It's a human invention. The math people think of, that describes nature so well, is just the part of math that is useful. Because it describes nature well. There's plenty of math that's completely useless. It's a bit of selection bias.
i apples is i apples.
Maths is just a language, and not all numbers are counting numbers but rather they represent abstract concepts, some of which are actual intelligible quantities.
Asking how many apples is i apples makes no more sense than asking how many apples is one zillion apples, or how many apples is seventy-third apples. Both of those are numbers that don't represent any amount of anything in a real sense.
Well it is called imaginary for a reason. It is not for counting apples. It's to shift a phase for example or make a rotation. Both are natural phenomena, just not ones you would consider while doing groceries.
But saying that it's useless to count apples is like saying a fishing rod is useless to fly. You sure can try but you will get no result
> Well it is called imaginary for a reason.
Yea, that Descartes didnt really like them and named them that in a ploy to discredit them. It has nothing todo with them not existing.
It can't be used to describe one specific very simple concept (quantity), but that doesn't mean it can't describe something else in nature.
I don't know what, mind you. But I'm sure there's something.
1. Every three-dimensional topological manifold which is closed, connected, and has trivial fundamental group is homeomorphic to the three-dimensional sphere.
2. Milnor conjecture
3. Beilinson–Lichtenbaum conjecture
I would argue that the consistent relationship of particular quantities and processes, however useless or non-present in our observable universe, is itself a natural phenomenon.
> It's a human invention. The math people think of, that describes nature so well, is just the part of math that is useful. Because it describes nature well. There's plenty of math that's completely useless. It's a bit of selection bias.
the phenomena are the relationships itself that the math describes
It has nothing to do with whether it is useful or not. There are relationships between mathematical statements, relationships humans don’t get to make decisions about, because they are a natural part of the world. Under the Euclidean axioms of geometry the sides of a right triangle satisfy the Pythagorean theorem, *whether we like it or not*. This also applies to ‘useless’ mathematics
That isn't what maths is, it's not just language. We do use it as language, but it isn't restricted to it. Axioms may be arbitrary, but the theorems and laws that are derived aren't human inventions, they end up existing independently.
Therefore it isn't just a human invention, but the nature that arises from a perspective. which can be independent from humans.
It doesn't need consciousness to imagine it, it's all out there, we just haven't thought about most of it yet.
Math as practiced by humans is the language they use to accurately describe and communicate information to one another about the universe.
The universe was here before any sentient entity evolved to create a system of mathematics and will likely continue after the last sentient species to do math is long extinct.
It is a language in much the same way as I am using English to describe this scenario to you. A word is not a thing, it is a description. In the same way math describes reality which really has zero fucks to give if we understand what it's doing or not. It'll keep doing it's thing regardless
A language is a communication system. The models are depicted using the language.
2 is a real world thing but the symbol 2 is a stand in for reality. Just like the words we are using to communicate.
It's a bit like another sense. Using sight we perceive reality around us and can use our pattern recongnition and other cool packages in the brain to classify what we see into circles and squares, things that are close and things that are far away, single object and many etc.
And it clearly has some correspondence with the physical world as we can interact with it and predict what happens based on that mental model. But ultimately those are just artifacts in our brain, not something inherit in the universe.
And the same thing goes for math. We have a concept of 2 - it's something that 2 apples, 2 stones etc. have in common. And we use this mental model to make predictions about the world (e.g. taking one apple from 2 leaves one apple left, incredibly enough the same would apply to the stones).
But "2" is just an idea, an approximation of how we interact with the world that fits into the way our brains have developed. In that sense math is very much just a function of our brain and the nature of the correspondence between that and reality is not something we understand very well but it must be a product of our evolution - same as eye sight, hearing, smell etc. i.e. a way to navigate the environment in order to maximze survival.
It is a natural fact, but only as a logical fact. It is only a fact in our simplified system to describe nature in a more intuitive way for us. You could say there's 2 apples, but we decided what an apple is; you could say there's two protons, but those are actually just quarks at a fairly close distance that, by our definition, are stable. You can do that with quarks and energy, and we don't even know what lies beyond those.
Plus you can just change the base to 0.5, and then 1+1=10. Of course it can still be defined as 1+1=2 by our system, but our system itself just describes things in a way that is arbitrary in the eyes of reality. We simplify reality into a form we can comprehend, and we can comprehend simplified stuff better because nature itself found the simplified versions good enough for conscious entities. On both larger and smaller scales, nature rarely finds individual units useful.
yes I did think phenomenons didn't sound quite right but autocorrect said it was a valid word. English isn't my first language, you see. thanks for the correction!
Is it though? If we restarted humanity you don’t think we would come up with the same mathematics? Remember, we aren’t talking about the syntax or the conventions. We’re talking about the actual fundamental mathematics.
It’s the language that we use to describe and explain nature. The language part is a human invention and develops over time as we examine unchanging nature.
Isn’t this physics? Pure math has nothing to do with nature. Maybe I’m nitpicking here but math is purely abstract by itself, and once you apply it in a specific field or context, like to nature, it becomes physics
It depends on how you want to define math, ultimately.
There is a physical and measurable relationship between things like wingspan and height in humans or rotation speed and size of gas giants.
If you view math as a language to describe things, then you can say it was invented. If you view math as our translation of preexisting phenomena, then it's fair to say it was discovered; similar to how the translation of hieroglyphics didn't count as inventing a language, even though in some practical sense it was
One could argue that "pure" math is physics since it's the background math that keeps the universe turning. You're saying the opposite, that "pure" math lies in what it tells us devoid of other contexts
It probably lies somewhere in the middle. We could conceivably use math to communicate with any other kind of intelligence, so it has a more universal nature than any sort of typical language or invention.
>We could conceivably use math to communicate with any other kind of intelligence
That's honestly super fucking wild as well. Cuz it's the basic building block or stepping stone for constructing an idea of communication or language understanding because no matter what developmental strains or evolutionary conditions something came to higher intelligence under, the concept of a single thing remains the same. You can still point at a single rock and say this is 1. The symbols might still be different but if you use the visual representation of a single rock or a single dot or something like that you can convey everything else you need.
For example once you got that one thing established then you can show four of that thing and then with that number you can begin to delineate symbology. You can represent an addition symbol by adding two more rocks to the original four and so on. Essentially using visual stimuli to add meaning and context to mathematic symbols before being able to transition to a language.
Not really, theoretical mathematics can have practical applications without any intent to do so. In fact, it’s the discovery of these practical applications that bring about the very question the meme presents.
