# Poll: Do you believe mathematics is a human invention or a human discovery?



## brackenspackle (Jun 17, 2013)

In other words, do you think that mathematics exists independently of humans, or do you think that we invented it and designed it for our purposes? I'm curious to see which types believe the former and which the latter.


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## RandomNote (Apr 10, 2013)

Dont know.


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## Sun Lips (Jan 28, 2013)

Interesting question. I would say that humans discovered math. A good deal of mathematics were discovered while trying to explain the natural world, so it seems to me that those numbers were there before we found them.

Although, one could argue that the physical laws were there, but that we had to invent the processes by which to understand those laws using numbers. Hmm.


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## WitKnee (May 22, 2013)

Math is innately everywhere. You just have to look and understand.


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## DAPHNE XO (Jan 16, 2012)

I think humans discovered it for example; infinity existed before we could really understand what it meant.


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## Hunger (Jul 21, 2011)

Mathematics is the way the linear mind interprets the universe. It is a system that assigns numerical value to the everything. As I'm not particularity gifted in the realms of mathematics I could be wrong, but I assume that is an invention of the human intellect. A ruler of sorts, to measure the world we live in & the one we have yet to uncover via calculating sequences. I'm going to say it is an invention of the linear mind based on patterns observed throughout the universe.


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## rwells (Jun 25, 2013)

I would say that humans discovered math, although to some extent we have invented purposes for it separate from what it may naturally be. 

For example, it's always been true that in a right triangle, the square of one side plus another will equal the square of the longest side; however, the Pythagorean theorem uses this for purposes beyond how it's used in nature. 

In other words, even if humans aren't recognizing or using math, it's always been there.


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## Monsieur Melancholy (Nov 16, 2012)

I would say it's both. It's an academic discipline man has invented to explore and better understand the things he discovers.


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## Saira (Feb 2, 2012)

This is like when kids say that "Isaac Newton invented gravity". People can't _invent_ laws of physics and mathematics; they can only understand them and learn more. It's like unwrapping a gift; all you see is the paper, but then you start tearing it and more and more of the present shows through. And it doesn't gradually materialize as you tear the paper; it was already there, just hidden.


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## an absurd man (Jul 22, 2012)

Mathematics is a human construct, developed over time to describe observed patterns and phenomena. If we are talking about systems like algebra, calculus, and differential equations, etc., then it's obvious that these systems were constructed by humans to understand and manipulate our environment using notation we could understand. The question then is, are the deeper, intrinsic patterns that we observe and use mathematics to describe, the "real" mathematics? That is, does mathematics exist independently of the constructed systems that we learn about in school? I could be wrong, but I think this is purely philosophical in that there's no right answer. I think, and I am content in calling the deeper, intrinsic patterns in nature to be just that: patterns, and mathematics the abstractions we use to, in most cases, approximate them. Many times there are no patterns; nature is chaotic, stochastic.


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## Whippit (Jun 15, 2012)

I found an interesting quote by Einstein while I was thinking about this: 



> For any one who is pervaded with the sense of causal law in all that happens, who accepts in real earnest the assumption of causality, the idea of a Being who interferes with the sequence of events in the world is absolutely impossible.


The interesting thing about this is that on first read this sounds like it's about God, but if you think about it, it's equally about Us. The OP question is a bit odd because assumes that humans are somehow not part of the natural order of things. Mathematics isn't so much something that we discovered, but something that we are. Math was grown into our brains because of the fact that our grey matter can somehow simulate the greater Universe for survival purposes. 

We have the ability to not only regard the Universe, but also ourselves, ourselves regarding the Universe, which allowed us to to take it a step further and codify our reasonings to rarefied, and surprisingly useful degrees. The fact that this is possible is also the same fact that allows us to exist in the first place in an evolutionary sense.

(I only mostly believe everything I typed)


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## Elyasis (Jan 4, 2012)

Math is a language. You can say 1 + 1 = 2 but what does that mean to nature? It's like the difference between time and humans construct to understand and segment it into meaningful parts. It's a way of perceiving and understanding the universe in a more simplified form. It doesn't exist outside of our own perception of it existing.


