Discussion Was the concept of math invented or discovered?

[Freebandzgang]

I believe that math was invented to explain the universe and how it works but im very curious as to what you guys think!

 

[EvisceratedJester]

I haven't gotten around to reading it yet, but I'd imagine that you might enjoy the book What is Math? by Eugenia Cheng.

As for the question, I generally side a bit more with the view of math having been discovered or that it's a product of both discovery and invention, though I might be wrong.

 

[0bebe0]

Math is the language in which the universe communicates with us. Numbers like Pi=3,1419... are constant throughout the world and they never change. I think math was created right after Big Bang and we as humans, only just recently discovered it.

Similiar thing with Laws, like the Laws of Thermodynamics. Humans have created a way to describe it and comprehend it, but the Laws where there all along.

I actually like your question

 

[Freebandzgang]

Math is the language in which the universe communicates with us. Numbers like Pi=3,1419... are constant throughout the world and they never change. I think math was created right after Big Bang and we as humans, only just recently discovered it.

Similiar thing with Laws, like the Laws of Thermodynamics. Humans have created a way to describe it and comprehend it, but the Laws where there all along.

I actually like your question

I like your response a lot. It really made me think. But for example with Pi, didnt we Invent pi to represent the circle? When the universe started, there was no pi, we created the idea of pi (and all other things) to be able to represent the phenomenons in the universe.

 

[Higurashi415]

Math is obviously invented, as every field of math starts with a set of axioms from which we humans derive the rest using logic and other things. The axioms are arbitrary, and of our choosing. It's totally a human construct; a useful one at that, the most useful one in many ways

 

[0bebe0]

I like your response a lot. It really made me think. But for example with Pi, didnt we Invent pi to represent the circle? When the universe started, there was no pi, we created the idea of pi (and all other things) to be able to represent the phenomenons in the universe.

Pi appears in many places, but most often with circles, spheres and other curves. Pi is defined as ratio between circle circumference and circle diameter. You cannot create or even imagine a circle that breaks Pi, that's how it is in our world.
There are more math constants, like Euler's number for example and they never change

There is also a youtube video about how colliding blocks give out Pi as a number of collisions - it may interest you

Math is obviously invented, as every field of math starts with a set of axioms from which we humans derive the rest using logic and other things. The axioms are arbitrary, and of our choosing. It's totally a human construct; a useful one at that, the most useful one in many ways

I don't think that's true. If you have for example 5 animals in a herd and one of them dies but two more are born, you now have more animals that you started with. It doesn't matter if you know math or use arabic numbers, roman numers or just count them using your fingers. You don't have to assume that, +2 > -1 because that statement was true way before planet Earth has formed.
There has never been a case of infinite water source, like in Minecraft. If you take water from a lake into a bucket, the amount of water in the lake lessens. Therefore I think that math has been discovered, based on our observations and experiences in real world. In our dreams, rules of the math don't have to apply

 

[Darkover]

a computer with infinite storage and processing power could create every possible image of everything that's possible with a set number of pixels and colors recreating every possible event that we can see with our eye inside this universe i think math is discovered we merely uncover them

radius R
diameter d = 2 * R
circumference = pi * diameter
area of a circle = pi * R^2
surface area 4* pi * R^2
enclosed volume V = 4/3 * R^3 *pi
volume formula for the sphere= (4/3)*pi*R^3

 

[Crow_88]

I would say that math is discovered. There are are constants throughout the universe that exist whether we are here to interpret them or not. That being said, the base 10 system of math we use is a construct. So I'd say math was definitely discovered but we needed to create a way that we could explore, understand, and use it.

 

[Higurashi415]

I don't think that's true. If you have for example 5 animals in a herd and one of them dies but two more are born, you now have more animals that you started with. It doesn't matter if you know math or use arabic numbers, roman numers or just count them using your fingers. You don't have to assume that, +2 > -1 because that statement was true way before planet Earth has formed.
There has never been a case of infinite water source, like in Minecraft. If you take water from a lake into a bucket, the amount of water in the lake lessens. Therefore I think that math has been discovered, based on our observations and experiences in real world. In our dreams, rules of the math don't have to apply

I think you're conflating mathematics with physical reality. Math can absolutely say that 2<−1; it entirely depends on the axioms you choose. Even using the same axioms, if we're working with complex numbers instead of real numbers, the concept of one number being greater than another doesn't even apply. Mathematics is not just an observation of reality.