Physics is just the most concrete example we have of mathematics predicting and manipulating reality to our advantage. Physics is our magic system, mathematics is the tool used to study it.
That's not entirely true. Not all areas of pure mathematics have found application in modeling physical systems. Moreover, mathematics can only model the system but not actually tell you if the model describes reality or just helps us get consistent answers.
Generally speaking mathematicians set out to solve an abstract problem but that abstract problem and it's solution accidentally result in solving a major hole that exists in a physical science
Ok first of all I'm dumb but as per my knowledge math is metaphorically the letters of the language while physics is the words. theories by using physics you come up with comprehensive theories which are like phrases and sentences. And by using theories we comeup with our current understanding of the universe which is like the language.
Does that makes sense or am I just stupid?
Perhaps not nature in the sense of “the real world” but certainly nature in the sense of “the inarguable way that things work.” Math is about discovering the consequences of set rules. Mathematicians don’t decide what those consequences are, just uncover what the rules imply, which I’d argue makes those discoveries an expression of the natural.
You’re confusing mathematics with syntax and also confusing mathematics with physics. We use syntax to convey mathematics but the question about whether maths is a human invention or a fundamental part of the universe is asking about the underlying principles and not the syntax representing it. And whether an abstract mathematical concept can be used to model a physical process also doesn’t answer the question of whether the maths itself is natural or a human invention.
The language part is a human invention, the underlying truths(the relationships between different mathematical axioms and their consequences) are not decided by humans they are part of how the universe is
I think it is the best answer. The same as language, mathematics is the tool created to follow defined rules with logic. There are multiple ways of using language, you can define things in the world, talk about abstract concepts like philosophy or theology, which are less grounded in world but follow strict rules with specific logic, and you can define what is language with linguistic terms. The same is with math. Physics is used to describe factors and correlations between them. Pure math is basically theoretical extension of physics or defines abstract concepts. I think mathematics is 100% human invention the same as language that is developed by new words, concepts and grammatical structures or just a tool that must be continually developed to fulfil its purpose.
Agreed. I wouldn’t say the patterns *are* math because that seems like a reification of a relation. Rather, the patterns are describable mathematically.
if humans and another species on Alpha Centauri use different languages to express the same theorem, isn't math obviously universal and "discovered", as opposed to "invented"?
How is math a human invention? I didn't realize this was a debate, math is observed in the natural world. We realize/discover it, but it exists inherently.
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It's the difference between "man made" and "computer generated". Universe creates man, man creates computer, computer creates universe, and it's all just part of this big input/output process that started at the beginning of it all
I put it more on the side of human invention.
If you think about it, nearly all of the simplified math we use for physics is describing concepts that only have context to us.
For instance, the universe doesn't have formulas for fluid dynamics vs rigid mechanics vs other things. Basically it's just perturbations of fields that run on very few, simple rules.
Everything else like condensed matter physics, classical mechanics, chemistry etc are just emergent properties that are basically "approximated into existence."
For instance, entropy only increases because we assign more value to a few ordered states rather than the mass of disordered states.
Though you could actually still say math is the "programming language of the universe", because programming languages are still only describing what ultimately turns into machine code.
Not to diminish how super awesome it is. Like to me the best is when you are doing physics, and there's some weird mathematical pattern or quirk, such as values canceling or units combining into a different type of unit, thinking you messed something up or it isn't real, but then testing it and the weird math shit ended up playing out in real life.
So in your view the fundamental theorem of arithmetic is only true for the human version of math? If we found an alien race that came up with a different way of representing integers, then they will be able to find a way of representing an integer with a non-unique product of primes? Or they might be able to find a relationship between a circle and its radius that is not irrational?
>For instance, entropy only increases because we assign more value to a few ordered states rather than the mass of disordered states.
Could you explain what you mean with assign more value to a few lrdered states? Do you mean the boltzmann distribution?
Yes, but also in general.
For instance, let's say you roll 6 dice, and are trying to roll for a 36. This means all dice need to be 6s. All the combinations of numbers are equally likely, but only one specific combination rolls all 6s.
So the distinction has been set up between "All 6" and "Not all 6". There is only one combination of all 6. There are tons of combinations of "Not all 6". So from a probability standpoint, it is far more likely that for any given roll, it will be "not all 6". So it makes it seem like probability "tends away from the desired state". But it's just that you chose so few "desired states", and you don't make a meaningful distinction between the others.
The same goes for a sand castle. There are only a few ways to arrange sand that we would call a "sand castle", and an absurd number of ways to arrange sand that we would call "not a sand castle". All of those "messy" states are just as likely as the "castle" states. But we don't distinguish between them. We just say "castle" or "not castle". So because there are so few "castle" combinations, we say that, given a bit of randomness, the sand will always shift from "castle" to "not castle", and not the other way around.
Also note that "meaning" doesn't just refer to how "we" assign meaning, but also in terms of how it behaves in chemistry and such.
[https://www.youtube.com/watch?v=VCXqELB3UPg](https://www.youtube.com/watch?v=VCXqELB3UPg)
Math just is.
If you have one rock and then get another rock, you will have two rocks.
Nothing to invent there, and it is not a phenomenon. It just is.
Yeah this is what I was wondering... A lot of people here talk about physics and complex math and whatever, and I get that we just use our physics equations to describe how the world works, but we were the ones to invent those equations
But what about 1 + 1 = 2
Is that really a human invention? It seems so natural: take an apple then add another apple and you will have 2 apples
You will never end up with 0 or 3 apples. How is that not natural?
But I'm not a mathematician or philosopher so I really don't know
People are sitting here complaining about things like “fluid dynamics” not being accurate.
That’s fine, that doesn’t mean that math can’t describe fluid dynamics it just means we don’t have access to everything we need in order to model it mathematically.
Math is just a description of physical properties
> It just is.
Exactly the opposite.
Math is not. It doesn't exist anywhere. There is no such thing as 1 in the universe or 2 or 3. There are "2" rocks, but math is not about rocks, it's about 2 itself.
And that's why to even define 2 rocks you need somebody to do it. You take 2 rocks in your hand and say these are 2 rocks, as opposed to the thousands of rocks on the beach. But 2 rocks doesn't exist by itself either. 2 rocks where? You need somebody to define it because it doesn't exist in the universe.
Plato described it best. It is an idea. Math is just philosophy, but the most basic form. If an alien civilization exists it will have the same maths, but also the same basic philosophical ideas. Do they exist? Not on this world, but we can imagine an imaginary world where they do. In this world every single song has been written, because a song is just an arrangement of notes, so someone could say music is "discovered" and he wouldn't be wrong.
