Was maths discovered or invented?

I heard the usual buzz arising from the mathematicians in our TOK group. "How can math be discovered? Did we find math equations on rocks?" Mathematics is the study of patters; shapes, quantity and assumptions. It is a system of explaining/understanding the world. (Definition taken from the Math group presentation - do not know source). Sometimes Math is referred to the perfect system of knowledge. I think this is because Math, unlike the Natural Science cannot be 'falsified' I believe math rests on logic and reason, by definition they are backed by facts.

Moreover, math is used in most of the areas of knowledge. It has various uses in the real world, and is applicable universally. For example, there is math in natural sciences; when calculating moles in chemistry. Or even in art, the shapes used, especially tessellations by M.C. Escher. Although can we classify tessellations as art? Or are tessellations geometry that happens to look good? How can we decide if something is art?

The most interesting aspect of math for me is the everyday use of 'theoretical math.' The prime example that jumps to mind is algorithms. Algorithms are slowly creeping into everything in life, it is used in RSA algorithm which is used to encrypt messages. Our internet security and encryption is all based on algorithms that deals with theoretical math - "pure math" and is very complicated.

So was math discovered or invented?

In my opinion it is more a combination of the two options. I feel like mathematics was strongly influenced by nature. For example, perhaps early humans saw 6 peas in a pod, or 5 petals. Then humans came up with symbols to represent the quantity, and that was how mathematics was discovered. Although it is difficult to answer this question. We have to look at what we mean when we say "discovered" is it to find (something or someone) unexpectedly or in the course of a search. or "invented" create or design (something that has not existed before); be the originator of.  The key part is "something that has not existed before" can we really say math never existed before? Math has always been a part of nature, from our genes - chromosomes, mitosis which involves duplication (doubling number of chromosomes) and yet was it really there?

Overall, I think the best answer is to go with both were needed for mathematics to exist. Without mathematicians pursuing more and inventing theories based on previous knowledge perhaps discovered, we would not have math today. 

 
However math cannot answer all questions.
http://www.slideshare.net/plangdale/introdutory-presentation-on-reason-for-tok 

Sources:
https://www.quora.com/Why-does-pure-mathematics-have-any-real-world-applications
 http://www.livescience.com/38936-mathematics.html