Both kinda. I would say things like the pythagorean theorem are discovered. But I kinda see it as a translator we made to solve these problems too. Math just really includes a lot of stuff, so I say some things about it were discovered and some invented.

I agree with this! Mathematics are laws of nature and as such not created, at least not by us. But the mathematical language we use to interpret and understand math is created. So it depends on which one you mean when talking about it. 1+1=2 and always will no matter what language no matter if you have no language for it. That is not something that was created to be by someone nor is it something that can be changed. Math doesn’t change. It can’t be changed. I once got into an argument with someone online because they insisted that if you solve equations different ways you get different answers and both/all are equally correct. Things like that makes me unreasonably upset because part of why I love math is because it’s so clear and defined and strict. It’s either right or wrong and there are logical rules for how and why. It destroys my world if you mess with that. There are very few situations where there can be more than one correct answer, and that’s only with algebra and only in theory. The person I argued with insisted that some mathematical rules had been changed. That’s not a thing.

Thats the point GaiasDotter is trying to make here.
To math there is the laws of its logic and then there is the language used to describe them.
Here, 'Mathematics' is referring to the laws themselves.

But I've been pointing out the **current context**, I dont get what youre disagreeing on.
In said context, 'Mathematics' refers to **Mathematic Laws, its Axoims and the Logical Consequences thereof**.
You could also read 'Mathematics' as 'Mathematic Laws' - but if we do that, we also need to distinguish 'Mathematic Language' as well, as the term "Math" or "Mathmatics" encompasses both, at least for your everyday use.
[But even if we were to ignore the context, the term 'Mathematics' per definition describes an area of knowledge encompassing all things numbers.](https://en.wikipedia.org/wiki/Mathematics)
If we go beyond basic application, mathematics essentially is the process of discovering and proving abstractions using logic.
I dont know how it is for others but my professors very much differentiate math from its notation and the ways to describe its laws, as the way you "write" math is irrelevant to its function.
So I'll conclude once again:
How math works? Discovered.
How its written? Created.

*"One, Mathematics is the language of nature.*
*Two, Everything around us can be represented and understood through numbers.*
*Three: If you graph the numbers of any system, patterns emerge.*
*Therefore, there are patterns everywhere in nature."*
**Source:** Maximillian Cohen in Pi (1998)

The best answer I’ve heard to this that goes along with what you’re saying and went something like “we create the basic rules for math, but we discover all of the implications of those rules”.
For example we’re the ones that decide the rules for how factoring numbers works, so in that sense it’s “created”. But stuff like the prime number theory wasn’t explicitly created by those decisions but arises by the interplay of the lesser rules, and thus is “discovered” instead.

How would you respond to the idea that the language itself *is* the math, and we chose the part of it that is most useful to describe what we want rather than it being an inherent property of the system itself?
For support I’d point to the fact that there’s really nothing in math that can’t be changed by varying your base assumptions. 360° is 2π is 256 degrees (in an 8-bit computer simulation), and even 1+1=2 can be changed with the right axiom choice.
I’d also point to the fact that we can use math to describe systems that cannot actually exist off the page. For example a 4 spatial dimension system doesn’t exist in the real world, but that doesn’t stop me from rendering one with numbers.

Well the thing is that the pythagorean theorem isn't correct on earth since it only applies to euclidean spaces, and since the earth is round and therefore not euclidean, it differentiates by a tiny amount to triangles on the worlds surface. Becouse of gravitational distortion there are no euclidean spaces in the universe, so the pythagorean theorem somewhat only applies to a completely fictional mathematical space, which just happens to be reasonable close to our real world (since the sphere that we live on is quite big and gravitational distortion isn't that strong).

Even if you disregard if the earth is round or not, the laws of general relativity say that there will always be gravitational distortion and therefore not euclidean space.

For vectors you need to have a movement that follows precisely a straight line (at least for a discrete moment), which doesn't really exists. I dont know what you want to do with calculus, since it usually is even farther from the real world than geometry (at least in my experience). If you want to give an argument against what I said you could use the trigonemtric Pythagorean theorem which does work on spheres, but as for all statements, it could be argued back that this is just an increasingly precise approximation of the real world. Since there are way to many variables and small errors, it isn't possible to completely calculate the real world and it isn't necessary to do so. It isn't that pythagoras is completely broken or unusable, it is just that all mathematical concept have a slight disconnect from the real world. This does actually apply to all sciences since it is always necessary to approximate since the real world is way to complex. However if you venture deeper into mathematics and take a look at the actual axioms it becomes apparent how big this disconnect actually is (especially compared to physics). Dont get me wrong, that's something I like about mathematics, since it allows for proves that are always and deterministically right under their set of propositions, which isn't possible in physics where even the most advanced theorys are never provable but just hoped to be right.

In engineering, mechanical first but electrical engineering even more so, Pythagoras and calculus are both extremely important to some real life problems. We operate on the basis as you say, that no measurement is perfect and that there is a theoretical “pure” truth of what that measurement really is.
The vectors don’t need to follow a straight line though, do they? Something can have a centripetal acceleration and a tangential acceleration vector which won’t be subject to non Euclidean geometry in an instant. The forces calculated on it might need to be in order for it to be measured, but the object does in fact have an orthogonal velocity vector which can be cross multiplied with the measurement vector to find the distended angle if the true velocity vector were known.
I’m sure the same thing applies to electrical signals especially when it comes to interpolating data from any of the above. There is a degree of removal from the real world here but it seems more of a removal away from the lies of measurement instruments and towards the true values created naturally, reinforcing the idea that mathematics was discovered rather than created

Well the thing is that you are always approximating the problem and, in case of vectors, looking at it in discrete steps. As I said it close mimics real live and approximates it and is obviously useful on it. I just think that the approximation removes mathematics from the real world, while in your opinion this connects math with the real world. This is kinda why this argument has no real answer and both sides are valid. I guess I work more with abstract math, while you use it more in engineering which impacts our respective opinions.
For all the maths I did in the last year I probably couldn't tell you any direct or obvious real world application (besides some 3d calculus and differential equarions). For example Algebra and topology are important for the complete rest of mathematics (especially algebra) but dont have direct connections with the real world and are purely abstract. From that abstract standpoint without any obvious connection to the real world and surrounded by axioms, that people just agreed on, it's kind of hard to see mathematics as something we discovered and not created.
This is a strong contrast to engineering which is probably why we wont agree.

Yeah I think I get it. If you only ever deal with stuff on paper it must feel very ethereal. Topology and algebra are again things engineers use for things like the pressure on the inside of an engine based on air to fuel ratios.
I'm unsure what you mean about discrete vectors though. The whole thing about engineering measurements is knowing that your discrete number could be calculated and measured more accurately ad infinitum because the true value is irrational, but also this is mostly because the irrational measurements are the SI units themselves which is slowly being corrected eg with the Avogadro number, Planck lengths etc.
Again this kind of puts us in a confusing place regarding discovery and invention but I think draws towards the idea that there is an existence of a pure value especially if you were to stop using the old yardstick and go and count the atoms and distances with some sort of quantum microscope

Numerical systems were created, but I believe mathematics as a whole was discovered. Once an actual system of numbers (whether it’s decimal or hexadecimal or whatever) is created, I think those numbers can then be used to explain and analyse many different concepts that always existed. A specific formula for a certain problem or topic was not created, it was discovered using the numbers that were created.
In a way, numbers themselves are also discovered rather than created (1, 2, 3, etc always existed as concepts, it was just up to humans to create names and systems for those numbers. Just like fire always existed, or even more advanced concepts like complicated processes in the brain or in physics. They weren’t created, they were discovered. Then, inventions were created/invented using those discovered things).

A good example would be pascals triangle in different languages, even if you don't know numericals of say korean, and are shown a pascals triangle with korean numerals you could tell which one a one and which is a 5. Because the triangle is universal not the symbol.