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## Auringonpaiste (Aug 8, 2011)

well of course it exists independently of humans. Maths just gives definition to the concepts. 2+2 is still equivalent to 4 without having numbers. This concept is much like how language can exist without words.
That's a dumb question.


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## Loupgaroux (Mar 9, 2013)

Also note that our entire system of numbers work in facets of tens. Since we have ten fingers to count on - that's a human construct for sure. 
Other intelligent life forms may count in sets of twos, or threes, or twelves, or something totally different. They may not consider one being a one, two eyes twos, three rocks threes & so on & so forth. Hard for us to wrap out heads around because our mathematic language is built upon tens. That being said, the language in which we have developed for mathematics is a human invention, but the existence of negatives, multiples, singles & etc is something we've evolved to understand. 


Even if one doesn't understand the existence of simple numbers, amounts & lack thereof, they still exist. Most animals are believed not to have the ability to count. Cats I know don't for sure. If a mother cat has a litter of five kittens & one is lost or separated from her, she will most likely not notice as her comprehension of the difference between four & five doesn't exist. But regardless of the fact that she doesn't recognize this subtraction, it still exists. 


It's all really a if a tree falls in a forest & no one is around to hear it, does it make a sound kind of thing.


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## Splash Shin (Apr 7, 2011)

Yes it's a discovery. 2+2= 4 even if drooling jimmy doesn't know how to tie his own shoes.


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## Devil (May 12, 2011)

Mathematics is a notation. It's an application by which we can quantify the known and unknown universe. In that sense yes it is an invention. All the systems and measurements we use are man-made, derived from human intelligence and not infinite or absolute. Mathematics is not a discovery because the maths we know is still limited within the capacity of the human mind. For instance we have aleph numbers to represent the cardinality of infinite sets, this happens because we can't within the notations we know count, for instance, how many real numbers exist between 0 and 1.
That said mathematics is the tool which we use to understand the universe and it is used to make discoveries. As someone earlier said think of mathematics as the language. It doesn't take away the axiomatic nature of some of the discoveries rather it is the language that we used to understand that which we discover about the universe.

To put it simply, mathematics is an invention, a human construct. The things we derive from mathematics are discoveries.


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## ThatOneWeirdGuy (Nov 22, 2012)

Math is just a way for *subjective* beings to objectively measure the universe. The number system could have been invented very differently, but maintained the same core abstract concept. I'm not sure what to put. I guess discover or Somewhere in between.


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## Scelerat (Oct 21, 2012)

I'd say that mathematics is a human invention used to describe phenomena that exist independent of humans.


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## Eos_Machai (Feb 3, 2013)

_Math is a human invention.

_
It's a language yes. But more universal than i.e. english, because it's very _abstract_. I suppose that alien civilizations have developed mathematics as well. 

But it's still a language that can describe a lot of features of the universe, not the universe itself. The numbers are not "out there" in some platonic realm of forms.


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## Bardo (Dec 4, 2012)

Eos_Machai said:


> _Math is a human invention.
> 
> _
> It's a language yes. But more universal than i.e. english, because it's very _abstract_. I suppose that alien civilizations have developed mathematics as well.
> ...





Elyasis said:


> Math is a language. You can say 1 + 1 = 2 but what does that mean to nature? It's like the difference between time and humans construct to understand and segment it into meaningful parts. It's a way of perceiving and understanding the universe in a more simplified form. It doesn't exist outside of our own perception of it existing.


I would argue that it does exist outside of our perceptions and not only can it describe the universe itself, well, it sort of is the universe.

Much more advanced concepts than 1 + 1 can be seen to operate in nature. The fibonacci sequence and the elaborations of it in geometry - the golden ratio, the golden rectangle and the spiral it creates manifest themselves in the formation of pine cone segments, sunflowers, the anatomy of humans and the positioning of joints around the body, the reach of tree branches relative to the trunk, snail shells, it's errrverywhurr.

The Measure of Beauty Created in Nature:the Golden Ratio

Watch Video Nature by NumbersFibonacci Sequence & The Golden YouTube at blinkx

...and it gets worse, there is computer code in the fabric of matter, we are basically expressions of code in the same way a 3D image is on a screen.






