many people still argue whether math was discovered or invented... i would like to see what people on MS think.

That's a damn fine question, decapitator. Perhaps one of the most taxing I have seen on the Metalstorm pages!

Firstly, we should start with a little word play:

If something was invented, we mean, upon its creation, that it never before existed.

If something on the other hand was discovered, we mean that it already existed, possibly having always been.

I think -- and forgive me for injecting the metaphysical here -- that the archetype of mathematics will have always existed; meaning, somewhere, there has always been a need for a tool in which to calculate the world: one which can be pinned down with cold hard facts. The need may have been there, but nothing more.

As a system of logic and equation; something of a tool -it could not have been used (could not have truly existed) before there were thinkers (mathematicians) there to use it.

Therefore I am going to say, before further thought on the subject, that mathematics was invented out of nesseccity. It was invented, by what could eventually be called mathematicians, in order to better understand the material world.

Cheers.

I think that they were discovered, they have always existed, but just that we didn't notice it before and when we discovered them, we invented many complicated things with them that maybe they give the impression that they was discovered.
Good thread!

Yeah, cool thread. I never thought about this topic really. But well, now is the time haha.

Alright, I think mathematics always have existed, we just gave it names, symbols and shapes for us to understand it and use it as a tool. Look at the shape of a triangle, lots of mathematics there, many calculations are in it. We figured out that there are certain patterns in it, we gave it symbols and thus we could use it. For example computers we have invented, mathematics have always existed, we just gave it a shape for us to handle it. Thats what I think.

Wow it gets me thinking , and well I must say that it was discovered , It always existed if not then How God would have made all of this , and not only that but since early years early early years ... people used Math it just that they didn't noticed, also when they made the calendar they were using math , and so on ...This is an excellent Thread and it is so interesting to think , but again I think it was discovered like many other things if not then how would have the inventors invented many things before math was discover ..and this happens a lot there's things that exist but we don't see or haven't discovered ....Great thinking

Mathematics is built upon structures existing only in human mind (shapes, numbers and so on). Therefore mankind never actually discovered it, just invented. It's an international language used to describe certain properties and in a long run also laws of universe.

Written by Guest on 20.05.2006 at 10:06

Mathematics is built upon structures existing only in human mind (shapes, numbers and so on). Therefore mankind never actually discovered it, just invented. It's an international language used to describe certain properties and in a long run also laws of universe.

You said what I thought, but couldn't write down. Great post! (IMO)

I think it's a little bit of both, actually... allow me to explain.

Although I believe that mathematics are a tool that we outselves have developed in order to better understand the world around us and make sense of things, I think a lot of things in mathematics were actually discovered rather than invented. They were always THERE, but we've attatched values to them and built systems around them, many of which are synthetic and exist to make sense of things that are otherwise incomprehensible to us. I'm not a mathematician, but here are two examples to try make sense of what I'm saying:

First, the example of phi, the ratio of about 1.618, also known as the "golden ratio" - images done in this proportion are aesthetically appealing, architechure which respects it is efficient, etc. Nature follows the ratio. Was this invented? No. it was measured and deduced, and is therefore a discovery. But on the other hand, we see different number bases being used in different cultures - we for instance use 10. Then there's the dozen, and systems with the base of 60 (the Sumerians) ,and so on. Clearly, these systems were used because they were, due to the nature of life, the most efficient - these are therefore invented.

Therefore, to put it in other words, the core principles were discovered, but the systems around those principles were invented. Sorry it's not a simple answer, but mathematics isn't simple either

Written by Avenant on 20.05.2006 at 13:01

First, the example of phi, the ratio of about 1.618, also known as the "golden ratio" - images done in this proportion are aesthetically appealing, architechure which respects it is efficient, etc. Nature follows the ratio. Was this invented? No.

Actually, the case of phi showing in nature is more of a myth than anything else. Same with architecture. For example the idea that Egyptians knew the golden ratio is completely thrown away and it's not even proven pyramids use this ratio. Despise that, many people believe it. As far as I know, the greatest paintings don't necessary have the phi proportion.