Math is the grammar of the universe, it’s the rules that govern everything which is why we can do things like predict stellar bodies without any actual trace of them at the time and later those predictions can be remarkably accurate. The study of mathematics seeks to translate these fundamental rules into forms we can understand. In terms of the symbols, counting structure (base 10 and base 4 for example), and notation, these were created as translational elements of mathematics for human comprehension but without those, the rules of mathematics will continue to function as they have since the dawn of time.
TL;DR the rules of mathematics were discovered, the symbols expressing our understanding of mathematics were created. Overall math was a discovery process for humans.

Nature of the universe has been discovered thanks to invention of numbers and mathematical analysis
It's like the man-made language of every scientific discoveries in order to ease the understanding of our world in cohesive way

Yes, but there was a numeracy(?) to how the universe operated even before us. There were still instances of one thing, two things, red things, blue things, and so on, all of which can be counted and operated on.

True, but things like imaginary numbers and vectors don’t literally exist in nature, they’re just tools for expressing the nature of the universe.
Two-ness exists, but i-ness doesn’t really.
There are other systems for expressing direction and magnitude than vectors, but vectors are an extremely simple way of doing so.
So parts of math were discovered, and other parts of math were created.

Its an already as 'setting' in existence therefore it is discovered. Even without us Math will be the same. The only difference is how we interpret the mathematical infos like graph in calculus, 3d shapes in geometry, etc.

it depends what the definition is, I think of "maths" as our created framework that is based on the observed "true maths" that exists in our universe and likely beyond if a beyond exists.

>it depends what the definition is, I think of "maths" as our created framework that is based on the observed "true maths" that exists in our universe and likely beyond if a beyond exists.
Perfectly summarized.

>it depends what the definition is, I think of "maths" as our created framework that is based on the observed "true maths" that exists in our universe and likely beyond if a beyond exists.
Perfectly summarized.

there's arbitrary parts of mathematics that we've just decided on such as a circle being 360 degrees, using a base 10 that are invented rather than discovered

That aren't even the interesting arbitrary parts. The far more interesting stuff lives in the axioms for example the axiom of choice beeing equivalent but not the same as the lemma of zorn. Also how the inductive property of natural numbers is notable in a few different ways. If you stray from the common axioms it gets even clearer that our axioms which create the whole field of mathematics are arbitrary and you could build a complete number system without ever defining natural numbers integers or even reel numbers (see for example the surreal number system).

Sorry, I was taking a break of studying math for university and kinda forgot that axioms aren't really covered in school (the debate if Math is discovered or invented is one we sometimes have for fun between math students so I am used to just use the stuff we learn).
Axioms are unpropabale basic assumptions. These are like the core foundation which are then used to expand with the commonly known theorems. For example two very important axioms of geometry are, that you can draw a straight line and an circle. There can than be used to prove more complex stuff, like for example pythagoras theorem. As you might already noticed while working with paper, it is not easy to draw a perfect straight line or a circle. With tools, like a compass, it is easier, but even that circle is never perfectly round. Indeed it is impossible to create a perfect circle the real world, but it is still a reasonable assumption that it is possible to draw a perfect circle, for mathematical purposes. This is why those axioms are vaguely based on the real world but dont mirror it exactly.

The other stuff I wrote is about explicit axioms which govern how numbers work in mathematics. It's quite fascinating: in formal mathematics everything is defined, so there is actually a reason why 1+1 equals 2 and it is possible that this is always true. The surreal numbers I mentioned are a number system which work separate from the numbers that are thought and used in school (they even encompass stuff like multiple infinitys and much more). It is possible to build the known numbers as a part of the surreal numbers, but on a basic level the surreal numbers behave completely different compared to the ordinary numbers used in school, which is due to the fact that they use an completely different set of axioms. I mentioned them to show that even the numbers we use are completely arbitrarily chosen and kinda made up (and I talk not about stuff like everything beeing in base 10, but a bit deeper inside the very essence of how the numbers operate)

Since I am not american I cant really say how this would work at a college. All I can take as an reference point is what's taught in the bachelor of mathematics in the university of bonn (germany). As far as I know other german university's cover similar stuff in their mathematics bachelors, but the uni of bonn has the reputation of beeing harder and doing more diverse topics, so I dont have a complete picture what thaught at other universities.
But what I can say with certainty is that axioms will be taught if you want to study mathematics (I bet also will be important in math courses outside of germany since all of modern mathematics realies on them). There you will learn for example how numbers are created and defined. At least for me that was the first thing we did (we took a few weeks until we were allowed to do addition and substractions in the same way as it is used in school, since we first needed to establish and prove all the rules). This will encompass a collection of proves that we proved as homework. For example a cool thing to prove is to show that for two natural numbers a and b a+b = b+a, which is something that you use since elementary school without ever getting explained why it is right. If you are interested in this stuff you could Google peano axioms. These are the basic rules which create the natural numbers (all positive integers) and it quite fun to prove stuff about addition and multiplication that you would normally take for granted.
What we didn't do, but which is also quite easy and entertaining is proving stuff by geometry. The common axioms are just that you can draw a circle and a straight line and with enough work you can use this to prove, for example, pythagoras theorem. Euclid wrote a whole book series about these proves before mathematics was a thing.
The stuff about surreal numbers is something I learned for my own entertainment. I can recomend the book surreal numbers by D.E.Knuth. But this is what the other refers to as hard core mathematics and might not be a enjoyable read when you never done anything about proves, infinitys, or set theory.
One thing that might be important to add if you think about studying mathematics (at least in germany I have no idea how it is in the rest of the world, but i assume its probably similar): if you study mathematics it self you wont be calculating stuff or even seeing numbers. (The last time I had a math exercise with numbers higher than 10 is about 1.5 years ago.) Studying mathematics is about proving that stuff is true. While this is extremely entertaining it is probably very different from what is done in school and something to be aware of. The cool part is that you then know where all the formulas come from, which just popped up out of nowhere in the school time. And the other cool thing is that once you proven something to be right, it is always and under all circumstances right (a big diffrence to for example physics).
I hope this wall of text answered you question and wasnt to much. If you have any further questions, feel free to message me.

As I said peano axioms and euclidean geometry is quite easy and entertaining once you get the hang of it and wikipedia as a lot of sources about it. If you have the time and want to try it, it is even outside a major not a bad idea. It's essentially proving stuff that is used on a daily basis in addition and multiplication, while learning problem solving skills (which is basically everything math is about). But I understand it's not something for everybody, but I can recommend giving at a try.
Glad I could answer your questions and good luck on the major you will be choosing.

Doesn’t this just prove further than math is discovered not created?
The language we use to describe the math is created, but the actual mathematical principles exist regardless of our understanding or ability to model them.

Well the axioms I mentioned are constructed in a way that results in the same kind of mathematics. There are also axiomatic set that are completely disconnected from the real world or any applications. But since they are kind of unusable outside of their own axioms they aren't really researched.
For example wheel theory has no applications I know of and is incompatible with standard operations (its mainly known for being able to divide by zero). Theoretically you could always just create your own axioms and make your own set of mathematics.

Right, but even when doing that you’re just making a new language to create new models. The actual underlying principles that these models model is real and discovered

We're *creating* a language to describe *discoveries* about the workings of the universe.
So... both?
In cases where the language and the workings closely align, you'd probably call it a discovery.
In cases where we're somewhat off-base or half-true, you'd probably call it a creation.

