Math: Did we discover or create it?

[virtualmeet]

As to the dictionary, though. Yes, it is an incredibly stabilizing factor, when well and thoughfully used. However, in several threads hereabouts, people have attempted to use a definition out of the dictionary that was soooo broad and general, that it included (at first glance) and number of non-too-related concepts. They then concluded that at least two of those concepts were "identical" since they both fit the definition...

You're right when saying that we should be careful when using a dictionary definition because it can lead us to much more confusions...

In fact, I don't like the definition above because it's too restrictive: this definition suppose that we must have three conditions (...sounds, words and grammar) . why "sounds" and not "gesture" (language used for persons with hearing difficulties) ? There are other questions about the accuracy of this definition

Some of you can say that I have to make a difference between "A system of communication" and a "language". So now, we have also to define exactly what's "A system of communication" :lol:

...Goldwater's famous gaff, "listen to what I mean, not what I say!"

 

I agree with you two hundred percent :P

[Ahsmohdean]

God created it, and we discovered it and continue to discover the truth of the universe, this is what science is.

[questor]

Math is interesting! it is the same in all languages in that the results are constant. it is communication on a certain subject, it is language of a type, and it is certainly a science, in that it is ''to know''. it is pure, it is truth, and it is immutable. it is a concept discovered by man upon which all men can agree. wouldn't it be nice if other sciences could be so definite?

[sergey500]

We created math. Math is just something we use to subsitute our world we digits or X and Y's. That is as basic as I can say it. We created math, not discovered it. Discovering something is finding something that already exists, which is not the case her. Numbers are inside our minds, we created them. So in a sense all numbers are imaginary.

[kamil]

Yeah, we did create math in the sense that we created X's and the Y's and 0's and 1's etc. But that is just the representation of a concept which has already been used by nature. And nature would still function in a mathematically logical way even if we didnt exist in it!! All we did is put this logic in a formal way whcih can be found in textbooks, therefore my vote would have to be 'We discovered it'.

We ceated the word apple, buit not the fruit itself.

 

BTW, 'We discovered math' and 'We discovered math and improved it' is the same thing since they both claim that 'we discovered math' and isnt this discusion all about 'We discovered Vs We created'. Im sure both sides agree we have made a contribution ot our understanding of it.

[Guadalupe]

Hi, everyone. I'm new here. I saw this forum for the first time on a thread about Evolution and Intelligent Design, you know, the classic debate.

 

Anyway, here's something I can't understand or figure out: math.

 

We all know how important math is on the world, not arguing that. However, there are people that think that we discovered the laws of math, while others say that we created them (kinda like a language). There is also debate about if it's really a science or not? So, what do you think?

 

Is math something we created and improved, or something that was there just to be discovered?

 

 

Hi Edge, :confused:

 

I did some research and found that math was indeed created. Math, are equations to find solutions to problems. Math, are like tools were first created, then they were improved upon to help solve other problems in other fields where math is used.

 

My research also finds that laws of math were not discovered, they were created.

 

B)

[woog]

Hi I'm new here. I have a bit of unease at what the term "math" encompasses. For instance at one end there is math, a body of truths. At the other end is "doing" math. Perhaps how we define it is important to this debate?

 

It's a description of nature, in the same way a photo is represents reality in a sense. For instance, "all humans have a head, two arms and two feet" is a description of reality (not always true) and a conclusion one may arrive at after a bit of contemplation.

 

Did we create this fact or was that "truth" already there. Did we create the discription used: "human", "head", "arm" etc? I think mathematics generally is understood to cover the truth and the description, which I find need to be separated for this debate.

[Pyrotex]

Hi I'm new here. I have a bit of unease at what the term "math" encompasses. For instance at one end there is math, a body of truths. At the other end is "doing" math. Perhaps how we define it is important to this debate?...Did we create this fact or was that "truth" already there?...

Excellent question. YES! How we define 'math' is crucial to this debate. Also how we define 'language' and perhaps even 'created' and 'discovered'.

 

Without a solid foundation of definitions, this debate will be mostly a game of tennis with opinions flying over the net, and no referee to call the out-of-bounds. Even then, it still is fun.

 

We could narrow this down to the first 'math'. B)

 

Was Euclid's Geometry an act of discovery or invention?

[woog]

How we define 'math' is crucial to this debate. Also how we define 'language' and perhaps even 'created' and 'discovered'.

Without knowing it, we seem to be heading down a path not too dissimilar to that of mathematicians at the turn of the 20th century. Both in terms of the discussion, as well as trying to define explicitly the concepts in point. I'm referring to the axioms of mathematics here.

 

Was Euclid's Geometry an act of discovery or invention?

Euclid's geometry can still be separated into objects such as 'lines' and 'points', and the body of truths about these objects.

 

Perhaps we could narrow this further: the concepts commonly referred to as 1, 2, 3... did we create these concepts? What about the relationships between these objects?

[Pyrotex]

...Perhaps we could narrow this further: the concepts commonly referred to as 1, 2, 3... did we create these concepts? What about the relationships between these objects?

Well, Socrates and Plato were pretty sure about what they (Mankind) were doing, and they lived moderately closer to the beginnings of math than we do.

