Is mathematics invented or discovered?

Is mathematics invented or discovered?

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Kind of both, it depends on whether you view the axioms we use as "natural" in a certain sense, it is discovered from the axioms, but those you could say are invented(AC especially).

I'm gonna say invented

Numbers just kinda happen if you pay attention.

is this guy as epic as he is made out to be? he seems uber pretentious

Neither, it's made up.

Inventing is discovering things from the set of inventable things.

Discovered, obviously.
>brainlets think that PI didn't exist before humans thought about it

brainlets even think that pi doesn't exist period because it's not rational

...

this
fucking brainlets

thing is, set like this doesn't really exist

Is the set of inventable things discovered or invented? In other words, does the set of invented things contains itself?

I would say that applied mathematics was mostly if not entirely discovered. We just played with numbers and discovered formulas that happen to work in specific situations.

As for mathematics in the sense of what we see written, it is just symbols invented to describe how something works or to describe a property, or an operation.
For example, when you write a differential equation that describes a system, you solve it by discovering a solution. The system operated under this solution even before you existed. You simply discovered how it works.
The differential equation itself is just describing what the system is doing and thus is inherently discovered and not invented.
In contrast, the definition of symbols or words to describe mathematical operations or phenomenon is invented. If it were the Chinese who were the innovators in the field of mathematics and had more influence worldwide, we would be using Chinese characters in maths.

A set is always contained in itself, brainlet

If the sum of the squares of the two sides of a triangle are equal to the square of the remaining side, then that triangle has a right angle.

Pythagoras died and it didn't stop being true, if the earth was vaporised it wouldn't stop being true, it was true before the first replicating cell existed on this planet.

Maths is discovered, all we invent is a way to interpret it.

...

that's a class not a set

I'd say "discovered".
"7" was a prime before anyone worked that out; Even before "primes" were defined.
Just as the laws of thermodynamics were true before they were written down.
"Invention", to me, implies the creation of something new, which didn't exist before. The telephone is an invention. No one "discovered" telephones.

The "invent" argument comes from the fact that numbers are abstractions. You can't point to the concept of "seven-ness", only to an example of seven objects. Newton's laws are equally abstract. The Solar System is a concrete example of them in action, but the laws themselves aren't physical.

We "invent" proofs, but "discover" the properties of number, fields, rings, etc.

What user meant is: does the set of inventable things belong (as an element) to the set of inventable things? Sets S with the property that 'S belongs to S as an element' are usually autoreferential and thus not well defined.

invented

concepts like "7" don't just exist independently, they're in your mind

You could say everything is discovered. Shakespeare just discovered the combination of letters that made hamlet. It's a tough one

No there is unironically a perfect platonic realm where numbers exist that we use our spirit to unravel. You're trapped in the materialist coil that the Demiurge has built around you, set yourself free.

Count Mathula, winner of Fields medal.

>I am suddenly given the delightful mental image of Villani counting "a-ONE! a-TWO! a-THREE! AH-AH-AH! to Bert and Ernie

Why does he wear the spider?

He wants to have a calling-card; an eccentric affectation that he and he alone is known for.

It's his way of being a fop. I am happy that there is at least one fop left in this world.

He's like a French Bill Nye, but with a Fields Medal and he also likes anime.
He's both epic and pretentious.

Because that guy is so much of a weeb that he dresses like an anime villain.

Now he's also a politician and still always looks like he's at a fucking anime convention.

fop?

that's a crab

Numbers are equivalence classes. You can concretely tell when two group of objects have the same quantity of individuals, even without numbers. "Seven" is just a name you use to describe a set that has "this many" objects

why does that motherfucker dress like the berries and cream guy?

also we invent the axioms and then discover their implications

>>He wants to have a calling-card; an eccentric affectation that he and he alone is known for.
that's how we ended up with fedora-wearing nerds. if there's so little interesting and memorable about you that you resort to fashion affectations then you need to just stop trying.

>sum
>squares
>two
>sides
>triangle
>equal
>square
>right angle
These things have to be defined first, and for the abstract stuff like equality, a definition has to be invented. So like a previous poster said, I feel the foundations are invented while the rest is discovered.

Math is invented as a product of human mind. However, it approximates the real, divine structure of nature. So it is not fully made up.

by the definition, "the abstract science of number, quantity, and space"
it was clearly discovered, you autists. the concept of numbers existed way before we humans claimed it

Platonists say that, but not all mathematicians are Platonists.

As I see it we invent structures and discover things about those structures. Like most philosophical questions however it comes down to a question of semantics (thanks based Wittgenstein) and the answer depends on how you define 'invent', 'discover' and 'mathematics'.

I like this interpretation.

there's a difference between inventing something and just giving a name to something that already exists.

does a triangle exist if you don't construct it using axioms and whatnot?

You are dumb. It's more fun when he actually is a person of merit, and he knows it (French politician, celebrated mathematician), and he adds on top of that his own little branding.

The difference between the fat fedora and another eccentric is that the fat fedora is held in contempt because he doesn't have anything real behind himself, and is also fat (being fat is almost never cool), while an eccentric with real cred gets to be an eccentric with real cred and it's cool.

Its roughly the same princple as "an attractve guy can do goofy shit and it's okay, but some fat random guy just looks stupid doing the same thing." It operates on pre-selection, social proofing, aesthetics etc.