Euler's Identity is an absolute example of mathematical beauty, something that we've proved beautifully without really understanding it completely, and it's things like these that really make mathematics seem like the code of the universe, that we are cracking piece by piece
[Here's a brief explanation of what makes the identity so amazing, although there are probably better resources out there](https://en.m.wikipedia.org/wiki/Euler%27s_identity#Mathematical_beauty)

I disagree that math is a language. Mathematical language and mathematical notation are not what people mean when they say “math”. Math usually refers to concepts, like two and two is four.
https://en.m.wikipedia.org/wiki/Definitions_of_mathematics

According to Pythagoras’ theorem, the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. This is true for all right-angled triangles on a level surface, so it’s a discovery.

Yeah but there are no true eucledian surfaces in the universe (on the earth due to living on a sphere and in space and the earth due to tiny amounts of gravitational distortions), so pythagoras theorem doesn't hold inside the known universe and only works in an fictional, arbitrarily defined space. It is a really good approximation of the real world, but it isn't really a real world concept. It is even questionable if an right angle is a real concept, since the universe is discrete.

Once axioms (base assumptions) are set, math is discovered. Because axioms have to be set, math is created as a whole. If math was recreated, the axioms might change though they are often pretty natural choices. In a universe that ran by very different rules, the axioms picked are more likely to be different leading math that looks different to our own.

It's really both. Mathematical methods that work are discovered, but they way we express them,.the symbols we use, and the ways we use to implement the discoveries are created.
There might actually be an easier way. It we can only create it after we've discovered what that easier way is.

„Math“ merely verbalises what is nothing more than geometrical logic. It exists in the absence of humans beings, it works perfectly, with or without a mind to perceive it. It was discovered.

I disagree. "Math" was created as a way to work with geometrical logic. The formulas that fit together are discovered, but math as a concept of calculating things were created.

This debate is as old as time and has been addressed by some of the greatest philosophers who've ever lived so you're not likely to settle it on a reddit forum of all places.

Math major here - a lot of people are confusing math and physics here. Math isn't the "language of the universe" or anything like that. It's a set of tools that helps us describe phenomena. The phenomena are discovered, but the tools used to describe it - math - is entirely created.
Sure, some of it aligns well with physical concepts. Natural numbers are logically tied to quantities of whole things, for instance. However, that doesn't make the math any more innate. Euclidean geometry aligns well with our understanding of the universe, but according to relativity the universe is only locally euclidean.
Even basic facts are entirely a construction. 1+1=2 isn't true in every number system. We define what 1 means and we define what + means. These have real-world analogues, but the analogues we choose only make sense because of our particular circumstances. It may be just as logical that 1+1=1 given the right definitions.
So, in conclusion, math is created. While certain theorems and the like are discoveries, they're discoveries only in the systems we created. We may well have created different systems, in which case there'd be different things to discover.

The mathematical equations and theorems are directly logical and proven. They are the same no matter where you are, when you exist, independently of anything. They had been discovered. On the other hand, the notation used has been made-up, therefore its been created.

If you can't consult the ancient historical scrolls for the answer, you will probably have to settle for religious belief and faith for the answer to this one. Def do not go by Reddit popular opinion though.

Hey, Christopher Columbus/earliest "Native Americans" who arrived in this country via the Bering Strait/Vikings ... was America created or discovered?
I think we all agree — America was created first. Not by a person, but created. Then it was discovered.

Math was created to describe stuff that just happens. I guess you could say it's both? People discovered inherent rules about how things work and then created math to describe those rules.

Math is just the mechanisms the universe works by, it existed since the creation of the universe, therefore we discovered it. But math isn’t just numbers, it’s not even physical at all, it’s more like how an action exists even though it isn’t physical. If the universe was like a house, math is like a frame.

Even among mathematicians and scientists over hundreds of years, there is no consensus, no correct answer. It is certainly a combination of both. Inventions as well as discoveries. Humans invented mathematical concepts by abstracting them from that which exists in nature. So I ain't voting.

All mathematical theorems stem from axioms. These axioms might be what works in our life, but they dont have any verification or any way to be proven (which is why they are axioms). Since these axioms are "arbitrarily" decided/created without any real way of deciding if they are true and without any foundation to support them, I would say that mathematics is rather created than discovered.
On the other hand the stuff that stems from mathematics, for example a huge part of physics, is discovered and not created since it relies on real world observation, which is why the line is a bit blurred.

Yep true.
This is my interpretation:
>I mean, what does 1+1 really mean? It's an abstract thing. We created it and gave it the value of 2. It could be anything else. Is there a law of the universe that says 1+1=2 ? What if we discover an alien species ,which for purpose of my argument, has the same writing system as humans and our 2 is their 5 and vice versa for example. In their world 1+1 is 5 but in our world it's 2.
>It's like a different language. Means the same thing, but looks different.
>We use our math language do describe the universe.
>Aliens may use a different language to describe it, but it may look like nonsense to us.
>Math was created to understand something discoverable.

The exponential notation that we use for numbers (usually with base 10) is quite intuitive (at least from our perspective). This is why scientists send messages containing π or e encoded in binary to the stars, since they suppose that alien civilisations will also settle on a similar kind of number system. And Binary (base 2) makes sense there since it is what is encodeable in electric signals, so the reasoning is that every civilisation with computers or even lower technology would be able to make sense of the signals (for example avoiding having to explain what this weird symbol: 5 or this weird symbol: 3 means, since binary just uses boolean without intrinsic symbols). However if we venture in more abstract mathematics there are indeed systems to create completely different kind of numbers, which may brake this. My favorite example are the surreal numbers who not only encompass all reel/school numbers (not complex number if you have them in school), but also infinitely many infinitys and infinitesimals. In this system there is a sense in which 0.1 and infinity have the same distance from 0. If aliens would use this number system (which would be possible, since its basic rules aren't that hard, we just sadly dont have a efficient notation for it) then they might not even have the idea to encode stuff like we do it and the differences would be far greater than 1+1 being 5. And of course there is always the possibility that they choose an axiomatic system that is completely incompatible to ours (or dont use axioms at all like we did a few hundred years ago, which would be a shame)

Not exactly, but the letters used to form the word sky is created by us.
The same for numbers, we label time by numbers, time has existed long before anything existed, but we created clocks/hourglass to better understand them.
We use Math to understand Physics, like to get the density of any liquids, we set the water's density as default which is 1000kg/m^3 and compare that to other liquids. It's like putting a name tag to things.
That's just my opinion on the subject anyway.
Edit: I think a better example is launching a missile to hit something specific. Yeah we know that anything thrown upwards will go down, we do know they go down at the rate of 9.81 m/s^2, but how can we make them hit a certain coordinate? We created formulas for projectile motion.

Exactly. That's why math was both created AND discovered. 9.81 m/s^2 always existed; it was eventually discovered by us.
But "meters" and "seconds" were created by us.

Creation implies the creator had any choice in the end result. You can't create 'different' math that gives different results.
You could erase all mathematical progress from existence, start over, and in the end math would work the exact same.
Sure, the number symbols are human inventions, and you could use different ones, but the symbols aren't 'math', the underlying system is.
Edit: Some people have told me it's more complicated than this, and I think I've changed my mind.

> You can't create 'different' math that gives different results
My good sir, that's literally all of graduate math and beyond. Modern algebra, a major part of mathematics, deals in the study of "algebra"s, which are - by definition - structures which conform by arbitrary, human-created rules. An example would be Z/2Z, where 1+1=0.

Interesting! I suppose if you look at it that you could say parts of math are created. I'd still say the underlying 'engine' is still something objective. Maybe logic is the discovered part and math is the human creation?

It's closer to the opposite actually - the "engine" behind mathematics are the axioms, which are an arbitrary set of rules which must exist for anything else to work.
For example, the Hilbert axioms make up the "engine" behind geometry, and the proof of the Pythagorean Theorem is rooted in them. Essentially, these axioms make up the notion of "what is a point", "what is a line", etc - which although seem very obvious intuitively, needs to be formalised otherwise we run into issues.
From the axioms, then we can "discover" things present as a result - so a contention in the debate between discovery and creation is whether humans creating these arbitrary axioms are aware of the consequences of the axioms (thus creation), or if the consequences are discovered as time passes.

