Teach/Learn Mathematics

First off: What is Mathematics?
Is it discovered or created?
I believe that what we do and teach is created. What we express, usually incompletely, is discovered.
There seems to be parts in Nature. Some kind of fundamental discrete processes with parts. Objects and actions, we as humans have no part in. A wave comes to shore and brakes rocks and transforms them to sand. This process started before there were humans, and will likely continue once we are gone. On the other hand we can invent a discrete recurrent model to guide us in the many possibilities this process can take. We can produce in a computer soft sand and coarse sand.
Therefore we partly create mathematics and partly discover them.
When talking with young people about these mathematics, very likely they perceive it as something we discovered and godlike delivered it to them as revealed truth. This is wrong, the teacher should tell the students that they have to create mathematics in their head to know what are we talking about.
I do not know what fraction is discovery and what fraction is creation, what I know is that the student must create something in their heads, otherwise mathematics will not get socialized.