> If it is NOT true, they sometimes simply play "what if" and construct a new system where it could be true.

I trust you have some examples of this?

Complex numbers and Schwartz distributions (the thing the dirac delta is) come immediately to mind. “Not all numbers have square roots, but what if they did?” It seems like a common pattern.

I think they're talking about conjectures that are unproven but seem "likely true" and people build further math off the assumption. E.G Reimann hypothesis