>results.
>You can't create 'different' math that gives different results.
You technically can. Different writing system.
Math is like a language. It didn't exist before humans. We created it to understand the world around us.
Now there are many languages and if you translate the same phrase, it has the same meaning in those different languages.
You may argue it doesn't end up with a different result, which is true BUT, it's a different result in terms of writing. We created math (language) to DESCRIBE the universe around us (which can't change)

Math doesn't even work the same as it did a hundred years ago. E.g., the axioms we base (the nowadays most commonly used form of) set theory on were only formulated in the early twentieth century, and it wasn't the only way those could have been done. I don't believe for a second that we would arrive at the same mathematics if we started over.

Let's say humans don't exist, If there's 1 apple on the ground and another apple falls on the ground, how many apples are there on the ground? 2. Math was discovered.

Well the subject of math, like we learn in school was created
but math itsself
math is logic, and logic was always there
math was there before time, since, for time to happen, we need math
like, 1+1 is always 2 and had always been and will always be, we just invented the numbers to make math understandable
yall feel me? 😭

Logical abstractions to help human beings predict the behavior of the systems they observe. It is often very useful. However, the Universe is under no obligation to obey our predictions and could throw a curveball at any point in time and space.

This isn't a totally clear answer. I went with discovered, my reasoning being that mathematical laws themselves are discovered. The relationship between a sin wave and cos wave, that 0! = 1, or the Pythagorean theorem would be exactly the same if you were to restart human civilization and they started rebuilding our knowledge. That implies that these laws are discovered.
Math certainly has conventions, and many of the specifics of our mathematical system are created. We use base ten, circles have 360 degrees, the symbol 3 means three times the value of the symbol 1. If we restarted the human civilization, these things may change.
However I would say that the vast majority of mathematicians have lived their lives attempting to discover things, not define convention, and thus that's what I would say principally makes up math. It's like archaeology. First you have to build a few tools like brushes, tweezers and shovels. Then you use these tools to make discoveries of long buried civilizations or whatever. We had to create a few tools like a base ten number system, but with those tools we make discoveries.

I feel like if we somehow lost all knowledge and records, math would be rediscovered the same way and we would come to find ourselves using similar if not the same algorithms that we use to solve problems today

Did someone create the fact that two apples are two apples? No, math was discovered just like physics. Which makes sense, since physics is just applied math. And chemistry is just applied physics. And biology is just applied chemistry. Together, they are The Sciences.

im not about to argue over this but everything in our universe and world functions a certain way. these functions definitely exist outside of people. they're consistent and tied to laws of science and order.
just because we use symbols to represent what we're talking about, that does not mean we invented the thing we're talking about.

Yep true.
This is my interpretation:
>I mean, what does 1+1 really mean? It's an abstract thing. We created it and gave it the value of 2. It could be anything else. Is there a law of the universe that says 1+1=2 ? What if we discover an alien species ,which for purpose of my argument, has the same writing system as humans and our 2 is their 5 and vice versa for example. In their world 1+1 is 5 but in our world it's 2.
>It's like a different language. Means the same thing, but looks different.
>We use our math language do describe the universe.
>Aliens may use a different language to describe it, but it may look like nonsense to us.
>Math was created to understand something discoverable.

There wasnt a "math out there" it was created the maths we know could be completely different
Also it depends on technically what u are saying tho theres a lot of depends

pretty sure maths is just pattern recognition. amounts always existed, but the idea behind coming up with ways to measure stuff or count is just a weird thing we torture ourselves with.

math had to be discovered right? i mean if some motherfucker spent god knows how much making every single problem and situation known to man work seamlessly, then he had to have gone insane

My friend is getting her masters in some math bullshit and she said it was discovered, though I could not truly follow her reasoning. To my monkey brain it was created

It was discovered. Just like many other species we stumbled upon math to help us understand things. Other species that do math are bees, ants, crows, dolphins.... basicaly many inteligent species or hivemind bugs.

Math was created to describe the world around us.
It wasn't discovered. I would only say it was discovered only if every possible math "problem" had a real world solution. I.e. 1+1=2 ... where in the universe you get that equation? Nowhere. It's abstract and with no meaning in the universe.
But what does have meaning in the universe is for example conservation of energy. We used the math we created (as humankind) to understand what it does. Math was here thousands of years ago, and only "recently" (almost 200 years ago) we discovered Conservation of energy. We had no idea it exists.
Math is a tool we created to understand the universe.
If we ever find aliens, and send them 1+1=2 as a proof that we are an intelligent species, they propably wouldn't understand it because they might have created a different tool to understand the universe. Like a different language.

Both kinda. I would say things like the pythagorean theorem are discovered. But I kinda see it as a translator we made to solve these problems too. Math just really includes a lot of stuff, so I say some things about it were discovered and some invented.

I agree with this! Mathematics are laws of nature and as such not created, at least not by us. But the mathematical language we use to interpret and understand math is created. So it depends on which one you mean when talking about it. 1+1=2 and always will no matter what language no matter if you have no language for it. That is not something that was created to be by someone nor is it something that can be changed. Math doesn’t change. It can’t be changed. I once got into an argument with someone online because they insisted that if you solve equations different ways you get different answers and both/all are equally correct. Things like that makes me unreasonably upset because part of why I love math is because it’s so clear and defined and strict. It’s either right or wrong and there are logical rules for how and why. It destroys my world if you mess with that. There are very few situations where there can be more than one correct answer, and that’s only with algebra and only in theory. The person I argued with insisted that some mathematical rules had been changed. That’s not a thing.

>Mathematics are laws of nature Are they the laws of nature or just tools we created to understand those laws?

Thats the point GaiasDotter is trying to make here. To math there is the laws of its logic and then there is the language used to describe them. Here, 'Mathematics' is referring to the laws themselves.

Yes but I disagree. Mathematics by themselves aren't the laws but something we came up with to understand the laws hence why my vote is for created.

But I've been pointing out the **current context**, I dont get what youre disagreeing on. In said context, 'Mathematics' refers to **Mathematic Laws, its Axoims and the Logical Consequences thereof**. You could also read 'Mathematics' as 'Mathematic Laws' - but if we do that, we also need to distinguish 'Mathematic Language' as well, as the term "Math" or "Mathmatics" encompasses both, at least for your everyday use. [But even if we were to ignore the context, the term 'Mathematics' per definition describes an area of knowledge encompassing all things numbers.](https://en.wikipedia.org/wiki/Mathematics) If we go beyond basic application, mathematics essentially is the process of discovering and proving abstractions using logic. I dont know how it is for others but my professors very much differentiate math from its notation and the ways to describe its laws, as the way you "write" math is irrelevant to its function. So I'll conclude once again: How math works? Discovered. How its written? Created.

*"One, Mathematics is the language of nature.* *Two, Everything around us can be represented and understood through numbers.* *Three: If you graph the numbers of any system, patterns emerge.* *Therefore, there are patterns everywhere in nature."* **Source:** Maximillian Cohen in Pi (1998)

No, physics are laws of nature and are discovered. Math are a tool we completely (theoretically) craft to serve this purpose.

But theorems and laws arent made they are discovered. Only the tools in which we understand math are created. But the math itself is discovered

Yep this. Is what I tried to say but ki.da failed lol

The best answer I’ve heard to this that goes along with what you’re saying and went something like “we create the basic rules for math, but we discover all of the implications of those rules”. For example we’re the ones that decide the rules for how factoring numbers works, so in that sense it’s “created”. But stuff like the prime number theory wasn’t explicitly created by those decisions but arises by the interplay of the lesser rules, and thus is “discovered” instead.

