Was math invented or discovered?

[Nick]

I know it's an age old question, but I'd love to hear some personal viewpoints on this.

 

[Cognisant]

The decimal system was invented, whereas Pi was discovered.

 

[GodOfOrder]

Are you describing the symbolism and means of representation, or are you describing the principle?

A base ten system is arbitrary, the existence of ratios and proportions between things in a measured and constant way is not.

Similarly, logic exists not in symbolism, but as pure natural mechanics of reality. If this, then that. This statement is always true, assuming that its conditions are met, because it is valid.

So while we have devised means to represent these things, true math is the things themselves, not our constructed symbolism.

 

[BigApplePi]

Invent/discover:math & co.

The decimal system was invented, whereas Pi was discovered.

Excellent point. There is a reality of well-defined forms and their relationships out there. We invented symbols to deal with them and their relationships hidden are searched for and uncovered. Sometimes there are fascinating hard-to-believe results.

A question could be asked: what kind of forms and relationships? Math has a pretense to precision. Chemistry, physics, geology and biology struggle. But the social sciences don't have this precision. Psychology, economics and medicine fail. All they have is statistics we find hard to define. What would be the mathematics of love? How much money do we need? What is the best medicine? We can't answer those yet.

 

[MissQuote]

If you were to consider math a universal language of pure truth, then it has been discovered and what has been invented is our means of communicating said language.

 

[MissQuote]

If we were to have contact with intelligent life from elsewhere than our own planet, then a discourse of even the most simple mathematical pattern, then building in intricacy and difficulty from there, would be the easiest means of communicating intelligence for both parties, initially. I think.

 

[Architect]

Originally discovered of course, then continually invented. This occurred when our remote primate ancestors realized that more predators is worse than fewer predators, and thus discovered the concept of Numbers and their relation to each other.

 

[travelnjones]

I tend to think of it as invented. I generally see the question, what is number as the most basic question of math. The best answer I have come up with is "recognition of sameness in objects". I see that as invented as sameness is often arbitrary to the need of the counter.

Many of maths other operations become out growths of sociology for me. Addition comes out of the action of planning resources, Subtraction giving some to someone else. Multiplication planning yield. Division planning for multiple groups.

Well it's a thought anyway.

Oh if anyone can tell me why the square root of a number is the addition of that many odd number, I would really be happy. Not being sarcastic I noticed that one day and it bugs me why that works that way

 

[BigApplePi]

Oh if anyone can tell me why the square root of a number is the addition of that many odd number, I would really be happy.

What? Can you ask that again?

 

[BigApplePi]

Originally discovered of course, then continually invented. This occurred when our remote primate ancestors realized that more predators is worse
[*] than fewer predators, ...

*You meant "better" didn't you, since we discovered the predators were us ... after we inventing hunting?

 

[travelnjones]

What? Can you ask that again?

Sure i think i stated it wrong. Its the square of a number not square root.

So the square of 1 is 1. That is the addition of 1 odd number from the number line which is 1.

So the square of 2 is 4. That is the addition of 2 odd numbers from the number line which are 1 and 3, therefore 4.

So the square of 3 is 9. That is the addition of 3 odd numbers from the number line which are 1, 3 and 5 therefore 9.


1,3,5,7,9,11,13,15,17,19,21,23,25,27, etc

I don't understand why this relationship exists, perhaps something about factoring.

 

[BigApplePi]

Sure i think i stated it wrong. Its the square of a number not square root.

So the square of 1 is 1. That is the addition of 1 odd number from the number line which is 1.

So the square of 2 is 4. That is the addition of 2 odd numbers from the number line which are 1 and 3, therefore 4.

So the square of 3 is 9. That is the addition of 3 odd numbers from the number line which are 1, 3 and 5 therefore 9.


1,3,5,7,9,11,13,15,17,19,21,23,25,27, etc

I don't understand why this relationship exists, perhaps something about factoring.

Here is a formula: (x + 1)² = x² + 2x + 1.

In words, to get to the square of the next number, use what you did for the square of the number and add twice the (number minus one) plus one.

So 4² = (1 + 3 + 5) + (2 x 3) + 1 where (2x3)+1 is the next odd number.

You can make a picture of this by drawing a square and marking off units.

 

[joal0503]

mathematics to me is a language used exclusively by humans (non living machines aside), so id guess id say yes, it was invented by humans.

the truths/processes/patterns/whatever they are called, that are described by mathematics, certainly NOT invented by humans. But of course that doesn't mean some thing/being/unknown system didnt invent them...

 

[BigApplePi]

You guys may have seen my signature:
••• The perfect ratio of the around to the across was created by God. What does this have to do with decimals expanded which were created by man? •••

I could have changed the 2nd "created" to invented, but wanted the question to remain instead to keep the contrast.