Mathematics: created or discovered?

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Number and ratio are abstract ideas which do not exist in nature apart from the brains of sentient biological beings who formulate them. Mathematics is created by intelligent beings. It is inspired by natural occurrences. Nature provides the dots. Sentient beings connect them.

ruveyn

Like I said, the naturally occurring order would be there, we just wouldn't understand it. Since the Fibonacci Sequence does occur naturally in nature, we were able to gain access to the Golden Ratio, as the two "are intimately connected". Does a tree exist without your knowledge of it? The idea of existing is an abstract concept in itself. Proportions, ratios, patterns, these all exist in nature whether we recognize it or not. How would Fibonacci have discovered his beautiful sequence, if not for observations in nature.

Human attraction is said to be based on the ratio within the face. We find people attractive whether their facial ration is inverse to our own. Attraction is an abstract concept and yet, subconsciously, we are using ratios and mathematics to determine ideal mates. Maybe the two can't be separated. Maybe you have to have both. Maybe there was no chicken/egg debate. Maybe mathematics as a created form of study was inspired by natural occurrences, but that those natural occurrences wouldn't have been there without mathematics waiting to be discovered? I believe connections are already there, we just have to discover them. North America was there before it was "discovered" was it not?

Just because we're too slow to connect the dots doesn't mean the dots haven't been connected by nature.

Nature is not sentient. Nature does not make patterns. Sentient beings do.

ruveyn

Do the sentient transcend nature? If not, does recognizing patterns mean "making" them?

It could be that Mathematics was both creatred and was discovered.

The components of the patters exist outside our skin. The patterns are in our heads. Nature makes the dots. Sentient beings connect them.

ruveyn

Patterns are predictable phenomena. A universe consisting solely of a perpetual motion machine is highly predictable. It's behavior follows a pattern, but are you claiming that patterns cease simply because no sentient beings observe it?

If being predictable depends on consciousness, what is accuracy? What does it mean to even be incorrect?

Patterns are an artifact of sentience. The components of the pattern are natural or man made according to natural physical laws.

Without sentient beings the number one would not exist.

ruveyn

I think this topic is one of those questions that's impossible to answer.

I think it is the same to "explore" or to "create" maths.
The question is how would be the maths of intelligent non-humans.
I think as more complicated maths is, as more possibilities are there to explore.
At the end there would be infinitely options in maths.
But every civilization could only "explore" or "invent" a small part of these options.
So in other non-human civilization the lower levels of maths would be the same, but not the higher levels.
So I think that the lower levels are explored. I'm unsure on the higher levels.
(It is also possible to think that all knowledge of the world is explored, maybe it is also possible to say that higher maths are both discovered and invented)

There are elements of both creation and discovery in mathematics.

It is not a strict either-or proposition.

Example: Using stones to count cattle was a creative idea but it was predicated on the notion that a stone could be matched to animal and an animal to a stone is a discovery. The creative part is the idea of matching of stones with animals. Here is something discovered: piles of stones can be divide into two equal portions or one portion containing one more stone than the other. Odd and Even were discovered once we had piles of stones to play with.

ruveyn

How could some one be able to create Mathematics when Mathematics can be so complitcated at times?

It is a Paradox.
It is both and nothing of them at the same time.

The difference to normal explorations is that even an idiot could explore new lands. A explorer must not be clever.
He or she should be good at notice new things.
When you want to find new things in maths you should be creative and intelligent.

(I had another idea. Are mathematically rules older than the universe or could mathematically rules only exist with the universe?)

(Sorry for my English, I'm unfocused, and not a native speaker)

The best mathematicians are very, very smart.

That's a good point.

I have to wonder, if this is a case of being "created" vs always having existed, if we put it in other terms would it still correlate to our notions on this topic. For instance, instead of math, use North America. Did North America exist before Columbus crash landed on the coast of Florida in 1492?

If you believe math is a purely created thing, and thereby does not exist without intelligent sentient beings to "explore" it, do you also believe that without intelligent sentient beings to "explore" it, the Americas did not exist?