I like to say that we discovered the patterns, but we invented the language to describe said patterns

How would you respond to the idea that the language itself *is* the math, and we chose the part of it that is most useful to describe what we want rather than it being an inherent property of the system itself? For support I’d point to the fact that there’s really nothing in math that can’t be changed by varying your base assumptions. 360° is 2π is 256 degrees (in an 8-bit computer simulation), and even 1+1=2 can be changed with the right axiom choice. I’d also point to the fact that we can use math to describe systems that cannot actually exist off the page. For example a 4 spatial dimension system doesn’t exist in the real world, but that doesn’t stop me from rendering one with numbers.

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Good for you. Sadly I get no bitches 😔

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(Also watch Morbius a Morbillion times)

It's always Morbin' time

Me too. I only get whores 🥺

Adachi 😳

Adachi?!

Well the thing is that the pythagorean theorem isn't correct on earth since it only applies to euclidean spaces, and since the earth is round and therefore not euclidean, it differentiates by a tiny amount to triangles on the worlds surface. Becouse of gravitational distortion there are no euclidean spaces in the universe, so the pythagorean theorem somewhat only applies to a completely fictional mathematical space, which just happens to be reasonable close to our real world (since the sphere that we live on is quite big and gravitational distortion isn't that strong).

You're still buying that "earth is round" nonsense?

You're still buying that "earth exists" nonsense?

Even if you disregard if the earth is round or not, the laws of general relativity say that there will always be gravitational distortion and therefore not euclidean space.

Please say sike

Of course I'm joking. Everyone knows the world is really a hemisphere carried and the backs of four giant elephants.

That rides on the back of a giant turtle swimming through space. The turtle is really important! Can’t believe you failed to mention the turtle!

I love how I keep seeing (well, recognising) refs now I've started reading those books at last

Always makes me silly happy to find references I recognise. I love the series they are fantastic!

Currently on the second book, and I love the absurdism

I’m envious that you have so much wonder ahead to discover! 😍

and the elephants are on the back of a turtle named A’Tuin?

What about using the Pythagorean theorem on singular points in space eg vectors/calculus/kinematics?

For vectors you need to have a movement that follows precisely a straight line (at least for a discrete moment), which doesn't really exists. I dont know what you want to do with calculus, since it usually is even farther from the real world than geometry (at least in my experience). If you want to give an argument against what I said you could use the trigonemtric Pythagorean theorem which does work on spheres, but as for all statements, it could be argued back that this is just an increasingly precise approximation of the real world. Since there are way to many variables and small errors, it isn't possible to completely calculate the real world and it isn't necessary to do so. It isn't that pythagoras is completely broken or unusable, it is just that all mathematical concept have a slight disconnect from the real world. This does actually apply to all sciences since it is always necessary to approximate since the real world is way to complex. However if you venture deeper into mathematics and take a look at the actual axioms it becomes apparent how big this disconnect actually is (especially compared to physics). Dont get me wrong, that's something I like about mathematics, since it allows for proves that are always and deterministically right under their set of propositions, which isn't possible in physics where even the most advanced theorys are never provable but just hoped to be right.

In engineering, mechanical first but electrical engineering even more so, Pythagoras and calculus are both extremely important to some real life problems. We operate on the basis as you say, that no measurement is perfect and that there is a theoretical “pure” truth of what that measurement really is. The vectors don’t need to follow a straight line though, do they? Something can have a centripetal acceleration and a tangential acceleration vector which won’t be subject to non Euclidean geometry in an instant. The forces calculated on it might need to be in order for it to be measured, but the object does in fact have an orthogonal velocity vector which can be cross multiplied with the measurement vector to find the distended angle if the true velocity vector were known. I’m sure the same thing applies to electrical signals especially when it comes to interpolating data from any of the above. There is a degree of removal from the real world here but it seems more of a removal away from the lies of measurement instruments and towards the true values created naturally, reinforcing the idea that mathematics was discovered rather than created

Well the thing is that you are always approximating the problem and, in case of vectors, looking at it in discrete steps. As I said it close mimics real live and approximates it and is obviously useful on it. I just think that the approximation removes mathematics from the real world, while in your opinion this connects math with the real world. This is kinda why this argument has no real answer and both sides are valid. I guess I work more with abstract math, while you use it more in engineering which impacts our respective opinions. For all the maths I did in the last year I probably couldn't tell you any direct or obvious real world application (besides some 3d calculus and differential equarions). For example Algebra and topology are important for the complete rest of mathematics (especially algebra) but dont have direct connections with the real world and are purely abstract. From that abstract standpoint without any obvious connection to the real world and surrounded by axioms, that people just agreed on, it's kind of hard to see mathematics as something we discovered and not created. This is a strong contrast to engineering which is probably why we wont agree.

Yeah I think I get it. If you only ever deal with stuff on paper it must feel very ethereal. Topology and algebra are again things engineers use for things like the pressure on the inside of an engine based on air to fuel ratios. I'm unsure what you mean about discrete vectors though. The whole thing about engineering measurements is knowing that your discrete number could be calculated and measured more accurately ad infinitum because the true value is irrational, but also this is mostly because the irrational measurements are the SI units themselves which is slowly being corrected eg with the Avogadro number, Planck lengths etc. Again this kind of puts us in a confusing place regarding discovery and invention but I think draws towards the idea that there is an existence of a pure value especially if you were to stop using the old yardstick and go and count the atoms and distances with some sort of quantum microscope

nice adachius pfp

Adachius 😎🦇

I wouldn't say that we made it to solve real world or theoretical problems but that we applied a discovered theorem(s) to solve problems.

Math was created. The principles in it were discovered for most part

Numerical systems were created, but I believe mathematics as a whole was discovered. Once an actual system of numbers (whether it’s decimal or hexadecimal or whatever) is created, I think those numbers can then be used to explain and analyse many different concepts that always existed. A specific formula for a certain problem or topic was not created, it was discovered using the numbers that were created. In a way, numbers themselves are also discovered rather than created (1, 2, 3, etc always existed as concepts, it was just up to humans to create names and systems for those numbers. Just like fire always existed, or even more advanced concepts like complicated processes in the brain or in physics. They weren’t created, they were discovered. Then, inventions were created/invented using those discovered things).

A good example would be pascals triangle in different languages, even if you don't know numericals of say korean, and are shown a pascals triangle with korean numerals you could tell which one a one and which is a 5. Because the triangle is universal not the symbol.

That’s a good point yeah

The way we interperet it was created, but the fundemental patterns and principles are naturally occuring.

I’ve never seen such a split poll in my life

I saw one more even than this last week, also two options

you must be new here

Eh at the time I made the comment it was like 49-51. I always forget comments like this don’t age well

fair

Math is the grammar of the universe, it’s the rules that govern everything which is why we can do things like predict stellar bodies without any actual trace of them at the time and later those predictions can be remarkably accurate. The study of mathematics seeks to translate these fundamental rules into forms we can understand. In terms of the symbols, counting structure (base 10 and base 4 for example), and notation, these were created as translational elements of mathematics for human comprehension but without those, the rules of mathematics will continue to function as they have since the dawn of time. TL;DR the rules of mathematics were discovered, the symbols expressing our understanding of mathematics were created. Overall math was a discovery process for humans.

Nature of the universe has been discovered thanks to invention of numbers and mathematical analysis It's like the man-made language of every scientific discoveries in order to ease the understanding of our world in cohesive way

But math is just the language humans use to comprehend the universe. Even before humans existed the universe went about its business

Yes, but there was a numeracy(?) to how the universe operated even before us. There were still instances of one thing, two things, red things, blue things, and so on, all of which can be counted and operated on.

There’s always going to be two things no matter what language or symbols you use to represent the idea that you understand that.

