Was Mathematics discovered or invented?

Mathematics is difficult to put into a category of invented or discovered. We can look at Math from both of these aspects. It is not argued that numbers are real and can be found in nature, along with Mathematical formulas and patterns. This is a fact. Mathematics also has a certain set of it's own rules, this makes it set within it's own boundaries. We can therefore go along in agreement that Mathematics was discovered, and is being discovered (to a certain extent). However on the other end of the spectrum Mathematics is an invented science, although it can be found in nature. Formulas are seen naturally but there had to be a way in which to define the true answer/formula, in this sense we can see that Math is invented. If we take the example of pi, it is an invented sequence of decimals that can be applicable to all of these formulas. In that matter or the idea, Mathematics is invented. We cannot categorize Mathematics into discovered or invented.

short historical paragraph

Compare these two claims.  Which of these views do you think is closer to the truth? 

“In a very real sense the study of history is concerned with a subject matter more objective and independent than that of the natural sciences.  Just because historical matters is in the past, is gone… its objective reality is guaranteed; it is beyond being altered for any purpose whatsoever.” - G.R. Elton

“Though God cannot alter the past, historians can.” - Samuel Butler

In my personal opinion G.R. Elton claims that history can not be altered due to the fact that it has already passed and therefore cannot be changed. I would have to strongly disagree with this due to my personal view that History is not an objective art, it is in fact; how it is told. However, each persons perspective on the matter can change how it is viewed in the future. As an example, I have the opinion that the Boeing 757 flight 77 from Virginia to LA really did crash into the pentagon on September 11, 2001. I believe this because my aunt works at the pentagon and was in the parking lot when it happened, she watched the plane crash into the building. My friend Jose Daniel believes that the plane never hit the pentagon, that it was a conspiracy theory in which the governments aim was to destroy the building, this is because there is no video footage of the plane hitting the pentagon. We can both, however, agree that the building was destroyed on September 11, 2001; that is historical fact. Historical facts can become skewed due to different personal opinion, this is why I personally agree with Samuel Butler rather than G.R. Elton, because history can become skewed due to a subjective viewing of the facts.

History KI's

1. To what extent is history an accurate examination of human activity of the past?
2. To what extent can history be trusted to give us the accurate information and truth?
3. How does the interpretation of history affect how it perceived today?