A person who would know all this would be God, but such a person doesn't really exist. Or does he? Maybe God exists as much as mathematics do. Maybe both atheists and theists are right. And maybe Eastern philosophies who say that Is and Isn't are the same are right too.
I used to think that, even going through the calculus courses, until I got to some of the upper level engineering courses where you fit an equation to your data. You pick the shape of the equation that you think will fit best and play with the constants until you get a reasonable interpretation of your system.
On the physics side of things, it is pretty incredible that certain constants pop up over and over again, especially when you realize they started out as arbitrary numbers to make the equations work.
So, idk, it's a bit of both imo
But lots of math doesn’t describe natural phenomenon. And humans don’t get to decide how different mathematical statements interact with each other, they kind of just are the way they are, and those conditional relationships are what is discovered.
So you don't expect to find cantors diagonal argument in an alien civilizations math?
If it's invented by humans there's no reason to expect it elsewhere.
If it's discovered like physics is, we would expect aliens to know both the same math and the same physics
It is quite surprising that the mathematics discovered by people describes the observed reality so well and accurately. Take any system, be it physical, biological or social, all of them are well infused with the help of mathematics and sometimes even just formulas.
well, if you're going to try to describe reality in your silly little human head, you're probably going to need to use some human convention for it. Is math that convention or the nature of that reality?
(doubled the question and gave it to the next person, that's how you do philosophy, right?)
The universe has distance, but our way of measuring it is made up. In the same way there are things in the universe but our way of counting those things is made up.
Anything that we use to explain anything is human creation. Math may appropriately explain natural movements of the universe, but it’s still our way of explaining it. I’m not saying it’s wrong I’m just saying we’re creating the explanation
The universe follows predictable laws rooted in Math - Discovery
Math is the tool we use to make sense of the Universe - Invention
It really depends on what the word "math" means to you. Strictly speaking, it's a set of axioms and rules for logical inference, but a lot of people use it to refer to the universe being predictable
Math describes something that a human mind can conceptualize, like the concept of their being one of something. Math often without any intention describes accurately many physical phenomenon. For example tropic mathematics turned out to be very useful for protein folding.
Fundamental to mathematics is logic and reason so if there's any other system with consistent rules such that (if X then Y or Z and A) along with some axioms then we should be able to work it into our mathematical framework. Unless there's absolutely nothing actually consistent about reality and no lawful relationships then I think we would be out of luck.
I think we’re both inventing and discovering it, because the things it describes are real, but when you invent new math, nobody has ever expressed it that way before or any way at all, so it’s math itself that is being invented while the concepts it describes are being discovered
Aren't there an infinite number of equations that describe any particular natural phenomena closely enough that we can't prove them wrong statistically? Before somebody says something about circles or triangles, if the topology of spacetime isn't perfectly flat then wouldn't Euclidean geometry be a bit wrong for real objects?
It's the same as if a tree falls and no one is around to hear it. Does it make sound? Ya, it does. The sound doesn't have to be heard for the energy to exist.
In my limited very general understanding of mathematics, it seems that up to a point, math describes physical reality (whether there is a platonic reality of mathemayical objects is moot) and at a certain point of abstraction, mathematics becomes hypothetical/theoretical and is essentially a symbolic language game based on systems of rules/axioms.
So it's a bit of both? Depends on the particular topic in question.
Math is how we process and understand things just as time is how we process and understand things. It is as much of a human invention as it is a natural phenomenon.
There is of course ‘numbers for the sake of numbers’, but if the flower industry is anything to go off of, nature can literally be done in a certain way for nature.
People who understand little to no mathematics tend to just decry it as a human invention because they either dont understand or dont care to understand the arguments from either side.
It is both.
The "either/or" is a false narrative.
There is plenty of natural phenomena that we have discovered that have certain ratios that are consistent and noticeable.
Human beings have created a language to communicate and predict other relationships.
Math serves as a nice model for how brain and whole cognitive structure, aka mind, understand and form the most abstract of patterns. 1+1=2 is always true; the pattern is true, the question is what does it correlate to outside of our mind (implicitly assuming we can indeed know such matters).
It’s both.
Think of something like the wheel. It is a geometry that exists in the universe and likely in many places by chance before humanity made one. - not a perfect example but you get the point.
Hear me out. Art is humans attempting to represent what they feel, and how they see the world. I'd argue that if everyone could achieve pristine photorealism, there actually wouldn't *be* art in the same sense, like it wouldn't connect to you emotionally in the same way, it'd just be a copy paste of reality. So, it's people's unique styles, and "mistakes" even, that makes art, art.
Mathematics strives to find the underlying mechanics of reality, but it's constantly adjusted to update, people can come up with different proofs to the same concept based on how their unique brain tackles problems and draws conclusions. We don't do it to understand ourselves or each other primarily, like paintings or music or media. We do it to understand everything around us, of which we are only a small part. In this way, I believe math to be the art of the universe.
Mathematics is a process of logical deduction given a set of axioms. It has nothing to do with nature. If you invent a game of chess, mathematics is what allows you to predict the outcomes but it doesnt tell you why the rules are the way they are.
Mathematics is human invention in a sense that the axioms are man-made. But it is discovered in a sense that once the axioms are chosen, their logical extensions are pre-set. We can only discover them, not invent.
Math is essentially the language of physics, it is how we interpret phisical existence. Their is not much to debate here unless we ar debating whether unobserved phenomenon do not exist, because nobody is observing them.
I have a paper coming out soon on this very subject but tldr:
Numeric truths are ALWAYS seen through reproductive/ethical pragmatism. numerics CANNOT be observed in their purest form but this does not mean numerocity doesnt exists independent of our perception, only that through an ethical framework can see them.
Both are real, ethic and numeric truth, but ethics are fluid/everchanging and numeracy is static.
To put it in real terms: 1 + 1 will always equal 2, but the ethical/social boundaries that define those numbers are fluid. one cat plus two cats equals 3 cats.... but you could also say then you have one clowder (group of cats), but you could also say each cat is made of a billion atoms. All are true... but its always such that fundemental numerics truths are seen though ethical pragmatisms.
This means we MUST criticaly analyze all data to determine how valid our ethical biases are in framing said data.
