Is mathematics discovered, developed, or both?

[Jehanne]

I think that it is discovered.  The fact that reality exists in the form of matter and energy means that things such as 2 + 2 equal 4 are fundamental truths of our existence, hence, they are discovered not developed.  They are simply brute facts; to quote Mr. Spock (during a low-budget, 3rd season episode directed by the master himself, Gene Roddenberry):

Physical reality is consistent with universal laws. Where the laws do not operate, there is no reality.

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