 

These ancient Greeks concluded that there existed "ideals" that we could discover. A person could create a square or a triangle, but only because we had come to understand that there was an "ideal square" and an "ideal triangle" that had previously been discovered, or un-concealed or conceptualized by the mind of Man. These "ideals" existed from the beginning of the Cosmos, long before Man came upon the scene. There were also ideals of "beauty" and "love" etc.

 

To them, math was an exercise in "discovery", not an exercise of "invention" or "creation". But that was just their humble opinion, right? :confused:

[woog]

I agree totally with you.

 

Though now that you mention it, and with a bit more thought, I'm finding unsease with "discovered", "created", and "exists".

 

When I think about the meaning of "discovery", I think of "finding what is already there" or something along those lines. But when applying "already there" to mathematics in what sense do I mean? For instance in what sense does the complex number i exist, if at all?

 

As an interesting aside, mathematicians I know often describe research as "creating new mathematics". I get the impression that most believe what they do is discovery, even though they don't refer to it this way. For instance instead of "discovering a new theorem" its "proving a new theorem", and "creating new branches of math" instead of "discovering new branches".

 

I just want to add finally that coming across new ideas in mathematics I sometimes feel they seem a bit arbitrary and contrived at first, but as I delve deeper into the theory and begin to glimpse the beauty of its implications, I start to think that perhaps there is nothing arbitrary about these definitions at all. One example is group theory and perhaps even early algebra.

[Qfwfq]

Pyrotex, (sorry for getting back so late!) I'll point out that I wasn't talking bases I was talking about algebra, group theory and the likes. I tell you, mathematicians don't give a damn about reality. Really.

 

Definition of language? Forget what those silly dictionaries say. Here's my effort:

 

language: noun Any means of comunicating ideas, concepts, information, opinions, emotions, instructions, insults etc. from one individual to others that share the symbolism involved. May also be a tool for manipulating the represented asserts and deriving what conclusions may be drawn and/or for persuading others of these. Must have a lexicon with associated semantics, may have syntax and grammar.

 

How does that sound? How about a gesture with the hand accompanied by a throaty grunt and a grimace? There can be a lot of semantic variety there, according to subtle differences in the gestures and grunt.

 

Languages that we speak and write arose out of practical necessity, just like math. In comparison though, math has gone quite far beyond practical necessity. Did somebody "discover" English, Hindi or Japanese?

[Qfwfq]

As an interesting aside, mathematicians I know often describe research as "creating new mathematics". I get the impression that most believe what they do is discovery, even though they don't refer to it this way. For instance instead of "discovering a new theorem" its "proving a new theorem", and "creating new branches of math" instead of "discovering new branches".

 

I just want to add finally that coming across new ideas in mathematics I sometimes feel they seem a bit arbitrary and contrived at first, but as I delve deeper into the theory and begin to glimpse the beauty of its implications, I start to think that perhaps there is nothing arbitrary about these definitions at all. One example is group theory and perhaps even early algebra.

By the nature of math being very much based on consequentiality, which exalts its being a tool as well as a way of comunicating, there certainly is a lot of discovery in it, this is the very reason it is so much a topic of research.

 

Basically, once you have defined and constructed (a sine qui non by the modern point of view), there begins the work of deriving the consequences. This may make the branch more or less interesting or exciting. Given a "framework", amazing and beautiful things may be discovered, a conjecture may turn out to be true or false. These are by no means arbitrary but the framework is. What may be less arbitrary about frameworks is whether a given one will be exciting and challenging to work out... or trivial!

[kamil]

In a way we discovered math, and in a way we created it.

The Universe works mathematicaly, whether we exist or not. So in that sense the math concepts were always around. But we were the first to put these concepts on paper, and then extend their uses and meanings.

We may have created the language math. Just like we created the word 'apple'. But that doesnt mean we created an apple. But now we are able to form sentences using the word, use it when playing scrablle.

 

I think with maths its simimlair.

[Qfwfq]

Just like we created the word 'apple'. But that doesnt mean we created an apple.

That's the idea, I distinguish between the language and what it might describe. But I differ:

 

The Universe works mathematicaly, whether we exist or not.

This is why math is helpul in understanding reality. Strictly, I ought to say a part of math, that which describes the universe.

 

So in that sense the math concepts were always around.

We may have created the language math.

What are "math concepts"? Is an apple a "concept"? Math is the language and method, not the apple. Numbers are handy for counting apples, this doesn't mean that numbers are apples or that apples are numbers. Neither is an RC circuit a differential equation or vice versa.

[Tormod]

The Universe works mathematicaly, whether we exist or not. So in that sense the math concepts were always around.

 

How do you know that the universe works mathematically? We interpret it that way, but that does not mean that the universe does.

[vin]

First want to say Hi, This seems like an interesting forum.

My take on this matter. I've thought about it for a few years now as a couple of classmates and I used to have this discussion over beers occasionally.

 

First I would start by defining math,

 

Math: mathematics is the body of knowledge justified by deductive reasoning, starting from axioms and definitions

 

The definitions and axioms themselves can be either discovered or created. I would say most are created by the mathematician with inspiration from some outside source, be it the bahavior of numbers, the physical world, or some other system that the mathematician is studying.

 

The deductive reasoning is discovered. A mathematical system is deterministic, the system itself behaves independently of how it is observed.

If a theorem is proven and the mathematician dies before writing the proof does it make the theorem any less true?