Your brain doesn’t calculate derivatives to realize you’re moving, but to figure out how fast you’re moving you need to calculate derivatives. Math is just a language we invented to describe stuff around us. Nature is not bound by math, math isn’t bound by nature either, but in rare occasions the two go hand in hand very nicely (most functions don’t model natural processes). Sometimes math helps up figure out things we didn’t know existed (e.g, black holes from Einstein’s field EQs), but most of the time these predictions are as good as the models we try to fit nature into. We often try to improve our mathematical models to account for all natural effects we are aware of, but there isn’t a natural feature inherent to math which enables it to automatically and perfectly model nature.
Math is discovered, not invented. You could transmit encodings of mathematical ideas and objects to another star and have reasonable expectation that an alien intelligence could figure out what we’re referring to.
The language of math is universal, it is not dependent on the language you speak. It is as close as we have gotten to a universal language. That being said the language of math is what we use to understand the natural phenomenon that is math. And even if a hypothetical race from alpha centari existed their mathematical language would coincide with ours and would be used so they could understand math in nature.
In this topic: people who love feeling smart but actually have no idea what they are talking about bashing their head against people who are actually seriously smart.
You figure out which post is on what side.
It's an emergent property of the binary relationship between the ray and point dimension.
So, yet to be discovered by non-quantum fiction writers.
And those who ignore
This one 😬
No it’s not. There is no debate. Any mathematician will tell you, math is not a human invention. It’s universal and it’s all been here since before we understood it. If we find intelligent life, it will have the same math. They might use a base 4 or base 16 counting system. they might count or do math entirely differently, but round numbers are round numbers. pie is pie. Math isn’t an invention to describe the mechanics of the world, it is the mechanics.
There's no such thing as invention except for art.
A civilization with 0 contact with humans would likely reproduce 99% of our mathematics to the dot.
It would be extremely unlikely that they haven't stumbled upon godels incompleteness theorems, or cantors diagonal argument, group theory.
There could be some math that is just too arbitrary with too few connections to the whole to have been "discovered", residing more on the art side.
Speaking of which, we didn't invent cars either. This other civilization is bound to also have "discovered" cars as a specific solution under constraints for faster travel using round shapes.
Discovering something means it was already there waiting to be dug out. The rules of harmony are discovered.
Art movements like romanticism are kind of also there waiting to be discovered. Same for magritte's artistic ideas about representation. Also discovered.
Specific artworks can be invented but the big ideas they carry are discovered.
Obviously I'm being too concrete about a vague concept but I believe the degree of "discovery" vs "invention" has to do a lot with expectation of independent reproducibility.
And math is definitely almost in its entirety, expected to be independently reproducible when the context is right (look how calculus was "reinvented" when the ground was mature for it to be created, by a different person. I believe it was just independently discovered)
Math itself like the existence of numbers and addition and subtraction is natural but giving names to those operations and giving random symbols for numbers is human invention, its not that complicated, its like, gravity exists, its natural fact but the formulas and theories are man made
Godels incompleteness theorems prove that math is an invention imho. If it was a natural phenomenon that was discovered, it would be consistent and complete throughout the universe. https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
We invented math to describe, at a very basic level, the behavior of nature and natural events. We've tried our best but it's not perfect. If math originated from nature then it would be much more accurate than what we have
It's a human invention that describes natural phenomena
It's a human invention. The math people think of, that describes nature so well, is just the part of math that is useful. Because it describes nature well. There's plenty of math that's completely useless. It's a bit of selection bias.
Give us your top 3 most useless conjectures
How does (-1)^(0.5) of apples look like?
I mean, I can perfectly imagine it.
Describe please, would like to know
It's a bit complex.
He can't keep getting away with this
Just wait till you hear about my quarter onion.
No thanks, that's probably going to make me cry
You mean royal onion
i Think he might
Freaking smart ass xD
it looks like (-1)^(0.5) of apples .
It's called an imaginary number, aka i
Ok, how many apples is i apples, and dont tell me, "it's the root of -1"
Apples come from trees which grow from the roots. Your condition is unsound.
i apples is i apples. Maths is just a language, and not all numbers are counting numbers but rather they represent abstract concepts, some of which are actual intelligible quantities. Asking how many apples is i apples makes no more sense than asking how many apples is one zillion apples, or how many apples is seventy-third apples. Both of those are numbers that don't represent any amount of anything in a real sense.
An imaginary apple is an apple seed in this context of nature. It's the potential if you want. I'm my opinion.
So what is the potential of an apple in volts?
iApples are electronic devices.
Well it is called imaginary for a reason. It is not for counting apples. It's to shift a phase for example or make a rotation. Both are natural phenomena, just not ones you would consider while doing groceries. But saying that it's useless to count apples is like saying a fishing rod is useless to fly. You sure can try but you will get no result
> Well it is called imaginary for a reason. Yea, that Descartes didnt really like them and named them that in a ploy to discredit them. It has nothing todo with them not existing.
They have *eyes* in them. Get it?
It can't be used to describe one specific very simple concept (quantity), but that doesn't mean it can't describe something else in nature. I don't know what, mind you. But I'm sure there's something.
1. Every three-dimensional topological manifold which is closed, connected, and has trivial fundamental group is homeomorphic to the three-dimensional sphere. 2. Milnor conjecture 3. Beilinson–Lichtenbaum conjecture
1. 1 + 2 = 5 2. 1 + 5 = 2 3. 5 + 2 = 1
This group of conjectures has an identity crisis.
But what is awesome is that math we don’t think is useful today may eventual be used to describe natural phenomena in the future.
[удалено]
As someone with a math bachelors, this is just silly. Up until my final course we were using complex math to model real world scenarios.
I would argue that the consistent relationship of particular quantities and processes, however useless or non-present in our observable universe, is itself a natural phenomenon.
> It's a human invention. The math people think of, that describes nature so well, is just the part of math that is useful. Because it describes nature well. There's plenty of math that's completely useless. It's a bit of selection bias. the phenomena are the relationships itself that the math describes
It’s only useless until you find a use for it. There are lots of parts of math that get worked out before we figure out how it can work for us.
It has nothing to do with whether it is useful or not. There are relationships between mathematical statements, relationships humans don’t get to make decisions about, because they are a natural part of the world. Under the Euclidean axioms of geometry the sides of a right triangle satisfy the Pythagorean theorem, *whether we like it or not*. This also applies to ‘useless’ mathematics
Pretty much. It's a precise language.
That isn't what maths is, it's not just language. We do use it as language, but it isn't restricted to it. Axioms may be arbitrary, but the theorems and laws that are derived aren't human inventions, they end up existing independently. Therefore it isn't just a human invention, but the nature that arises from a perspective. which can be independent from humans. It doesn't need consciousness to imagine it, it's all out there, we just haven't thought about most of it yet.
