From my perspective this makes mathematics a combination of both invention and discovery. The axioms have always been welded into our universe, and humans have constructed a system in which we can explore them. This relates to Joshua Hills theory, a young student at Harvard,”So we discover the world around us, now how do we use and manipulate this world. Invent Mathematics.”
This theorem can be justified by the advent of numerals. The base 20 numeral system was invented thousands of years ago by the Pre-Columbian Maya Civilisation most likely used to count something as basic as cattle or other livestock. Without the invention of numbers we would be without a system that is used to illustrate how much there is. This relates to Hill’s theory as humans have discovered that there are a certain amount of livestock so they manipulate this into a way they can understand by creating the numeral system.
It is not only mathematical systems that seem to follow this theorem. As an example, the wheel; was it invented, or did a person discover that it requires less energy to roll a circular shaped object than it does to drag an equally massed un-circular object?
In conclusion this is a complex question where a multitude of assumptions have been and will be made. It has the ability to lead onto many other philosophical questions an example of this would be “If mathematical theory goes undiscovered, does it truly exist?”.
the advent of numbers. The base 10 numeric system was something invented thousands of years ago to count something as simple as cattle or live stock. With out the invention of numbers how would we have a system to portray how much of something we have. I believe that then using "invented math" things about the world and what not were able to be explained. If you look into just about any higher level mathematical proof you will find that many things will be assumed or "invented" along the way. It seems that things have been discovered about the world based on the foundation of mathematics that has been poured by the greats such as Newton, Liebtniz, and Pascal.
So we discover the world around us, now how do we use and manipulate this world. Invent Mathematics.
Mathematics clearly involves the invention of a language to express discoveries (or assist in making those discoveries).
For example, was the wheel "invented", or did someone discover that rolling a circularly shaped object requires less energy than dragging an equally massive object?