Your point seems to come from the fact that mathematics is the language of physics—emphasis on language. I can say 'pigs can fly' in English, but that doesn't mean it happens in the real world.

 

[Crow_88]

Math is obviously invented, as every field of math starts with a set of axioms from which we humans derive the rest using logic and other things. The axioms are arbitrary, and of our choosing. It's totally a human construct; a useful one at that, the most useful one in many ways

Math isn't arbitrary. That's why it's so cool. It is constant and universal no matter where you go!

 

[ForestGhost]

I think intuitively it seems like math is "discovered". We start with a set of basic first principles (axioms) that seem fundamental to the nature of reality, and we stack new results on top of those.

Things started to get a little weird in the 20th century, though. Mathematicians discovered that for a given set of axioms, either there are statements you can't prove, or the axioms give rise to contradictions. For example, there is something called the continuum hypothesis, which posits whether there is an infinity "larger" than the size of the natural numbers but smaller than the size of the real numbers, that can't be proven or disproven using the standard set of axioms mathematicians use (ZFC). This seems to make the choice of axioms all a bit more arbitrary -- there is no "perfect" set we can use that is capable of proving everything.

So I guess I would say that we "invent" the set of axioms and "discover" all the results based on that set.

 

[ALonelyFreak]

Are you guys math people? Or just asking for no reason?

 

[Higurashi415]

Math isn't arbitrary. That's why it's so cool. It is constant and universal no matter where you go!

Think of it this way: a set of axioms and a specific logic "spawn" a dark room. You can then light parts of it (never completely, as Gödel and @ForestGhost rightly pointed out) giving you the illusion of discovery when, in reality, you created the room in the first place.
Axioms are arbitrary, and there are infinitely many possible logics. Since mathematics is built from axioms and logic, it too is fundamentally arbitrary, that's what I meant.

 

[Halfhourdays]

Kinda both. Humans invented math (the study of patterns, many of which are numerical) and nature has many patterns...

 

[Crow_88]

Think of it this way: a set of axioms and a specific logic "spawn" a dark room that you can then light (never completely, like @ForestGhost and
Gödel rightly pointed out), giving you the illusion that you are discovering it but really you created it, it was you all along.

(Axioms are arbitrary, and you can create infinite different logics, and mathematics is made of axioms and logics together, which is why I say that mathematics is arbitrary)

My friend, no matter where you go in the universe, the underlying math is going to work the same. The things that are described by math operate in the same way. Even if humans make mistakes or use axioms or misunderstand it. The underlying mechanics being described remain and remain constant and consistent. Regardless of human invention or intervention, pi exists for example. But, if humans used something other than a base 10 system, pi would be a different number. But it would still function in the same way and exist regardless.

 

[Higurashi415]

My friend, no matter where you go in the universe, the underlying math is going to work the same. The things that are described by math operate in the same way. Even if humans make mistakes or use axioms or misunderstand it. The underlying mechanics being described remain and remain constant and consistent. Regardless of human invention or intervention, pi exists for example. But, if humans used something other than a base 10 system, pi would be a different number. But it would still function in the same way and exist regardless.

You're thinking of physics (or rather, physical reality, as physics is a mathematical model of physical reality and not physical reality itself) my friend, mathematics is a completely different thing

 

[Crow_88]

You're thinking of physics (or rather, physical reality, as physics is a mathematical model of physical reality and not physical reality itself) my friend, mathematics is a completely different thing

I'd say I'm not. It's just the example I'm using. You could also say that two things plus two other things has always made four. And that concept has always existed long before human intervention.

I think part of the point is that math isn't a concept. It is an objective system that underlies everything and is there to be discovered.

 

[Higurashi415]

I'd say I'm not. It's just the example I'm using. You could also say that two things plus two other things has always made four. And that concept has always existed long before human intervention.

Yeah but again, mathematics only says that 2+2=4 under a certain set of axioms, for example using Peano's axioms and classical logic. If you change the axioms or the logic, even basic arithmetic can look completely different.

 

[GhostInTheMachine]

Math was invented for us to be able to explain things we discovered, so it's a little of both.

 

[Crow_88]

Yeah but again, mathematics only says that 2+2=4 under a certain set of axioms, for example using Peano's axioms and classical logic. If you change the axioms or the logic, even basic arithmetic can look completely different.

