A lot of people who talk about math on the internet seem to phrase it as this cold austere thing where it doesn't matter what anyone thinks because theorems are theorems and it's all just axioms in the end. And while we all sort of work with that understanding (somewhere, deep down there), in our waking hours "experiments" are the most efficient and insightful way to check our work and intuition. If we come up with some great beautiful theory and, assuming all the work was done correctly, we find a simple example for which our results contradict something we know to be true (or hold dear) then we have to look more closely at the starting assumptions, potentially rejecting them entirely.

These kinds of mathematical experiments definitely do not "take place" in the real world. Having an infinite number of people who can see infinitely far in front of them should have been a clue to that. It's just a way to expand mathematical jargon into an idea that is easy to keep in your head.