The code developed for computers runs parallel to the mathematics being described in string theory, such hyper abstract webs of information overlapping perfectly in seemingly unrelated systems....we merely discover, no matter how intense it gets, no matter how complex, it's all discovery.


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## Elyasis (Jan 4, 2012)

Bardo said:


> I would argue that it does exist outside of our perceptions and not only can it describe the universe itself, well, it sort of is the universe.
> 
> Much more advanced concepts than 1 + 1 can be seen to operate in nature. The fibonacci sequence and the elaborations of it in geometry - the golden ratio, the golden rectangle and the spiral it creates manifest themselves in the formation of pine cone segments, sunflowers, the anatomy of humans and the positioning of joints around the body, the reach of tree branches relative to the trunk, snail shells, it's errrverywhurr.
> 
> ...



Not because it's math though. You aren't actually seeing math in action. Your mind is tuned to perceive it as a representation of the concept of the golden ratio/fibonacci sequences etc. That and what one thinks of as one object isn't actually a full solid object at all. Math is conceptual. It describes.


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## FearAndTrembling (Jun 5, 2013)

Math is used by humans to describe patterns/rules of the universe. Math itself is human but the underlying order which it describes is not. The universe is ordered, or else mathematics would not work. There are patterns, and math just helps us understand those patterns. A good essay on this subject is The Unreasonable Effectiveness of Mathematics. 



> You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or an eternal mystery. Well a priori one should expect a chaotic world which cannot be grasped by the mind in anyway. One could (yes one should) expect the world to be subjected to law only to the extent that we order it through our intelligence. Ordering of this kind would be like the alphabetical ordering of the words of a language. By contrast, the kind of order created by Newton's theory of gravitation, for instance, is wholly different. Even if the axioms of the theory are proposed by man, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the "miracle" which is being constantly re-enforced as our knowledge expands.


-Einstein

So I think the larger question is: Does the universe have order, or we do just apply, or force order onto it. I think the universe does have order and math describes that order.

I just say that the universe works a certain way, and math is like an instruction manual that came along with the universe.


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## Kelpie (Jun 23, 2013)

Mathematics itself is a human discovery insofar as it aligns with that which has or will at some point exist (not going to get into the concept of existence here). 

All scenarios in which humans use mathematics which do not align precisely with reality - or which describe that which could never exist outside of conceptual states - involve human invention.

The word "which" is starting to seem non-existent.


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## RhetoRick (Jun 26, 2013)

I lean towards math being a construct that describes naturally occurring phenomena. So math is the map of our discovery. Does not mean that the places on that map do not exist outside our conceptualization. It's not a map of Middle Earth or Narnia. It is a map of West Dover.


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## jocr1627 (Jun 23, 2013)

I love that the answers here have actually made sense. I agree with many of you. Certain principles of mathematics exist without the invention of mankind, though, since the system of math is interpreted and communicated through the lens of humans we can certainly conceive of things via the system that are subjective by nature, and not intrinsic facets of the universe.


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## Khiro (Nov 28, 2012)

It's a measurement of something that already exists. What we measure already exists, but the measurements themselves are of our own creation. 

Ultimately I think this is about semantics.


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## PandaBear (Jul 2, 2013)

I think it's part of the universe or we wouldn't be able to connect it to worldwide and difficult problems!


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## Van Meter (Sep 28, 2012)

JungleDisco said:


> I think humans discovered it for example; infinity existed before we could really understand what it meant.


Infinity is a conceptual idea and not something that has been found to exist anywhere, in fact it is probably absurd.






I really don't see how anyone can come to the conclusion that math is a human invention, the physical universe operates on a single determined math equation and would continue whether we acknowledged it or not. I see no reason to doubt the overall validity of our senses.


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## Vaka (Feb 26, 2010)

Human invention, not discovery. It's a part of the logic which rules our minds, only


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## userslon (Jan 29, 2013)

Math is a measure of something. As a result, I think that math is a form of communication between humans.. If anything, math is another language.