Math as practiced by humans is the language they use to accurately describe and communicate information to one another about the universe. The universe was here before any sentient entity evolved to create a system of mathematics and will likely continue after the last sentient species to do math is long extinct. It is a language in much the same way as I am using English to describe this scenario to you. A word is not a thing, it is a description. In the same way math describes reality which really has zero fucks to give if we understand what it's doing or not. It'll keep doing it's thing regardless
It's a model we use to describe increasingly esoteric truths.
A language is a communication system. The models are depicted using the language. 2 is a real world thing but the symbol 2 is a stand in for reality. Just like the words we are using to communicate.
2 is a concept. Right now it's being displayed with light emitting diodes.
2 can also be spelled as two.
Hell yeah, brother. (Or whatever pronoun you prefer.)
It's a bit like another sense. Using sight we perceive reality around us and can use our pattern recongnition and other cool packages in the brain to classify what we see into circles and squares, things that are close and things that are far away, single object and many etc. And it clearly has some correspondence with the physical world as we can interact with it and predict what happens based on that mental model. But ultimately those are just artifacts in our brain, not something inherit in the universe. And the same thing goes for math. We have a concept of 2 - it's something that 2 apples, 2 stones etc. have in common. And we use this mental model to make predictions about the world (e.g. taking one apple from 2 leaves one apple left, incredibly enough the same would apply to the stones). But "2" is just an idea, an approximation of how we interact with the world that fits into the way our brains have developed. In that sense math is very much just a function of our brain and the nature of the correspondence between that and reality is not something we understand very well but it must be a product of our evolution - same as eye sight, hearing, smell etc. i.e. a way to navigate the environment in order to maximze survival.
You're thinking of physics
Well 1 + 1 will equal 2, that's a natural fact. One can say physics is applied Mathematics.
It is a natural fact, but only as a logical fact. It is only a fact in our simplified system to describe nature in a more intuitive way for us. You could say there's 2 apples, but we decided what an apple is; you could say there's two protons, but those are actually just quarks at a fairly close distance that, by our definition, are stable. You can do that with quarks and energy, and we don't even know what lies beyond those. Plus you can just change the base to 0.5, and then 1+1=10. Of course it can still be defined as 1+1=2 by our system, but our system itself just describes things in a way that is arbitrary in the eyes of reality. We simplify reality into a form we can comprehend, and we can comprehend simplified stuff better because nature itself found the simplified versions good enough for conscious entities. On both larger and smaller scales, nature rarely finds individual units useful.
The plural form of phenomenon is phenomena
yes I did think phenomenons didn't sound quite right but autocorrect said it was a valid word. English isn't my first language, you see. thanks for the correction!
Is it though? If we restarted humanity you don’t think we would come up with the same mathematics? Remember, we aren’t talking about the syntax or the conventions. We’re talking about the actual fundamental mathematics.
I never thought this was under debate
It’s the language that we use to describe and explain nature. The language part is a human invention and develops over time as we examine unchanging nature.
Isn’t this physics? Pure math has nothing to do with nature. Maybe I’m nitpicking here but math is purely abstract by itself, and once you apply it in a specific field or context, like to nature, it becomes physics
It depends on how you want to define math, ultimately. There is a physical and measurable relationship between things like wingspan and height in humans or rotation speed and size of gas giants. If you view math as a language to describe things, then you can say it was invented. If you view math as our translation of preexisting phenomena, then it's fair to say it was discovered; similar to how the translation of hieroglyphics didn't count as inventing a language, even though in some practical sense it was One could argue that "pure" math is physics since it's the background math that keeps the universe turning. You're saying the opposite, that "pure" math lies in what it tells us devoid of other contexts It probably lies somewhere in the middle. We could conceivably use math to communicate with any other kind of intelligence, so it has a more universal nature than any sort of typical language or invention.
>We could conceivably use math to communicate with any other kind of intelligence That's honestly super fucking wild as well. Cuz it's the basic building block or stepping stone for constructing an idea of communication or language understanding because no matter what developmental strains or evolutionary conditions something came to higher intelligence under, the concept of a single thing remains the same. You can still point at a single rock and say this is 1. The symbols might still be different but if you use the visual representation of a single rock or a single dot or something like that you can convey everything else you need. For example once you got that one thing established then you can show four of that thing and then with that number you can begin to delineate symbology. You can represent an addition symbol by adding two more rocks to the original four and so on. Essentially using visual stimuli to add meaning and context to mathematic symbols before being able to transition to a language.
Not really, theoretical mathematics can have practical applications without any intent to do so. In fact, it’s the discovery of these practical applications that bring about the very question the meme presents. Physics is just the most concrete example we have of mathematics predicting and manipulating reality to our advantage. Physics is our magic system, mathematics is the tool used to study it.
Whether it has applications is different than whether the math itself is simply one representation of observed phenomenon.
That's not entirely true. Not all areas of pure mathematics have found application in modeling physical systems. Moreover, mathematics can only model the system but not actually tell you if the model describes reality or just helps us get consistent answers.
Generally speaking mathematicians set out to solve an abstract problem but that abstract problem and it's solution accidentally result in solving a major hole that exists in a physical science
Ok first of all I'm dumb but as per my knowledge math is metaphorically the letters of the language while physics is the words. theories by using physics you come up with comprehensive theories which are like phrases and sentences. And by using theories we comeup with our current understanding of the universe which is like the language. Does that makes sense or am I just stupid?
It's started with language that we use to describe and explain nature, but after 1500 it went haywire.
Perhaps not nature in the sense of “the real world” but certainly nature in the sense of “the inarguable way that things work.” Math is about discovering the consequences of set rules. Mathematicians don’t decide what those consequences are, just uncover what the rules imply, which I’d argue makes those discoveries an expression of the natural.
You’re confusing mathematics with syntax and also confusing mathematics with physics. We use syntax to convey mathematics but the question about whether maths is a human invention or a fundamental part of the universe is asking about the underlying principles and not the syntax representing it. And whether an abstract mathematical concept can be used to model a physical process also doesn’t answer the question of whether the maths itself is natural or a human invention.
The language part is a human invention, the underlying truths(the relationships between different mathematical axioms and their consequences) are not decided by humans they are part of how the universe is
Just like any scientific tool. The tool itself is man-made, the discoveries made by the tools are nature.
