers worry about that. Same goes with these sorts of questions.

Nope I've not read that. I should read more maths pop books
Hmm but with things like wave function - surely you have to have an understanding of something before you can really use it to its full potential?
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