And even if it was true, it would only mean we discovered a speciffic proportion and named it in the mathematical language as 1.618. It's like discovering a horse and naming it in some language. It's not like we discover part of a language then, only expand it.

im always torn between the two... if somebody said it was invented.. i could see how.. and on the other hand if someone said it was discovered...again... isee their point...this is a question that can lead to many ideas and interpretations... and nobody knows the true answer behind it

Mathematics is a purely human invention. I simply cannot be convinced otherwise. There is no possible way that the ever-evolving system of mathematics could have been "discovered". Discovery, as several people have pointed out, implies that it has existed and all we must do is acknowledge its existence. Like the discovery of an island or a new species of kangaroo.

Rather, math is a language for describing and making sense of the patterns found in nature. The basic system in use now, based on tens, was developed by Arabic people. Algebra was invented by physicists. Math is continually being built upon, as you can witness by the development of string theory and theories of gravity and multiple dimensions. Math is no more than a system of evolving rules, and it was only the possibility of those rules that existed before their creation by man.

Again, I can't stress enough that humans came up with math as a means of understanding physics. Lower level math, like counting and multiplication, were developed out of a need to quantify. Incans in Peru used math in quite a different way than we do; they kept records on bundles of string called quipus. Don't try to tell me that this system was discovered. No way. Human inginuity. It's what we're good at.

For all those who are arguing mathematics were discovered; what you are speaking of are the "patterns that exist in nature". These, yes, have quite obviously always been apparent; always existing. But it was the invention of mathematics -the invention- which human minds devised in order to better understand them.

Proud Autumns argument pretty much raps this argument up. To push it further, without any original thought, would be sheer folly.

Yes I see your point guys as if that it was an invention and like you my dear Daibh said , I think is both now that I see it better like the pytagoras formula and all of that of course it was invented , but at the same time the patters and all of that they alredy existed , so is one thing and the other one.. Great Topic

Written by decapitator on 20.05.2006 at 15:17

im always torn between the two... if somebody said it was invented.. i could see how.. and on the other hand if someone said it was discovered...again... isee their point...this is a question that can lead to many ideas and interpretations... and nobody knows the true answer behind it

Same as i .
Our world is based on mathematics. Most things happen with a mathematical explaination. I mean take the case of Newton's theory of gravity. He has found this theory by just looking to a fallen apple and asked himself why things fallen down.

But on the other hand mathematical are an invention of a human mind . Most of the ancient greece mathematical persons invent most the mathematics theories.

I'm in the middle

Written by Lupas on 21.05.2006 at 09:01

Our world is based on mathematics. Most things happen with a mathematical explaination. I mean take the case of Newton's theory of gravity. He has found this theory by just looking to a fallen apple and asked himself why things fallen down.

Our world based on mathematics? No.
As have been already discovered, the universe doesn't really reflect laws used in our mathematics and what follows, many things, which we find to be obvious, can be false in an universal scale. The universe simply isn't built in the same way as mathematical structures.
As for the Newton's example... In today's world Newtonian theories are deemed false, due to recent discoveries, which show our world isn't as Newton believed it to be.

I repeat, all elements of mathematics exist solely in human mind. They're used to better understand and explain various aspects of our world, but they do not perfectly reflect them.

Written by Guest on 20.05.2006 at 18:44

Mathematics is a purely human invention. I simply cannot be convinced otherwise. There is no possible way that the ever-evolving system of mathematics could have been "discovered". Discovery, as several people have pointed out, implies that it has existed and all we must do is acknowledge its existence. Like the discovery of an island or a new species of kangaroo.

Rather, math is a language for describing and making sense of the patterns found in nature. The basic system in use now, based on tens, was developed by Arabic people. Algebra was invented by physicists. Math is continually being built upon, as you can witness by the development of string theory and theories of gravity and multiple dimensions. Math is no more than a system of evolving rules, and it was only the possibility of those rules that existed before their creation by man.

Again, I can't stress enough that humans came up with math as a means of understanding physics. Lower level math, like counting and multiplication, were developed out of a need to quantify. Incans in Peru used math in quite a different way than we do; they kept records on bundles of string called quipus. Don't try to tell me that this system was discovered. No way. Human inginuity. It's what we're good at.