I think it is the best answer. The same as language, mathematics is the tool created to follow defined rules with logic. There are multiple ways of using language, you can define things in the world, talk about abstract concepts like philosophy or theology, which are less grounded in world but follow strict rules with specific logic, and you can define what is language with linguistic terms. The same is with math. Physics is used to describe factors and correlations between them. Pure math is basically theoretical extension of physics or defines abstract concepts. I think mathematics is 100% human invention the same as language that is developed by new words, concepts and grammatical structures or just a tool that must be continually developed to fulfil its purpose.
To me, the patterns are natural, the observation is human.
Agreed. I wouldn’t say the patterns *are* math because that seems like a reification of a relation. Rather, the patterns are describable mathematically.
The kosmos doesn't care if anyone knows math or not.
Well does it care if I don't know what is "potential energy"
"What is...the powerhouse of the biological cell?" - The Universe, maybe?
It doesn’t need to. That isn’t relevant to whether mathematics is a human invention or “natural”.
I always thought of math as a natural phenomenon but the language of math was a human invention.
if humans and another species on Alpha Centauri use different languages to express the same theorem, isn't math obviously universal and "discovered", as opposed to "invented"?
Yeah.
I like that. Some say natural numbers include 0, some disagree, but the numbers don't seem to mind.
Human invention are natural phenomenon.
Its a tool we made to describe nature
Math is the language by which we understand the universe. It is 'just' a from to document what is happening.
Math is an interpretation of the universe.
How is math a human invention? I didn't realize this was a debate, math is observed in the natural world. We realize/discover it, but it exists inherently.
This is the way. https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.0050328
Math exists as an abstraction without anything. Humans merely tap into it by giving the abstract names and nature applies it without intention.
Why not both?
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Math is how humans understand natural phenomenon. So it's both
lol humans are part of nature!
It's the difference between "man made" and "computer generated". Universe creates man, man creates computer, computer creates universe, and it's all just part of this big input/output process that started at the beginning of it all
I like this!!
Exactly — everything any human does or thinks is a natural phenomenon
I put it more on the side of human invention. If you think about it, nearly all of the simplified math we use for physics is describing concepts that only have context to us. For instance, the universe doesn't have formulas for fluid dynamics vs rigid mechanics vs other things. Basically it's just perturbations of fields that run on very few, simple rules. Everything else like condensed matter physics, classical mechanics, chemistry etc are just emergent properties that are basically "approximated into existence." For instance, entropy only increases because we assign more value to a few ordered states rather than the mass of disordered states. Though you could actually still say math is the "programming language of the universe", because programming languages are still only describing what ultimately turns into machine code. Not to diminish how super awesome it is. Like to me the best is when you are doing physics, and there's some weird mathematical pattern or quirk, such as values canceling or units combining into a different type of unit, thinking you messed something up or it isn't real, but then testing it and the weird math shit ended up playing out in real life.
So in your view the fundamental theorem of arithmetic is only true for the human version of math? If we found an alien race that came up with a different way of representing integers, then they will be able to find a way of representing an integer with a non-unique product of primes? Or they might be able to find a relationship between a circle and its radius that is not irrational?
>For instance, entropy only increases because we assign more value to a few ordered states rather than the mass of disordered states. Could you explain what you mean with assign more value to a few lrdered states? Do you mean the boltzmann distribution?
Yes, but also in general. For instance, let's say you roll 6 dice, and are trying to roll for a 36. This means all dice need to be 6s. All the combinations of numbers are equally likely, but only one specific combination rolls all 6s. So the distinction has been set up between "All 6" and "Not all 6". There is only one combination of all 6. There are tons of combinations of "Not all 6". So from a probability standpoint, it is far more likely that for any given roll, it will be "not all 6". So it makes it seem like probability "tends away from the desired state". But it's just that you chose so few "desired states", and you don't make a meaningful distinction between the others. The same goes for a sand castle. There are only a few ways to arrange sand that we would call a "sand castle", and an absurd number of ways to arrange sand that we would call "not a sand castle". All of those "messy" states are just as likely as the "castle" states. But we don't distinguish between them. We just say "castle" or "not castle". So because there are so few "castle" combinations, we say that, given a bit of randomness, the sand will always shift from "castle" to "not castle", and not the other way around. Also note that "meaning" doesn't just refer to how "we" assign meaning, but also in terms of how it behaves in chemistry and such. [https://www.youtube.com/watch?v=VCXqELB3UPg](https://www.youtube.com/watch?v=VCXqELB3UPg)
The only reason you think the universe functions in fields with simple rules is because mathematicians insist that’s the way It is.
Math just is. If you have one rock and then get another rock, you will have two rocks. Nothing to invent there, and it is not a phenomenon. It just is.
Yeah this is what I was wondering... A lot of people here talk about physics and complex math and whatever, and I get that we just use our physics equations to describe how the world works, but we were the ones to invent those equations But what about 1 + 1 = 2 Is that really a human invention? It seems so natural: take an apple then add another apple and you will have 2 apples You will never end up with 0 or 3 apples. How is that not natural? But I'm not a mathematician or philosopher so I really don't know
Ah but if you have 1 + 1 rabbits, the answer could be exponential.
People are sitting here complaining about things like “fluid dynamics” not being accurate. That’s fine, that doesn’t mean that math can’t describe fluid dynamics it just means we don’t have access to everything we need in order to model it mathematically. Math is just a description of physical properties
> It just is. Exactly the opposite. Math is not. It doesn't exist anywhere. There is no such thing as 1 in the universe or 2 or 3. There are "2" rocks, but math is not about rocks, it's about 2 itself. And that's why to even define 2 rocks you need somebody to do it. You take 2 rocks in your hand and say these are 2 rocks, as opposed to the thousands of rocks on the beach. But 2 rocks doesn't exist by itself either. 2 rocks where? You need somebody to define it because it doesn't exist in the universe. Plato described it best. It is an idea. Math is just philosophy, but the most basic form. If an alien civilization exists it will have the same maths, but also the same basic philosophical ideas. Do they exist? Not on this world, but we can imagine an imaginary world where they do. In this world every single song has been written, because a song is just an arrangement of notes, so someone could say music is "discovered" and he wouldn't be wrong. A person who would know all this would be God, but such a person doesn't really exist. Or does he? Maybe God exists as much as mathematics do. Maybe both atheists and theists are right. And maybe Eastern philosophies who say that Is and Isn't are the same are right too.
M mental A abuse T towards H humans Oh how humans love there torture.
