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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.


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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.


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.


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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.cockshottCockshott


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.slavojSlavoj


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=2eurekaEureka


>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?


an invented imperfect mirror of reality that seeks to be a discovered perfect mirror of reality. same thing with science as a whole.


Is it possible that math is partially 'real'? Some basic facts described by math seem to be 100% real (there is one not two suns in our solarsystem) while other concepts like infinity appear to be not real.


It was invented to describe reality.


I don't care


Invented but emergent from a very simple proposition that things can be counted. All mathematics depends on a set theory to describe what a number is, and from that the propositions of doing things with math like functions must follow those principles. You can of course invent a concept that didn't "naturally" exist, like a factorial or imaginary number (it's literally in the name that it isn't a "real" number and had to be invented, basically saying "you can't take the square root of a negative number, but what if you could?").

Newton and Leibniz were answering problems that already existed in mathematical proofs, and the need of a language to solve the problem of an infinitesimal. This isn't as automatic as you might think, if thinking about all the implications.

But no, there isn't a metaphysical hobgoblin "running the world on math" to determine how reality will unfold. That's always been nonsense in any serious view of reality. The first proposition, before you can even count something, is to acknowledge that such a thing exists, which is a whole other philosophical question. The set theory arises from noting that you can propose one thing, and another of the same thing, and consider them grouped together, and so on. It's a lot harder to say that multiples of some thing can't exist because reasons, than it is to accept that you can count things. It's actually an issue in some really primitive languages that don't have words for numbers, or only count so high, but it is not an insurmountable one. Native sense will tell us that there are many potential instances of some object, regardless of whether we have a numbering system or if we sense all of them in our space, however large we define it. The concept of "adding" or "multiplying" though is not written as an opcode in nature itself. It is an algorithm we carry out for our purposes in problem-solving, rather than the universe itself working out how many are in this group of things that we defined. The proposition of some stable system of matter, for example a ball comprised of so many atoms, is not contingent on a number of atoms simply comprising the ball, but some characteristics of the system as a whole. This is part of what led to a systems theory, to better describe these objects, particularly living objects.


Suppose mathematical abstract entities were real. Now suppose they vanished one day - what differences would we notice? They don’t have any causal powers, so when someone went about counting objects, they would carry out the same behavior and cognition as they did before numbers disappeared. If they took one thing, and another thing, they would come to the conclusion that they had “two things,” exactly like before.

In other words, viewing mathematics as “real” means multiplying entities beyond what is necessary, and therefore by Occam’s Razor, should be avoided.


Saying something is merely inelegant is missing the point. When we define objects casually, we're really substitute a lot of propositions about basic qualities of the thing, and we must in the end have some framework in which all of the objects of the world are related in some way, or can be related. So we have perhaps a very broad class of "physical objects", and then certain kinds of physical objects like fruits, then apples and oranges which have particular characteristics.
Saying "math is real" is nonsensical, because values couldn't exist without a relation to some fact, or some value we are interpreting as a fact in our imagination. It would be nonsensical to even think of numeracy without the assumption that objects can be grouped somehow, and we define characteristics of the group that make the objects part of it. For example, if we allocate a block of memory in a computer program and saying "we have an array of 100 Widgets", we are doing exactly that - the "group" is defined in reality by occupying an area of memory, rather than the declaration that the group simply is.


It was invented to model discoveries.
Math nor science do not show perfect parity with reality (unless you fragment some core ideas like basic arithmetic which is arguably perfectly representative of reality, one+one oranges = two oranges. problem being that this is no longer "math shows perfect parity of the real world" but "parts of math show perfect parity of the real world"), However even if they don't show perfect parity, they seem to do a pretty damn good job and is arguably always improving.


Maths is a toolbox full of tools, and these tools are as physical as a hammer or a pair of pliers. You may not recognize this because you use math tools with your brain instead of your hands. You may be tempted to mistake these physical objects in as immaterial or platonic, but all the information that is stored and processed by brains or calculating machines depend in it's entirety on matter and physical processes.

To make a hammer tool you have to discover in some sense a number of physical properties of matter that are related to mass, velocity, acceleration, force, lever action and impulse, but you also have to invent stuff like how to attach the weight of the hammer to a lever stick, for a modern hammer you need to invent metal production. Maths tools are analogous but because it's mental tools instead of hand tools it's less intuitive. The link between Information and entropy is harder to grasp than "oh look it made a big thud"


Discovered. Math exists, all mathematics that are done are in some way or form a deciphering of the 'language' of the universe into concrete numerical or equational form.


sry, or oranges are already fake as fuck, see this highly underrated comment (not mine, just based and noumenon pilled):


the question isn't very interesting. there isn't very much practical difference between invention and discovery in the first place. to invent and to discover are both to unveil something novel. it's why european settlers refer to things like "the discovery of america" which just as well be described as the invention of colonial states in the western hemisphere. was deep sea navigation discovered or invented? the astrolabe was invented, but doesn't work if you haven't discovered the relationship between sun declination and latitude.


Mathematics is an expression of truth. If you look at the various branches of pure mathematics, many don’t even remotely resemble what you probably had in mind (high school algebra or the basic college curriculum of calculus and linear algebra). Mathematics is similar to a programming language. You have some set of primitives, some set of operations you can perform, and from there you begin to derive the consequences of the operations you’ve defined. I guess you could say in that sense that mathematics is “invented” or “contrived”. Whether it is “real” or not depends entire on whether the system you have defined is useful for solving any real problems. Like if I define a logic about Barbie dolls, I define what properties Barbie has, what operations I can perform on her (brush her hair or undress her), etc… with a little effort we can make such a logic self consistent and valid. You obviously realize immediately that we probably can’t gain any useful or meaningful knowledge from that, so is it real math or not? I don’t see why not.


I just realized what point I was trying to make. Mathematics is obviously invented. It is just a framework within which you can systematize your reasoning about a given question or problem. However, the conclusions you derive from within that framework are discoveries. So a given branch of mathematics or logic is just a method for making discoveries.


math is invented. to say that math is "discovered" is idealism

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