Thought about this topic a lot lately and coincidentally I saw this topic on Youtube in a related video. A very interesting psychological/philosophical question that I've seen a lot of different answers on. Could speak a lot for human nature or reality.
My views: Both. I believe intelligence is how far an organism's consciousness/selfawareness is pushed into it's subconscious and that the subconscious is where all thought's/commands are processed, which is also the domain of mathematics. As man evolved and we got more and more intelligent our brains pushed far enough into the subconscious to discover mathematics, but that wasn't enough. In order to put that into fruition we needed the ability of invention, otherwise that discovery would be never brought to reality in the first place. It's a Yin/Yang sort of deal, one without the other is useless. Though if I was totally forced to pick a biased side and not both, I guess I'd have to give the technicality to Discovery? Any other smart people who'd like to tackle this idea? 



I think mathematics is invented. To me mathematics is a language and a tool created by people to try and give order to things.
Sorry if my explanation is a short and poorly worded, I'm lacking in the intelligence department. 

Can you feel that? That's my stupidity rubbing off on you. You are welcome.


The answer is 'yes'. Because people discovered that counting matters to civilizations, they invented several forms of mathematics.


Pure, salty evil.  次模試と持ち味め


isn't it both?
Many different methods and ways to do things would be disovered and invent new things or better things. and much more? 

1.000 words = half of a sentence


gornotck wrote: The answer is 'yes'. Because people discovered that counting matters to civilizations, they invented several forms of mathematics. The Egyptians formed the righttrianglehypotenuse theory long before Greek geometry, using knotted rope, since they needed to form triangular blocks for the outside of pyramids. Generally speaking, although the Romans and Hebrew used letternumbers, numerical systems didn't become popular with a civilization until they had something they wanted to COUNTLike, cattle, citizens, soldiers, slaves, etc. There's a good History of Math series on BBC (and Netflix), but Monty Python's Terry Jones did it better: https://www.youtube.com/watch?v=jrLQW1vQklE 

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Mathematics is a tool we created, as I see it. The answers were discovered but the means were invented.




1.000 words = half of a sentence


True, but a lot of big inventions came from accidents. Like Penicillin, or potato chips I'd still attribute those to invention. Maths is different though since the answers are already there, we need to come up with the proper sequence to understand them and 'see' them. 



1.000 words = half of a sentence


Here is the explanation to your pondering, Donald Duck in Mathmagic Land  https://www.youtube.com/watch?v=U_ZHsk0eF0 .


A new dawn approaches!!


Mathematics was invented as a way to help us understand the universe. Math didn't exist until people thought it up.




Mathematics was discovered, Mathematics is logic based after all and logic is prescriptive.


"I tell you, no; but unless you repent you will all likewise perish."


Both, I think it's like science and language. Like a science, the stuff's there to be discovered; we just need to invent a way to get there ; like a language, we invented it to be a tool for learning and discovery.


Let's have fun!


Math as in the language was invented. The underlying principles it can be used to represent were discovered. Indeed, new symbols are invented as new concepts are discovered. Take Gottfried Leibniz for example, who came up with the notation we recognized as an integral, ∫ among others.




 Is Mathematics Invented or Discovered?
 http://www.huffingtonpost.com/derekabbott/ismathematicsinventedo_b_3895622.html 1) Math is innate. The reason mathematics is the natural language of science, is that the universe is underpinned by the same order. 2) Math is a human construct. The only reason mathematics is admirably suited describing the physical world is that we invented it to do just that. If the universe disappeared, there would be no mathematics in the same way that there would be no football, tennis, chess or any other set of rules with relational structures that we contrived. Mathematics is not discovered, it is invented. This is the nonPlatonist position. 3) Math is not so successful. Those that marvel at the ubiquity of mathematical applications have perhaps been seduced by an overstatement of their successes. 

I am a cage in search of a bird.