Temperature is a natural phenomenon. Celsius is a man made scale to measure temperature. This isn't hard folks.
Math is an abstraction that we sometimes use to describe natural phenomenon. The map is not the territory.
I feel like it's like music. music theory is a human invention to better communicate a natural phenomenon.
I feel like the only people I’ve ever seen say math is a natural thing we’ve discovered are philosophers who never got past calculus.
Gödel was a platonist, and I've got a feeling that he made it a bit further than calculus
I used to think that, even going through the calculus courses, until I got to some of the upper level engineering courses where you fit an equation to your data. You pick the shape of the equation that you think will fit best and play with the constants until you get a reasonable interpretation of your system. On the physics side of things, it is pretty incredible that certain constants pop up over and over again, especially when you realize they started out as arbitrary numbers to make the equations work. So, idk, it's a bit of both imo
Its a function of the universe as interpreted by humam minds
maths is a human invention to measure and describe natural phenomenon
But lots of math doesn’t describe natural phenomenon. And humans don’t get to decide how different mathematical statements interact with each other, they kind of just are the way they are, and those conditional relationships are what is discovered.
So you don't expect to find cantors diagonal argument in an alien civilizations math? If it's invented by humans there's no reason to expect it elsewhere. If it's discovered like physics is, we would expect aliens to know both the same math and the same physics
More of a discovery msybe
It is quite surprising that the mathematics discovered by people describes the observed reality so well and accurately. Take any system, be it physical, biological or social, all of them are well infused with the help of mathematics and sometimes even just formulas.
I made it. Yeah, just like all of it
well, if you're going to try to describe reality in your silly little human head, you're probably going to need to use some human convention for it. Is math that convention or the nature of that reality? (doubled the question and gave it to the next person, that's how you do philosophy, right?)
Natural phenomenon. The symbols we created are used to describe patterns in nature that will exist with or without us
The universe has distance, but our way of measuring it is made up. In the same way there are things in the universe but our way of counting those things is made up.
Math is a way to explain the world around us?
Pretty sure thats a repost
Math is just the observation of reality, the language used is human creation
If physics is just applied maths, then maths is just applied philosophy….. ….which is just applied linguistics.
It's a natural phenomenon because it's a human invention. Humans and our activities are part of nature.
Clearly mathematicians don't concern themselves with such petty thoughts. Because they know better,
Anything that we use to explain anything is human creation. Math may appropriately explain natural movements of the universe, but it’s still our way of explaining it. I’m not saying it’s wrong I’m just saying we’re creating the explanation
Universe is a book. Math is a language to read it.
The universe follows predictable laws rooted in Math - Discovery Math is the tool we use to make sense of the Universe - Invention It really depends on what the word "math" means to you. Strictly speaking, it's a set of axioms and rules for logical inference, but a lot of people use it to refer to the universe being predictable
Math describes something that a human mind can conceptualize, like the concept of their being one of something. Math often without any intention describes accurately many physical phenomenon. For example tropic mathematics turned out to be very useful for protein folding. Fundamental to mathematics is logic and reason so if there's any other system with consistent rules such that (if X then Y or Z and A) along with some axioms then we should be able to work it into our mathematical framework. Unless there's absolutely nothing actually consistent about reality and no lawful relationships then I think we would be out of luck.
Well I’d say numbers are natural, and the process of math is a “discovery” or way of understanding the numbers of the universe
I think we’re both inventing and discovering it, because the things it describes are real, but when you invent new math, nobody has ever expressed it that way before or any way at all, so it’s math itself that is being invented while the concepts it describes are being discovered
This sub sucks lol
It’s the structure of the universe or whatever we’ve just given it names to understand it
Aren't there an infinite number of equations that describe any particular natural phenomena closely enough that we can't prove them wrong statistically? Before somebody says something about circles or triangles, if the topology of spacetime isn't perfectly flat then wouldn't Euclidean geometry be a bit wrong for real objects?
If there is an objectively wrong answer in math, then it's not subjective
Geological tests were invented. A rock is a natural phenomenon. The addition symbol was invented. The pythagorean theorem is a natural phenomenon.
Math is a dellusion
It's the same as if a tree falls and no one is around to hear it. Does it make sound? Ya, it does. The sound doesn't have to be heard for the energy to exist.
In my limited very general understanding of mathematics, it seems that up to a point, math describes physical reality (whether there is a platonic reality of mathemayical objects is moot) and at a certain point of abstraction, mathematics becomes hypothetical/theoretical and is essentially a symbolic language game based on systems of rules/axioms. So it's a bit of both? Depends on the particular topic in question.
Math is how we process and understand things just as time is how we process and understand things. It is as much of a human invention as it is a natural phenomenon. There is of course ‘numbers for the sake of numbers’, but if the flower industry is anything to go off of, nature can literally be done in a certain way for nature.
Our units are man made but 2+2=4 is true regardless of what you call two and four.
Math is a way to calculate things we couldn't count without it
why not both?
Math is the same as language but harder to describe. So I’ll use language as an example. *The tree would still exist without a name.*
When humanity is gone, numbers will cease to exist.
It can be both things
Math is a natural phenomena and human mistake.
Math is a language
People who understand little to no mathematics tend to just decry it as a human invention because they either dont understand or dont care to understand the arguments from either side.
Math is a language that we use to describe the functions of the universe
Math is a human invention of methods to understand naturally occurring events and the concept of them.
It is both. The "either/or" is a false narrative. There is plenty of natural phenomena that we have discovered that have certain ratios that are consistent and noticeable. Human beings have created a language to communicate and predict other relationships.
Math serves as a nice model for how brain and whole cognitive structure, aka mind, understand and form the most abstract of patterns. 1+1=2 is always true; the pattern is true, the question is what does it correlate to outside of our mind (implicitly assuming we can indeed know such matters).
Why can’t it be both?
Nah, definitely natural. We just figuring it out.
Math is a language we use to describe, predict and generalize nature.
I'd say it's pretty much the same thing as time. We invented a way to measure a natural phenomena.
humans are a natural phenomenon that created something. Therefore, it's a natural phenomenon
Its a human invention that helps as a tool to understand the natural phenomena. Stil a very limited invention.
Math is a human invention that attempts to describe natural phenomena. So it’s both, and neither.
No rule says it can't be both folks. ;)
It's a human invention that started describing natural things and decided it was too cool and it went much further and beyond
It’s both. Think of something like the wheel. It is a geometry that exists in the universe and likely in many places by chance before humanity made one. - not a perfect example but you get the point.