Id be curious to see that.

Yeah but again, mathematics only says that 2+2=4 under a certain set of axioms, for example using Peano's axioms and classical logic. If you change the axioms or the logic, even basic arithmetic can look completely different.

Okay, I see. Yeah. You're actually right.

 

[Higurashi415]

Id be curious to see that.

Imagine taking the entire real set and removing 4.
Now, when you move two whole steps ahead of 2 you can't possibly get to 4, it's going to be undefined, not because addition stops working but rather because 4 is no longer part of the set. If there is no 4th step to land on, what does "moving two steps from 2" even mean anymore?

Now let's put 4 back in, let's take a set that has every natural number. You naturally assume the rule of successors (2 is the successor of 1, 3 is the successor of 2, 4 comes after 3), but that's not necessarily the case. If the numbers are not ordered you can't possibly say that 2+2 is 4, because moving two steps from 4 could very well land you on the -3 square or +17. This isn't as abstract as it may sound at first, because most sets in reality are not ordered at all and probability is a decent tool at fighting this issue. Like, what's the likelihood that -3 is in the slots 2 steps ahead of 2? Suppose it's very low; I wouldn't bet -3 is there, because I'd probably be wrong.

Another thing is that there are many ways of defining the sum of two numbers. Again, this may sound very abstract but it really isn't. If a and b are complex numbers, a+b in the traditional sense doesn't mean much, because they each have 2 components. Even inequalities in the traditional sense are undefined, so a>b doesn't make much sense in and of itself. You can easily solve this problem by taking the norm of a and b and comparing them, but even the norm has many definition for different purposes.

 

[yxmux]

Math is both invented and discovered. We invent mathematical models and notations, and we discover mathematical properties that emerge from them along with their applications and vice versa.

 

[Crow_88]

Imagine taking the entire real set and removing 4.
Now, when you move two whole steps ahead of 2 you can't possibly get to 4, it's going to be undefined, not because addition stops working but rather because 4 is no longer part of the set. If there is no 4th step to land on, what does "moving two steps from 2" even mean anymore?

Now let's put 4 back in, let's take a set that has every natural number. You naturally assume the rule of successors (2 is the successor of 1, 3 is the successor of 2, 4 comes after 3), but that's not necessarily the case. If the numbers are not ordered you can't possibly say that 2+2 is 4, because moving two steps from 4 could very well land you on the -3 square or +17. This isn't as abstract as it may sound at first, because most sets in reality are not ordered at all and probability is a decent tool at fighting this issue. Like, what's the likelihood that -3 is in the slots 2 steps ahead of 2? Suppose it's very low; I wouldn't bet -3 is there, because I'd probably be wrong.

Another thing is that there are many ways of defining the sum of two numbers. Again, this may sound very abstract but it really isn't. If a and b are complex numbers, a+b in the traditional sense doesn't mean much, because they each have 2 components. Even inequalities in the traditional sense are undefined, so a>b doesn't make much sense in and of itself. You can easily solve this problem by taking the norm of a and b and comparing them, but even the norm has many definition for different purposes.

Yeah, where I got screwed up was thinking of underlying principles as the math itself. Whups!

 

[whiskeyblanket]

My view is such that math is a tool used to describe natural phenomena and the patterns behind them. It is discovered by those who study it, and the study of math was invented by people who were interested in describing natural phenomena. So, in short, yes!

 

[SilentSadness]

It's invented because the human brain is physical and imperfect, the idea of a certain number of objects is just an image created by the brain and not necessarily something that really exists. How can you have two cats if "cat" is just an arbitrary term to describe a collection of molecules, it's a categorisation created by the brain. You can see that mathematics breaks down when considering questions like the timeline of the universe, if the universe existed for an infinite time, then there would be a 1/infinity chance that the current time would be now which is effectively 0. If the universe existed for a finite time, then mathematics is a temporary phenomenon. Additionally, numbers like -5 don't actually exist, and are only used to denote the "debt" of 5 objects.

 

[Forever Sleep]

That's such a clever question. As other members have said, patterns exist in the universe that can be observed, predicted and measured. Clever physicists/ mathematicians have discovered these patterns. Maths and specifically algebraic equations is the language that was created to describe them.

So- to answer the question- I'd say both. The recurring phenomena was already there, waiting to be discovered but, brainy people invented maths in order to be able to describe it.