That pretty much covers my point of view...

There are so many diffrent types of Mathematics and equations, and they all fit and work so well together to find anything, and it was so well constructed, how everything fit in the right place, and stuff like that, i think it was discovered, it worked so perfectly, it would have to be discovered.

And there are so many structures within PC, and they fit and work so well together to make the box run. Every part of PC fits where it is supposed to fit. So I suppose PC wasn't invented, but discovered too, huh? xD

well.there is an order in anything, and everything has it's logic...well...part of this logic was called by humans philosophy, part of it chemistry, part of it, physics, and another part of it mathematics

Math is merely a tool developed in the human mind. Proportions exist in nature, sure, but they are unrelated to their description in mathematical language. Also, an awful lot of math has very little to do with the actual universe we live in. I would like to see someone show me a singular homology group!

Likewise, there are relations in mathematics that are inherent in our comceptualization of math, but that we do not know about and have to discover. It is perfectly possible to think of complete ordered fields without knowing they are isomorphic to the reals. Nonetheless, the concept of a complete ordered field is one we came up with on our own.

I hope this didn't get too technical. That sort of thing happens a lot when I talk about math.

Written by Guest on 26.05.2006 at 08:18

And there are so many structures within PC, and they fit and work so well together to make the box run. Every part of PC fits where it is supposed to fit. So I suppose PC wasn't invented, but discovered too, huh? xD

You never know it could of been Im just saying it works to perfectly to be invented, and computers were made with mathematics, but mabey they were discovered, mabey some lucky guy was walking down the road and found a computer and said "wow what is this odd looking contraption i think i will name it Com - pu - ter, computer".

I hear everything is discovered. The only thing invented was the universe.. Though, I don't know what to believe.

Written by Immortal Plague on 20.06.2006 at 03:58

Im just saying it works to perfectly to be invented

It works so perfectly, because it was made to work this way ;P
Although no, not always.

x = 0.(9)
10x = 9.(9)
10x - x = 9.(9) - 0.(9)
9x = 9
x = 1
1 = 0.(9)
Old, but I just love this

No doubt, maths was discovered, because the concepts of mathematics are universal, and due to this reason could be discovered by people anywhere in the universe (suppose this for a while)

...they were discovered...they have always existed...they couldn't be invented because they are perfect, and we. humans, arent...well our body is perfect...hehe...

Written by Guest on 23.06.2006 at 23:39

Written by Immortal Plague on 20.06.2006 at 03:58

Im just saying it works to perfectly to be invented

It works so perfectly, because it was made to work this way ;P
Although no, not always.

x = 0.(9)
10x = 9.(9)
10x - x = 9.(9) - 0.(9)
9x = 9
x = 1
1 = 0.(9)
Old, but I just love this

That is just bullshit dude. It various a lot if you use 0.99 or 0.99999999999999999999999999999
So it is kinda simple.. if it is 0.99 the difference to 1 is kinda considerable like 0.01 (little but you can consider it).. now if you are talking about 0.999999999999999999999999999999 the difference is 0.000000000000000000000000000001 (which is nothing).
All this to explain that the trick there is in the quantity of decimal cases you put in the (9) ^^

As for me, mathematics are DISCOVERED. The geometrical forms already existed before we know how to calculate their area for example. And this happens to all mathematics.. they are always in our world, but most of the time you dont realize it and dont need it.

Btw, you are talking to a pre-engineer, so you better watch out if you disagree with me kdg !

I don't actually care whether maths was discovered or invented....it exists and it's always been a pain in the arse...seriously....I have never managed to learn it....t'has always been one of the hardest subjects for me....and it'll always be....

Written by ilicit on 07.03.2007 at 22:07

That is just bullshit dude. It various a lot if you use 0.99 or 0.99999999999999999999999999999
So it is kinda simple.. if it is 0.99 the difference to 1 is kinda considerable like 0.01 (little but you can consider it).. now if you are talking about 0.999999999999999999999999999999 the difference is 0.000000000000000000000000000001 (which is nothing).
All this to explain that the trick there is in the quantity of decimal cases you put in the (9) ^^

In the (9), you put infinite number of 9's :
And "considerable difference"? Shows you aren't even taking a mathematical approach.