True, but things like imaginary numbers and vectors don’t literally exist in nature, they’re just tools for expressing the nature of the universe. Two-ness exists, but i-ness doesn’t really. There are other systems for expressing direction and magnitude than vectors, but vectors are an extremely simple way of doing so. So parts of math were discovered, and other parts of math were created.

quantum mechanics, signal processing, …

Damn. That sounds dope. Teachers should put it like that!

Its an already as 'setting' in existence therefore it is discovered. Even without us Math will be the same. The only difference is how we interpret the mathematical infos like graph in calculus, 3d shapes in geometry, etc.

it depends what the definition is, I think of "maths" as our created framework that is based on the observed "true maths" that exists in our universe and likely beyond if a beyond exists.

>it depends what the definition is, I think of "maths" as our created framework that is based on the observed "true maths" that exists in our universe and likely beyond if a beyond exists. Perfectly summarized.

>it depends what the definition is, I think of "maths" as our created framework that is based on the observed "true maths" that exists in our universe and likely beyond if a beyond exists. Perfectly summarized.

Like any science, facts are discovered, analyzed and the theory used to transmit knowledge is adapted after each new discover

there's arbitrary parts of mathematics that we've just decided on such as a circle being 360 degrees, using a base 10 that are invented rather than discovered

That aren't even the interesting arbitrary parts. The far more interesting stuff lives in the axioms for example the axiom of choice beeing equivalent but not the same as the lemma of zorn. Also how the inductive property of natural numbers is notable in a few different ways. If you stray from the common axioms it gets even clearer that our axioms which create the whole field of mathematics are arbitrary and you could build a complete number system without ever defining natural numbers integers or even reel numbers (see for example the surreal number system).

I like your funny words magic man

Sorry, I was taking a break of studying math for university and kinda forgot that axioms aren't really covered in school (the debate if Math is discovered or invented is one we sometimes have for fun between math students so I am used to just use the stuff we learn). Axioms are unpropabale basic assumptions. These are like the core foundation which are then used to expand with the commonly known theorems. For example two very important axioms of geometry are, that you can draw a straight line and an circle. There can than be used to prove more complex stuff, like for example pythagoras theorem. As you might already noticed while working with paper, it is not easy to draw a perfect straight line or a circle. With tools, like a compass, it is easier, but even that circle is never perfectly round. Indeed it is impossible to create a perfect circle the real world, but it is still a reasonable assumption that it is possible to draw a perfect circle, for mathematical purposes. This is why those axioms are vaguely based on the real world but dont mirror it exactly.

The other stuff I wrote is about explicit axioms which govern how numbers work in mathematics. It's quite fascinating: in formal mathematics everything is defined, so there is actually a reason why 1+1 equals 2 and it is possible that this is always true. The surreal numbers I mentioned are a number system which work separate from the numbers that are thought and used in school (they even encompass stuff like multiple infinitys and much more). It is possible to build the known numbers as a part of the surreal numbers, but on a basic level the surreal numbers behave completely different compared to the ordinary numbers used in school, which is due to the fact that they use an completely different set of axioms. I mentioned them to show that even the numbers we use are completely arbitrarily chosen and kinda made up (and I talk not about stuff like everything beeing in base 10, but a bit deeper inside the very essence of how the numbers operate)

Is that kind of math something everyone learns in college or is it based on your major?

Since I am not american I cant really say how this would work at a college. All I can take as an reference point is what's taught in the bachelor of mathematics in the university of bonn (germany). As far as I know other german university's cover similar stuff in their mathematics bachelors, but the uni of bonn has the reputation of beeing harder and doing more diverse topics, so I dont have a complete picture what thaught at other universities. But what I can say with certainty is that axioms will be taught if you want to study mathematics (I bet also will be important in math courses outside of germany since all of modern mathematics realies on them). There you will learn for example how numbers are created and defined. At least for me that was the first thing we did (we took a few weeks until we were allowed to do addition and substractions in the same way as it is used in school, since we first needed to establish and prove all the rules). This will encompass a collection of proves that we proved as homework. For example a cool thing to prove is to show that for two natural numbers a and b a+b = b+a, which is something that you use since elementary school without ever getting explained why it is right. If you are interested in this stuff you could Google peano axioms. These are the basic rules which create the natural numbers (all positive integers) and it quite fun to prove stuff about addition and multiplication that you would normally take for granted. What we didn't do, but which is also quite easy and entertaining is proving stuff by geometry. The common axioms are just that you can draw a circle and a straight line and with enough work you can use this to prove, for example, pythagoras theorem. Euclid wrote a whole book series about these proves before mathematics was a thing. The stuff about surreal numbers is something I learned for my own entertainment. I can recomend the book surreal numbers by D.E.Knuth. But this is what the other refers to as hard core mathematics and might not be a enjoyable read when you never done anything about proves, infinitys, or set theory. One thing that might be important to add if you think about studying mathematics (at least in germany I have no idea how it is in the rest of the world, but i assume its probably similar): if you study mathematics it self you wont be calculating stuff or even seeing numbers. (The last time I had a math exercise with numbers higher than 10 is about 1.5 years ago.) Studying mathematics is about proving that stuff is true. While this is extremely entertaining it is probably very different from what is done in school and something to be aware of. The cool part is that you then know where all the formulas come from, which just popped up out of nowhere in the school time. And the other cool thing is that once you proven something to be right, it is always and under all circumstances right (a big diffrence to for example physics). I hope this wall of text answered you question and wasnt to much. If you have any further questions, feel free to message me.

Thankfully I will not be in a heavily math related major as this all sounds way to complex for me. Thanks for answering my questions!

As I said peano axioms and euclidean geometry is quite easy and entertaining once you get the hang of it and wikipedia as a lot of sources about it. If you have the time and want to try it, it is even outside a major not a bad idea. It's essentially proving stuff that is used on a daily basis in addition and multiplication, while learning problem solving skills (which is basically everything math is about). But I understand it's not something for everybody, but I can recommend giving at a try. Glad I could answer your questions and good luck on the major you will be choosing.

Lemma feel your boobies

Doesn’t this just prove further than math is discovered not created? The language we use to describe the math is created, but the actual mathematical principles exist regardless of our understanding or ability to model them.

Well the axioms I mentioned are constructed in a way that results in the same kind of mathematics. There are also axiomatic set that are completely disconnected from the real world or any applications. But since they are kind of unusable outside of their own axioms they aren't really researched. For example wheel theory has no applications I know of and is incompatible with standard operations (its mainly known for being able to divide by zero). Theoretically you could always just create your own axioms and make your own set of mathematics.

Right, but even when doing that you’re just making a new language to create new models. The actual underlying principles that these models model is real and discovered

That's just a matter of units. You wouldn't say temperature was created because we measure it in degress Celsius or Kelvins.

Wouldn’t you consider math to be more related to language, which was created

The symbols was created, but the maths itself was discovered

We're *creating* a language to describe *discoveries* about the workings of the universe. So... both? In cases where the language and the workings closely align, you'd probably call it a discovery. In cases where we're somewhat off-base or half-true, you'd probably call it a creation.

>So... both? Yeah I guess, world worked the same before we created it. That proves we created math to understand the world around us. Like a tool

The way we interperet it was created, but the fundemental patterns and principles are naturally occuring.

Yup. I think people just say it’s invented because they can’t see the logic or purpose behind a lot of the things they are taught in school.

e^iπ + 1 = 0 Need I say more?

e^iπ = -1 Solved it for you. Frickin nerd, that wasn't so hard.

Yes. Imma need you to say a whole lot more

Euler's Identity is an absolute example of mathematical beauty, something that we've proved beautifully without really understanding it completely, and it's things like these that really make mathematics seem like the code of the universe, that we are cracking piece by piece [Here's a brief explanation of what makes the identity so amazing, although there are probably better resources out there](https://en.m.wikipedia.org/wiki/Euler%27s_identity#Mathematical_beauty)

Oh damn, that's actually really interesting.

