[ overboard / sfw / alt / cytube] [ leftypol / b / WRK / hobby / tech / edu / ga / ent / 777 / posad / i / a / R9K / dead ] [ meta ]

/edu/ - Education

Learn, learn, and learn!
Tor Only

Password (For file deletion.)

Matrix   IRC Chat   Mumble   Telegram   Discord

File: 1608528174046.png ( 268.29 KB , 1178x732 , 854a2e112976b7e92a52a193e6….png )


Is mathematics invented, discovered or both?


grug think counting bad


The symbols and methods of it have been invented and vary between times and places, much like conventional language, but the abstract rules and patterns of nature it was initially crafted to describe have been discovered.


Discovered. That is how Leibniz and Newton both came up with calculus, separately.


File: 1608528174680.png ( 275.37 KB , 900x900 , stop doing maths.png )

People independently (re)invent things all the time. I doubt this is because there's some spooky Absolute Knowledge that exists independently of humankind and can be "discovered". A much more likely explanation is that humans simply think alike.


why does this board attract the biggest /x/fags


In what manner does this have anything to do with conspiracies?


Cockshott has a video lecture on the origin of math.

TLDR: Math is a tool for solving problems, it is no different from a plow or tractor.


As a math-fag I used to believe that it was discovered largely. And I suppose you can take this stance, since the variables that determine the nature of the universe dictate that plants could exist, and then that plant would have the property that it could be grown in masses and be soft enough to cut, therefore farming was 'discovered' but I feel this is a bit sneaky. Like >>2348 said I don't really think we should view it any different to tools and therefore would be invented, like the sickle is invented, even though metal and plants always existed with the possibility of combining the two to cause a reaction in our world.


Mathematical knowledge is a tool invented by observing the mathematical process in nature.


If you are a materialist, then math is absolutely discovered. It is insane to think that aliens would have a math system where 2+2 is not 4.
Mathematical rules are objectal. They are real, objective, but not material. The same way the meaning of the word remains the same no matter who reads it or the number of rocks is independent of the viewer.
This is the reason why universe can be described in the mathematical languge, because math is discovered from the nature.


There is no Absolute Knowledge in a objective idealistic way, but there are concepts, that are independent of one's mind. How come we all know what a dog is? Why can we understand this word at all if everyone creates their own "dogness"?
If there are no universal concepts hidden in the words form then there is no reason why exchange of ideas is possible.


Do you know what a dog is? Mathematics is based on a social consensus just like the exact meaning of dog is.

Bringing up basic arithmetic as representative of the whole of mathematics only showcases your own ignorance.


> The same way the meaning of the word remains the same no matter who reads it
Try talking to anclaps sometimes.


There is no fundamental difference between them.
Unless you think that alien mathematics has triangles on the plane with sum of angles of 360 degrees.


"Social consensus" defines the form of the concept, not its content.
A clearer example would be "mass". You cannot feel mass itself, cannot describe it, yet everyone who can understand what mass is.
We do not just find similarities in objects and name them accordingly. We find the universalities that are hidden inside particulars and name these universalities.


You keep brining up these middle schooler examples but what about the Curry-Howard isomorphism? Or just infinitesimals?


It does define the context. Taxinomies change and with them changes what a dog actually is.


I would ask you, is evolutionary biology invented or discovered.


Everything in math is derived from the axioms which stem from reality. The same goes for infinitesimals.
I gave simple examples precisely because it is simple to see how they are connected to objective world. I do not understand how can you say that mathematics is absolutely created by humans. Do you think that before the rules of mathematics were "created" it was untrue that prime numbers are infinite or that there are only three linear independent vectors in a euclidian space?


No. Dog is a dog. You can create a word for another concept which intersects with a concept of dog or includes it.


File: 1608528179526.png ( 20.87 KB , 750x108 , Screenshot 2020-08-03 at 1….png )

Why would they necessarily even compose 2+2=4? This seems very intuitive and obvious to you, does pic related seem obvious to you? It is insane to think that aliens would have a math system where the line integral over a positively oriented, piecewise smooth, simple closed curve in a plane of functions L and M equal the double integral over the plane region bounded by the curve!

Why would aliens not use different axioms that also have some approximation to reality that we may not see? 2+2 may equal 4 in this alien mathematic but it may be a complex theorem as opposed to a basic result.

A plant always held the characteristics of being able to grown in groups, and soft flesh easy to cut, and yummy to humans, so was farming discovered, or invented? Spacetime always held the property of masses attracting each other, but is our 'finding' this discovery, or is our (not necessarily true) analysis of this phenomenon an invention? The same way two 'separate' objects always could be grouped to find 2 of them to get the sum 1+1=2.


That's a really nice idealist view of mathematics. The reality is that there are multiple sets of conflicting axioms and what you can prove depends on which ones you start with. There's a good reason most of mathematics was never formalized. Even today, the validity of proofs is based on consensus.


Consensus of what exactly? How is mathematics “not formalized”? Are Euclid’s postulates not a formalization?


this is just talking about CS though, not math.


Math is riddled with platonists and science is riddled with scientism and brainlets. Pop scientists are somehow many times worse.

Here's a hot take though. Math is a set of games with different axioms and rules. Philosophy is the same, a game of words, except with informal logic and words.


It was written for CS researchers but is is about proving things in mathematics. Just read it, it's short and easy to understand.


File: 1608528180295.gif ( 2.65 MB , 420x420 , 1572613661184.gif )

invented. it has no objective basis in reality. it's simply an abstract mental construct used to describe reality.


I can't believe this thread is still on the board. Let me bump it, edubros, so we can get some fresh answers.


Inventions are discovered. These are the same.


>why does this board attract the biggest /x/fags
>foundation crisis of mathematics is /x/ tier
The issue here is that it ignore what math has been historically, which is a "reflection" of reality.
We originally intuited mathematics, based on abstractions of the real world. Math got more and more complicated as technology did the same. Eventually it became entirely it's own thing, for itself. It also became increasingly formalized and axiomatized. This eventually made it into a sort of "game" of axiomatic principles, and things are discovered in the system.

So math was developed intuitively, then became a thing for itself and became foramlist and axiomatic. A game of axioms. Things were invented and discovered then and still are. Math doesn't exist "in reality".


Cockshott uploaded a recent video regarding this. Let me find it…
Food for thought comrades.


there are no numbers of anything "independent of the viewer". breaking objects up into quantities that can even be added in the first place is relies on Understanding. you can break things up infinitesimally, there is no universal objective guarantee of where to draw the line.


but then what guarantees that we see the same number of apples on my desk? couldn't we say that Number is but numbers are not outside of the mind?


>If you are a materialist, then math is absolutely discovered. It is insane to think that aliens would have a math system where 2+2 is not 4.

Some uyghas ain't aware if non-well ordered sets…


File: 1622694781784.png ( 107.85 KB , 1706x728 , principia.png )

>362 pages to prove 1+1=2


>principia matematica
Is that the book that gives your virginity back


Mathematical Platonism was refuted.
Post rem structuralism is probably correct.


Can you explain to us uneducated what this means?

Unique IPs: 12

[Return][Catalog][Top][Home][Post a Reply]
Delete Post [ ]
[ overboard / sfw / alt / cytube] [ leftypol / b / WRK / hobby / tech / edu / ga / ent / 777 / posad / i / a / R9K / dead ] [ meta ]