Written by Guest on 08.03.2007 at 07:42

Written by ilicit on 07.03.2007 at 22:07

That is just bullshit dude. It various a lot if you use 0.99 or 0.99999999999999999999999999999
So it is kinda simple.. if it is 0.99 the difference to 1 is kinda considerable like 0.01 (little but you can consider it).. now if you are talking about 0.999999999999999999999999999999 the difference is 0.000000000000000000000000000001 (which is nothing).
All this to explain that the trick there is in the quantity of decimal cases you put in the (9) ^^

In the (9), you put infinite number of 9's :
And "considerable difference"? Shows you aren't even taking a mathematical approach.

approach ? naa, i was following your teory dude.

as for me i will tell you that with a powerful calculator 9 x 0.(9) isnt = 9.. its = 8.(9) - and if it is like that x = 1 is wrong, cuz x is always = 0.(9)

so 1 = 0.(9) it is true if we are talking about normal stuff.. cuz 0.(9) is almost 1. but if you are talking about perfect equasions 1 != 0.(9) cuz it is a limit that tends to 1 but never reaches it.

understood?

although that is nice if you do it with a regular calculator, and it can really confuse lot of people with that, but please dont came here telling that mathematics is not 'perfect' with that crappy teory. If you can give me a good explanation, I'll be happy to argue it with you

Written by Guest on 20.05.2006 at 18:44

Mathematics is a purely human invention. I simply cannot be convinced otherwise. There is no possible way that the ever-evolving system of mathematics could have been "discovered". Discovery, as several people have pointed out, implies that it has existed and all we must do is acknowledge its existence. Like the discovery of an island or a new species of kangaroo.

Rather, math is a language for describing and making sense of the patterns found in nature. The basic system in use now, based on tens, was developed by Arabic people. Algebra was invented by physicists. Math is continually being built upon, as you can witness by the development of string theory and theories of gravity and multiple dimensions. Math is no more than a system of evolving rules, and it was only the possibility of those rules that existed before their creation by man.

Again, I can't stress enough that humans came up with math as a means of understanding physics. Lower level math, like counting and multiplication, were developed out of a need to quantify. Incans in Peru used math in quite a different way than we do; they kept records on bundles of string called quipus. Don't try to tell me that this system was discovered. No way. Human inginuity. It's what we're good at.

Nice way to cover your idea.. but is wrong imo in some aspects cuz you kinda contradize yourself in the middle. And i'll explain you why.

What you mention there, is mathematical forms and ways to calculate several things that humans had INVENTED of course. Nonetheless, they just made that to reach the results that are already out there, and always have been.
You can tell me that the Incans had another way to calculate the area of a square different that l x l = A^2. However, the result will ALWAYS be the same, cuz it is kinda physical like an island or an animal that you mention.

2 + 2 = 4 right?

Acording to nature (and regular numbers defined by man) if you have 2 camels and another 2 camels you have 4 camels. You couldnt call it '4'.. you could call it 'IV', or you could call it 'John', but there will be the same camels always in there.

Is this invented ? NOT AT ALL cmon..

Now, if you talk about the symbols like "+" or "=", yes they where invented for us to understand and express ourselfs about it, to work in team, to build things, to make new things, to understand the size of things, to have a perception that mathematics is in EVERYTHING physical.

You also say that that mathematics is being continuasly developed by man, and I am with you of course. You also said that algebra was invented by physicists.. and what is algebra ? Its just a fuckin' language to understand physical stuff ! I can invent a form that says that John x Jane = Sherman. Putting this in our language if John is 2 and Jane is 3, Sherman will always be 6.

Conclusion, mathematics is everywhere.. it was discovered cuz people tend to use math uncounscionsly, and in some time of history the genious's find out that they could build it, and find ways to work with it that could help us with our daily lifes or going walk in the moon