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## Elyasis (Jan 4, 2012)

Bardo said:


> I would argue that it does exist outside of our perceptions and not only can it describe the universe itself, well, it sort of is the universe.
> 
> Much more advanced concepts than 1 + 1 can be seen to operate in nature. The fibonacci sequence and the elaborations of it in geometry - the golden ratio, the golden rectangle and the spiral it creates manifest themselves in the formation of pine cone segments, sunflowers, the anatomy of humans and the positioning of joints around the body, the reach of tree branches relative to the trunk, snail shells, it's errrverywhurr.
> 
> The code developed for computers runs parallel to the mathematics being described in string theory, such hyper abstract webs of information overlapping perfectly in seemingly unrelated systems....we merely discover, no matter how intense it gets, no matter how complex, it's all discovery.


What you are failing to account for are the numerous occasions mathematics race ahead and far afield of what is observable in nature. Math in fact doesn't need to ever reflect reality. And that is why it is not a discovery. It can be used in fields that are such as physics or sheep herding. But Math can mean whatever you want it to... that's why it's a construct. 

It's descriptive of reality, not a facet of reality itself.


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## Vaka (Feb 26, 2010)

All of what we make sense of even in the most complex and deepest of ways doesn't have any part of reality outside of the fantasy we create in our minds. Math is part of that that fantasy. We're trapped in that mindset, though, and that's the only reality we know


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## Mr. Meepers (May 31, 2012)

> God made the integers; all else is the work of man


- Leopold Kronecker

Mathematics is simply a language and, as with any language, it is invented by human. Words are created and the language itself tries to be self contained as possible, but, perhaps humans have limitations of their own. For instance, can humans have abstract thoughts without language? I submit that we, humans, did not only draw inspiration from our natural world, but we had to draw inspiration from our natural world in order create the languages that allowed use to have thoughts about ideas unseen in our world. But such inspiration is just that, inspiration. That does not change the fact that humans created the language of mathematics and that many mathematical entities, including most numbers, don't actually exist in the physical realm (I can't pick up something and say, "That is 1 + i"). It is important to remember that there is more to math than just numbers, it is logic and numbers are just words and math is a language, and like all languages, it has a grammar. 
That all being said, once words are defined and the grammar is set, mathematicians discover the relationships between the worlds they discover. Now, these mathematical discoveries don't have to correspond to anything that exists in the physical world. Yes, that is correct, mathematicians discover concepts that don't actually exist. They use their own assumptions/axioms that don't have to apply to the physical universe, of course, as with a language, once we became more fluent in the language of mathematics we started to related more and more of what we observed in nature to the language of mathematics and eventually many ideas that were believed to have no possible applications, such as non-euclidean geometries, started to have applications.

So, to sum up: We invent the language of mathematics, we discover the relationships between the words we created, and then we see/filter the world though the lens/screen of mathematics.


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## Distort (Aug 31, 2012)

The framework is an invention, the underlying principles are a discovery.


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## Inguz (Mar 10, 2012)

Discovery. But the system or language that we use to interpret it is a human invention.


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## judowrestler1 (Mar 30, 2013)

The Axioms are invented and are completely arbitrary. You can have a system of mathematics with just about any set of axioms you want within certain rules. The theorems are discovered from there.


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## BlueSeven (Nov 19, 2012)

Either it is a human construct, and then it is one of the most useful human constructs we have been able to create, and so is noteworthy. Or it is something we have uncovered, and in that case, it is one of the most important discoveries we have made.


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## Vaka (Feb 26, 2010)

Chaos and order don't actually exist, so even the underlying principles would be completely human. One of the more interesting things to think about. It's only a discovery insofar as its an exploration of perceivable, human reality, but not actual reality.


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## judowrestler1 (Mar 30, 2013)

lycanized said:


> Chaos and order don't actually exist, so even the underlying principles would be completely human. One of the more interesting things to think about. It's only a discovery insofar as its an exploration of perceivable, human reality, but not actual reality.


Math has nothing to do with reality. Math is using logic on predefined terms and axioms to find out new things which will always be true. What most people think of as Math does have applications to reality but, that's a side effect and not what pure math is about.


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## Vaka (Feb 26, 2010)

judowrestler1 said:


> Math has nothing to do with reality. Math is using logic on predefined terms and axioms to find out new things which will always be true. What most people think of as Math does have applications to reality but, that's a side effect and not what pure math is about.


When I say reality, reality= perception and understanding of any part of the external, even abstractions


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