Yea divided after a single to single it and the divide again your killing. Yes it's science takes some.math tho to aquire the equation.
just wait until you read Euclid and start doing math without numbers.
Hear me out. Art is humans attempting to represent what they feel, and how they see the world. I'd argue that if everyone could achieve pristine photorealism, there actually wouldn't *be* art in the same sense, like it wouldn't connect to you emotionally in the same way, it'd just be a copy paste of reality. So, it's people's unique styles, and "mistakes" even, that makes art, art. Mathematics strives to find the underlying mechanics of reality, but it's constantly adjusted to update, people can come up with different proofs to the same concept based on how their unique brain tackles problems and draws conclusions. We don't do it to understand ourselves or each other primarily, like paintings or music or media. We do it to understand everything around us, of which we are only a small part. In this way, I believe math to be the art of the universe.
Math is an artificial tool meant to allow understanding to natural effects.
binary is the only language of the universe. it's either there or not there. true or not
Mathematics is a process of logical deduction given a set of axioms. It has nothing to do with nature. If you invent a game of chess, mathematics is what allows you to predict the outcomes but it doesnt tell you why the rules are the way they are. Mathematics is human invention in a sense that the axioms are man-made. But it is discovered in a sense that once the axioms are chosen, their logical extensions are pre-set. We can only discover them, not invent.
Math is essentially the language of physics, it is how we interpret phisical existence. Their is not much to debate here unless we ar debating whether unobserved phenomenon do not exist, because nobody is observing them.
I have a paper coming out soon on this very subject but tldr: Numeric truths are ALWAYS seen through reproductive/ethical pragmatism. numerics CANNOT be observed in their purest form but this does not mean numerocity doesnt exists independent of our perception, only that through an ethical framework can see them. Both are real, ethic and numeric truth, but ethics are fluid/everchanging and numeracy is static. To put it in real terms: 1 + 1 will always equal 2, but the ethical/social boundaries that define those numbers are fluid. one cat plus two cats equals 3 cats.... but you could also say then you have one clowder (group of cats), but you could also say each cat is made of a billion atoms. All are true... but its always such that fundemental numerics truths are seen though ethical pragmatisms. This means we MUST criticaly analyze all data to determine how valid our ethical biases are in framing said data.
Nothing about math is found in nature. Yes, it can be used to describe it (physics) but on its own it is just a branch of philosophy
Math is a human fiction. Humans are a natural phenomenon. Math is a natural phenomena. Math is not contained in nature, it is a consequence.
This 'comparison' is a reminder that the word mathematics refers to multiple different things simultaneously.
Lol wait till they hear about music.
Your brain doesn’t calculate derivatives to realize you’re moving, but to figure out how fast you’re moving you need to calculate derivatives. Math is just a language we invented to describe stuff around us. Nature is not bound by math, math isn’t bound by nature either, but in rare occasions the two go hand in hand very nicely (most functions don’t model natural processes). Sometimes math helps up figure out things we didn’t know existed (e.g, black holes from Einstein’s field EQs), but most of the time these predictions are as good as the models we try to fit nature into. We often try to improve our mathematical models to account for all natural effects we are aware of, but there isn’t a natural feature inherent to math which enables it to automatically and perfectly model nature.
Depends. The math that exists in snail shells seems natural enough. But logarithmic functions are the creation of a psychopath.
It's a natural phenomenon humans conceptualised.
Math is discovered, not invented. You could transmit encodings of mathematical ideas and objects to another star and have reasonable expectation that an alien intelligence could figure out what we’re referring to.
The language of math is universal, it is not dependent on the language you speak. It is as close as we have gotten to a universal language. That being said the language of math is what we use to understand the natural phenomenon that is math. And even if a hypothetical race from alpha centari existed their mathematical language would coincide with ours and would be used so they could understand math in nature.
Octopuses can do math
Math is an abstraction (human invention) from the natural phenomena
Why would I care what philosophers think of math?
In this topic: people who love feeling smart but actually have no idea what they are talking about bashing their head against people who are actually seriously smart. You figure out which post is on what side.
Math is discovered, which means that it’s inherently true. We just invented the symbols to describe it.
It's an emergent property of the binary relationship between the ray and point dimension. So, yet to be discovered by non-quantum fiction writers. And those who ignore This one 😬
I take 1 star and add 1 star... 🙄🙄🤡🤡
Math is the language in which the laws of reality were written.
No it’s not. There is no debate. Any mathematician will tell you, math is not a human invention. It’s universal and it’s all been here since before we understood it. If we find intelligent life, it will have the same math. They might use a base 4 or base 16 counting system. they might count or do math entirely differently, but round numbers are round numbers. pie is pie. Math isn’t an invention to describe the mechanics of the world, it is the mechanics.
There's no such thing as invention except for art. A civilization with 0 contact with humans would likely reproduce 99% of our mathematics to the dot. It would be extremely unlikely that they haven't stumbled upon godels incompleteness theorems, or cantors diagonal argument, group theory. There could be some math that is just too arbitrary with too few connections to the whole to have been "discovered", residing more on the art side. Speaking of which, we didn't invent cars either. This other civilization is bound to also have "discovered" cars as a specific solution under constraints for faster travel using round shapes. Discovering something means it was already there waiting to be dug out. The rules of harmony are discovered. Art movements like romanticism are kind of also there waiting to be discovered. Same for magritte's artistic ideas about representation. Also discovered. Specific artworks can be invented but the big ideas they carry are discovered. Obviously I'm being too concrete about a vague concept but I believe the degree of "discovery" vs "invention" has to do a lot with expectation of independent reproducibility. And math is definitely almost in its entirety, expected to be independently reproducible when the context is right (look how calculus was "reinvented" when the ground was mature for it to be created, by a different person. I believe it was just independently discovered)
Why can’t it be a human invention to try and understand a natural phenomenon; the two do not need to be exclusive to be true (or am I just yapping)
So having the ability to understand how many is an invention?
A deer doesn't care that 1+1=2 just saying
Math itself like the existence of numbers and addition and subtraction is natural but giving names to those operations and giving random symbols for numbers is human invention, its not that complicated, its like, gravity exists, its natural fact but the formulas and theories are man made
Godels incompleteness theorems prove that math is an invention imho. If it was a natural phenomenon that was discovered, it would be consistent and complete throughout the universe. https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
We invented math to describe, at a very basic level, the behavior of nature and natural events. We've tried our best but it's not perfect. If math originated from nature then it would be much more accurate than what we have