Here is an article filed under the category "Thoughts to Ponder": Edward Frenkel, a mathematician from Berkeley, posits that the university perhaps is just a giant simulation and we are simply participants. How would we know? Can we detect if we were? The article is an OpEd in the New York Times, and can be found here:
It is a very nice read, this article, and again, gives a sense for how mathematics seems different from other disciplines of study. Frenkel mentions that many mathematicians consider themselves Platonists, believers that everything exists in the ideal, and what we perceive in this world is simply real versions of that ideal. It works for me. I would believe that it would work for most all mathematicians, really.
Frenkel even goes so far as to say that the giant computer simulation that we exist in is, like all computer simulations, not entirely without anomalies, coding inaccuracies that render the coding conspicuous. Perhaps all of our logic in mathematics is simply facets of the coding that can be detected "from within"?
Certainly a "thought to ponder"....