Math is a language. We use math to describe natural phenomena. It's was created.

I disagree that math is a language. Mathematical language and mathematical notation are not what people mean when they say “math”. Math usually refers to concepts, like two and two is four. https://en.m.wikipedia.org/wiki/Definitions_of_mathematics

According to Pythagoras’ theorem, the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. This is true for all right-angled triangles on a level surface, so it’s a discovery.

Yeah but the mathematics used to describe it were invented. Like I said it's a language to describe natural phenomena.

The language to describe it has been invented by us, the phenomena is there all along and was discovered.

Yep

👍

Yeah but there are no true eucledian surfaces in the universe (on the earth due to living on a sphere and in space and the earth due to tiny amounts of gravitational distortions), so pythagoras theorem doesn't hold inside the known universe and only works in an fictional, arbitrarily defined space. It is a really good approximation of the real world, but it isn't really a real world concept. It is even questionable if an right angle is a real concept, since the universe is discrete.

Once axioms (base assumptions) are set, math is discovered. Because axioms have to be set, math is created as a whole. If math was recreated, the axioms might change though they are often pretty natural choices. In a universe that ran by very different rules, the axioms picked are more likely to be different leading math that looks different to our own.

Math is an abstract explanation of the problems around us.

It's really both. Mathematical methods that work are discovered, but they way we express them,.the symbols we use, and the ways we use to implement the discoveries are created. There might actually be an easier way. It we can only create it after we've discovered what that easier way is.

Math is all around us.. it’s like saying gravity was created not discovered.

Which would make that mister Newton a mass murderer

„Math“ merely verbalises what is nothing more than geometrical logic. It exists in the absence of humans beings, it works perfectly, with or without a mind to perceive it. It was discovered.

I disagree. "Math" was created as a way to work with geometrical logic. The formulas that fit together are discovered, but math as a concept of calculating things were created.

This is the best one I've seen so far. Very well put

Exactly. Advanced mathematical theories like calculus, algebra and trigonometry were invented.

This is the right answer

It was created to visualize the way of the universe, I guess

Math is a concept

math principles: discovered math itself: invented

I'd argue both. It's humanity's own interpretation of a preexisting universe

Math was discovered, the symbols and words were created

This debate is as old as time and has been addressed by some of the greatest philosophers who've ever lived so you're not likely to settle it on a reddit forum of all places.

Math was created to help us better understand and comprehend the universe’s complexities

Math major here - a lot of people are confusing math and physics here. Math isn't the "language of the universe" or anything like that. It's a set of tools that helps us describe phenomena. The phenomena are discovered, but the tools used to describe it - math - is entirely created. Sure, some of it aligns well with physical concepts. Natural numbers are logically tied to quantities of whole things, for instance. However, that doesn't make the math any more innate. Euclidean geometry aligns well with our understanding of the universe, but according to relativity the universe is only locally euclidean. Even basic facts are entirely a construction. 1+1=2 isn't true in every number system. We define what 1 means and we define what + means. These have real-world analogues, but the analogues we choose only make sense because of our particular circumstances. It may be just as logical that 1+1=1 given the right definitions. So, in conclusion, math is created. While certain theorems and the like are discoveries, they're discoveries only in the systems we created. We may well have created different systems, in which case there'd be different things to discover.

I guess it was created from small discovered parts

I'd say math is created because a lot of it takes place in an imaginary space

Math is largely created as a tool with which to describe nature, in my thinking.

Math was created as one of many methods of understanding the world around us

It was created to explain things on Earth. We used patterns and numbers to describe what we were seeing just not in words!

Both

We created the numbers, but the links between them and calculations were discovered

The mathematical equations and theorems are directly logical and proven. They are the same no matter where you are, when you exist, independently of anything. They had been discovered. On the other hand, the notation used has been made-up, therefore its been created.

Nah, A=L×W existed before we knew about it. We discovered it

Well that does not settle the debate at all

It has been always there. So it got discovered

Math can only be discoverd, if we lost all knowledge of it now in the future of re discovery it would be exactly the same

If you can't consult the ancient historical scrolls for the answer, you will probably have to settle for religious belief and faith for the answer to this one. Def do not go by Reddit popular opinion though.

Hey, Christopher Columbus/earliest "Native Americans" who arrived in this country via the Bering Strait/Vikings ... was America created or discovered? I think we all agree — America was created first. Not by a person, but created. Then it was discovered.

Which side r u on?

i thought it was discovered

Good I'm on yo side

Math was created to describe stuff that just happens. I guess you could say it's both? People discovered inherent rules about how things work and then created math to describe those rules.

The porque no los dos

Math is just the mechanisms the universe works by, it existed since the creation of the universe, therefore we discovered it. But math isn’t just numbers, it’s not even physical at all, it’s more like how an action exists even though it isn’t physical. If the universe was like a house, math is like a frame.

Even among mathematicians and scientists over hundreds of years, there is no consensus, no correct answer. It is certainly a combination of both. Inventions as well as discoveries. Humans invented mathematical concepts by abstracting them from that which exists in nature. So I ain't voting.

Math was discovered.

DUDE NO- math is the concept of counting/keeping track of things and making changes to the amount of those things. it was DISCOVERED

Thinking math is created is like thinking Newton created gravity.

Math is a language

both, math has always been around, we just named it. but we also created a good chunk of math that didnt technically exist in nature, i think.

All mathematical theorems stem from axioms. These axioms might be what works in our life, but they dont have any verification or any way to be proven (which is why they are axioms). Since these axioms are "arbitrarily" decided/created without any real way of deciding if they are true and without any foundation to support them, I would say that mathematics is rather created than discovered. On the other hand the stuff that stems from mathematics, for example a huge part of physics, is discovered and not created since it relies on real world observation, which is why the line is a bit blurred.

Mathematics is nothing but a tool used for various reasons and it's surely invented not discovered.

Yep true. This is my interpretation: >I mean, what does 1+1 really mean? It's an abstract thing. We created it and gave it the value of 2. It could be anything else. Is there a law of the universe that says 1+1=2 ? What if we discover an alien species ,which for purpose of my argument, has the same writing system as humans and our 2 is their 5 and vice versa for example. In their world 1+1 is 5 but in our world it's 2. >It's like a different language. Means the same thing, but looks different. >We use our math language do describe the universe. >Aliens may use a different language to describe it, but it may look like nonsense to us. >Math was created to understand something discoverable.

The exponential notation that we use for numbers (usually with base 10) is quite intuitive (at least from our perspective). This is why scientists send messages containing π or e encoded in binary to the stars, since they suppose that alien civilisations will also settle on a similar kind of number system. And Binary (base 2) makes sense there since it is what is encodeable in electric signals, so the reasoning is that every civilisation with computers or even lower technology would be able to make sense of the signals (for example avoiding having to explain what this weird symbol: 5 or this weird symbol: 3 means, since binary just uses boolean without intrinsic symbols). However if we venture in more abstract mathematics there are indeed systems to create completely different kind of numbers, which may brake this. My favorite example are the surreal numbers who not only encompass all reel/school numbers (not complex number if you have them in school), but also infinitely many infinitys and infinitesimals. In this system there is a sense in which 0.1 and infinity have the same distance from 0. If aliens would use this number system (which would be possible, since its basic rules aren't that hard, we just sadly dont have a efficient notation for it) then they might not even have the idea to encode stuff like we do it and the differences would be far greater than 1+1 being 5. And of course there is always the possibility that they choose an axiomatic system that is completely incompatible to ours (or dont use axioms at all like we did a few hundred years ago, which would be a shame)

Great read 👍🏻

Math is like a language. It was created

So when I say the word "sky," the sky I'm describing was created?