No it isn't an invent-able thing so it can't be contained within the set. It is discovered as part of the set of all possible discoveries which includes the set of all possible inventions. The last discovered member of the set of all possible discoveries is the entire set of all possible discoveries.

invented because you brainlets have to put scales and limitations on everything that you cannot comprehend.

m.youtube.com/watch?v=vwObck9twes

>It's another "we only use X percent of our brain" movie.
Why do they keep getting away with this?

Discovered, but the notation and specific topics we choose to focus on and group together is invented.

> Platonists
> Nominalists
A R I S T O T L E
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if we found the right answer for this question, would it impact how and why we do math research?

>is a spook invented or discovered?

its invented obviously

/thread

how do numbers exist outside of pixels and electro-magnetic radiation? if matter is always primary or force or energy, then how do maths exist at all outside of human nervous systems? am i missing something you’re all privy to thay laymen are not? correct me if i’m wrong here, it sounds like you’re trying to allude to platonic forms.

Well to answer, I must first ask you : is any science discovered ? Like, do you believe that we discover physical laws or invent them ?

Let's say you don't believe that any science is discovered, then I will ask you : can anything be "discovered" ? We first have to define "discover". Discovering, in our context, is having a grasp of something for the first time ever. This means that no other human being before had seen it this close, had understand how "what is under" stands. But the one who discovers reckons he's not the author of it : he didn't created it himself, it was here before him.

Then, I will ask you : what was beforehand, the universe or the man ? Of course, you'll answer : the universe was there before the man. There were chemicals reactions, galaxy coliding and stuff like that. This means that, for example, physical reactions existed before the man. Thus, the man didn't invented physical reactions. He discovered them by looking into details of what was happening around him, by experimenting and understanding underlying principles that preceeded him. And he described them using tools that he invented. This means that at least some science can be discovered.

Now that we both believe and understand that physical laws are discovered, let's apply the same reasoning for maths. We observe some stuff in reality : when I put a stone and a stone next together, there seems to be "more" stones than before. We then deduct a measure, that we'll call "quantity", and a principle : "putting stuff and stuff makes two stuffs". Through trial and error, we deduct some useful rules that apply to this measure "quantity" and we invent easy notations for it (numbers). This means that mathematic truths are discovered as well as physical laws, but we invent tools to manipulate them.


Feel free to attack me on my premises (eg : I assumed that we have a way to know that stuff exist before us, that "understanding" is universal), but you'll have to get pretty deep bro

What if math is neither invented or discovered but rather is derived.

Wtf is wrong with their chins? They look almost like the Bogdanoffs

t.brainlet

there is no difference

Seems the real question is whether there is some platonic existence of concepts or not

Hey that's Bertrand Russell's life work you're shitting on by saying that.

mathematics is discovered
notation is invented

I had the pleasure of listening to his lecture live. There were some problems with translation (he lectured in French) and he did q&a afterwards. He handled the problems and delays with patience and dignity (and he didn't have to, some organisation was really lacking), and was also extremely patient with q&a. He's an educator tho, it seemed that he really wanted to hear from younger people and students, and seemed a bit annoyed that older people asked almost all the questions. Also, he spoke english in q&a so the translators could rest as he saw they were having troubles with even the most basic scientific terms, and was very humble about his English skilk even tho they were awesome for a Fenchie.
His only sin is a spider and weird appearence, which he obviously does as a trademark. Wants to raise some eyebrows. And yes, he seemed tad bit arrogant, but really nothing you wouldnt expect from a PhD, let alone a Fields' medalist.

No

Pointless question that is a matter of definition.

as a subset, not as an element

definitions are invented, theorems are discovered. e.g. the fundamental theorem of calculus was discovered, but you can't say that the riemann integral was discovered. it's just a tool developed for computing volumes. lebesgue invented another tool for the same purpose and his tool was better so we sticked with it.

>It's more fun when he actually is a person of merit
if he's a person of merit he shouldn't need the affectations to be memorable

Discovered. If it would be invented, there should be some basis behind.

Does it matter?

would this actually work (if you aimed to the side at first obviously)?

If you've seen interviews with him you'll find out that he actually has a ton of spider ornaments that he wears, some of them custom made, I don't think he wears them just stand out or have a calling card, he seems to just genuinely enjoy wearing spiders. He also seems pretty Veeky Forums in general, much to the contrary of most mathematicians.

Yeah of course.

Which anime though?

Black Jack is his favorite manga.

>Black Jack is his favorite manga.
>Look this up
>It's actually true
And suddenly I have a new favorite mathematician

If I took it off, would he die?

It would be extremely unfashionable
A little surprised he isn't a Jojo's fag considering the author's fascination with fashion.

you're a big guy

What kind of a politician is he?
I remember him from Numberphile. Pretty chill dude.

4u

I think those categories are only mutually exclusive if you define them to be. Sad.

>some guys really believe in a magical realm where mathematical concepts exist.

Invented. Math is and always has been a relatively modern social construct. Cavemen weren’t calculating derivatives or writing proofs.

Cavemen also weren't observing other galaxies and didn't know what atoms were. Are space and particles inventions?

>dresses like an anime villain
Don't you mean, "dresses like an anime villani"? I'll see myself out.

Invented, unless we copied from aliens.

>is and always has been a relatively modern
>and always has been
such redundancies bother me

This guy looks like he's starring in a Doctor Who fanfilm.