Thanks for changing my opinion, you're right.

Not exactly, but the letters used to form the word sky is created by us. The same for numbers, we label time by numbers, time has existed long before anything existed, but we created clocks/hourglass to better understand them. We use Math to understand Physics, like to get the density of any liquids, we set the water's density as default which is 1000kg/m^3 and compare that to other liquids. It's like putting a name tag to things. That's just my opinion on the subject anyway. Edit: I think a better example is launching a missile to hit something specific. Yeah we know that anything thrown upwards will go down, we do know they go down at the rate of 9.81 m/s^2, but how can we make them hit a certain coordinate? We created formulas for projectile motion.

Exactly. That's why math was both created AND discovered. 9.81 m/s^2 always existed; it was eventually discovered by us. But "meters" and "seconds" were created by us.

Creation implies the creator had any choice in the end result. You can't create 'different' math that gives different results. You could erase all mathematical progress from existence, start over, and in the end math would work the exact same. Sure, the number symbols are human inventions, and you could use different ones, but the symbols aren't 'math', the underlying system is. Edit: Some people have told me it's more complicated than this, and I think I've changed my mind.

> You can't create 'different' math that gives different results My good sir, that's literally all of graduate math and beyond. Modern algebra, a major part of mathematics, deals in the study of "algebra"s, which are - by definition - structures which conform by arbitrary, human-created rules. An example would be Z/2Z, where 1+1=0.

Interesting! I suppose if you look at it that you could say parts of math are created. I'd still say the underlying 'engine' is still something objective. Maybe logic is the discovered part and math is the human creation?

It's closer to the opposite actually - the "engine" behind mathematics are the axioms, which are an arbitrary set of rules which must exist for anything else to work. For example, the Hilbert axioms make up the "engine" behind geometry, and the proof of the Pythagorean Theorem is rooted in them. Essentially, these axioms make up the notion of "what is a point", "what is a line", etc - which although seem very obvious intuitively, needs to be formalised otherwise we run into issues. From the axioms, then we can "discover" things present as a result - so a contention in the debate between discovery and creation is whether humans creating these arbitrary axioms are aware of the consequences of the axioms (thus creation), or if the consequences are discovered as time passes.

>results. >You can't create 'different' math that gives different results. You technically can. Different writing system. Math is like a language. It didn't exist before humans. We created it to understand the world around us. Now there are many languages and if you translate the same phrase, it has the same meaning in those different languages. You may argue it doesn't end up with a different result, which is true BUT, it's a different result in terms of writing. We created math (language) to DESCRIBE the universe around us (which can't change)

Math doesn't even work the same as it did a hundred years ago. E.g., the axioms we base (the nowadays most commonly used form of) set theory on were only formulated in the early twentieth century, and it wasn't the only way those could have been done. I don't believe for a second that we would arrive at the same mathematics if we started over.

Let's say humans don't exist, If there's 1 apple on the ground and another apple falls on the ground, how many apples are there on the ground? 2. Math was discovered.

God created math. Man discovered math.

Well the subject of math, like we learn in school was created but math itsself math is logic, and logic was always there math was there before time, since, for time to happen, we need math like, 1+1 is always 2 and had always been and will always be, we just invented the numbers to make math understandable yall feel me? 😭

The way we interperet it was created, but the fundemental patterns and principles are naturally occuring.

I think in a way that it's a bit of both. I say this because, it was created but the content for math to be possible was always there.

I mean, its both. The golden ratio and pi were all discovered quirks of the world, but we created many proofs and words for them and other things.

There is math we don't quite understand.

Logical abstractions to help human beings predict the behavior of the systems they observe. It is often very useful. However, the Universe is under no obligation to obey our predictions and could throw a curveball at any point in time and space.

This isn't a totally clear answer. I went with discovered, my reasoning being that mathematical laws themselves are discovered. The relationship between a sin wave and cos wave, that 0! = 1, or the Pythagorean theorem would be exactly the same if you were to restart human civilization and they started rebuilding our knowledge. That implies that these laws are discovered. Math certainly has conventions, and many of the specifics of our mathematical system are created. We use base ten, circles have 360 degrees, the symbol 3 means three times the value of the symbol 1. If we restarted the human civilization, these things may change. However I would say that the vast majority of mathematicians have lived their lives attempting to discover things, not define convention, and thus that's what I would say principally makes up math. It's like archaeology. First you have to build a few tools like brushes, tweezers and shovels. Then you use these tools to make discoveries of long buried civilizations or whatever. We had to create a few tools like a base ten number system, but with those tools we make discoveries.

Math was created by the Sumerians in Mesopotamia. 3000 BC

I agree with both: we created the symbols but discovered the actual logic and process.

Math is the language of the universe, humans had to discover this truth.

It would be discovered if everything in our world ran by it by the second

I feel like if we somehow lost all knowledge and records, math would be rediscovered the same way and we would come to find ourselves using similar if not the same algorithms that we use to solve problems today

Math was proved

It was discovered by Dr Dave Math in 1952

Did someone create the fact that two apples are two apples? No, math was discovered just like physics. Which makes sense, since physics is just applied math. And chemistry is just applied physics. And biology is just applied chemistry. Together, they are The Sciences.

Well, what is math anyway?

im not about to argue over this but everything in our universe and world functions a certain way. these functions definitely exist outside of people. they're consistent and tied to laws of science and order. just because we use symbols to represent what we're talking about, that does not mean we invented the thing we're talking about.

Created. Polynomials are made up, for example.

Was language made or discovered? We’re just creating patterns to describe other patterns

Yep true. This is my interpretation: >I mean, what does 1+1 really mean? It's an abstract thing. We created it and gave it the value of 2. It could be anything else. Is there a law of the universe that says 1+1=2 ? What if we discover an alien species ,which for purpose of my argument, has the same writing system as humans and our 2 is their 5 and vice versa for example. In their world 1+1 is 5 but in our world it's 2. >It's like a different language. Means the same thing, but looks different. >We use our math language do describe the universe. >Aliens may use a different language to describe it, but it may look like nonsense to us. >Math was created to understand something discoverable.

Both. 2 things can be true.

nobody made math it was always here so more discovery

Discovered. But im so shitfaced rn that you really shouldn't count my vote

Happy hour?

Both

There wasnt a "math out there" it was created the maths we know could be completely different Also it depends on technically what u are saying tho theres a lot of depends

Math is the devine language of the universe

pretty sure maths is just pattern recognition. amounts always existed, but the idea behind coming up with ways to measure stuff or count is just a weird thing we torture ourselves with.

It would be easier to create math, but we don’t get to decide what works, we have to find it.

I think the maths we use with base 10 is created

math had to be discovered right? i mean if some motherfucker spent god knows how much making every single problem and situation known to man work seamlessly, then he had to have gone insane

My friend is getting her masters in some math bullshit and she said it was discovered, though I could not truly follow her reasoning. To my monkey brain it was created

It was discovered. Just like many other species we stumbled upon math to help us understand things. Other species that do math are bees, ants, crows, dolphins.... basicaly many inteligent species or hivemind bugs.

Math was created to describe the world around us. It wasn't discovered. I would only say it was discovered only if every possible math "problem" had a real world solution. I.e. 1+1=2 ... where in the universe you get that equation? Nowhere. It's abstract and with no meaning in the universe. But what does have meaning in the universe is for example conservation of energy. We used the math we created (as humankind) to understand what it does. Math was here thousands of years ago, and only "recently" (almost 200 years ago) we discovered Conservation of energy. We had no idea it exists. Math is a tool we created to understand the universe. If we ever find aliens, and send them 1+1=2 as a proof that we are an intelligent species, they propably wouldn't understand it because they might have created a different tool to understand the universe. Like a different language.

The mathematical system was invented to discover the mathematical truths.